International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document discusses Reed-Solomon error correcting codes. It begins with an introduction to Reed-Solomon codes and their use in communication and data storage. It then provides details on Reed-Solomon encoding and decoding. The decoding process involves calculating syndromes, finding error locations using the Chien search algorithm, and determining error values using Forney's algorithm. Extensions of the inversionless Massey-Berlekamp algorithm are also described, which can compute the error locator and evaluator polynomials simultaneously without field inversions.
Comparison of Turbo Codes and Low Density Parity Check CodesIOSR Journals
Abstract-The most powerful channel coding schemes, namely, those based on turbo codes and LPDC (Low density parity check) codes have in common principle of iterative decoding. Shannon’s predictions for optimal codes would imply random like codes, intuitively implying that the decoding operation on these codes would be prohibitively complex. A brief comparison of Turbo codes and LDPC codes will be given in this section, both in term of performance and complexity. In order to give a fair comparison of the codes, we use codes of the same input word length when comparing. The rate of both codes is R = 1/2. However, the Berrou’s coding scheme could be constructed by combining two or more simple codes. These codes could then be decoded separately, whilst exchanging probabilistic, or uncertainty, information about the quality of the decoding of each bit to each other. This implied that complex codes had now become practical. This discovery triggered a series of new, focused research programmes, and prominent researchers devoted their time to this new area.. Leading on from the work from Turbo codes, MacKay at the University of Cambridge revisited some 35 year old work originally undertaken by Gallagher [5], who had constructed a class of codes dubbed Low Density Parity Check (LDPC) codes. Building on the increased understanding on iterative decoding and probability propagation on graphs that led on from the work on Turbo codes, MacKay could now show that Low Density Parity Check (LDPC) codes could be decoded in a similar manner to Turbo codes, and may actually be able to beat the Turbo codes [6]. As a review, this paper will consider both these classes of codes, and compare the performance and the complexity of these codes. A description of both classes of codes will be given.
1) Reed-Solomon codes are a type of error-correcting code invented in 1960 that can detect and correct multiple symbol errors. They work by encoding data into redundant symbols that can be used to detect and locate errors.
2) Reed-Solomon codes are particularly good at correcting burst errors, where a block of symbols are corrupted together by noise. Even if an entire block of bits is corrupted, the code can still correct the errors by replacing the corrupted symbol.
3) The error correction capability of Reed-Solomon codes increases with larger block sizes, as noise is averaged over more symbols. However, implementing Reed-Solomon codes also becomes more complex with higher redundancy.
Justesen codes are created by tilting (n,k) Reed Solomon codes over GF(2^m) into (mn,mk) binary codes for multiple burst error correction. They are very good for long block lengths. Alternant codes are variation of BCH codes with fixed rate and large minimum distance.They are subfield-subcode of a Reed-Solomon codes over GF(q^m).Goppa codes are designed distance d have additional property over Alternant codes that inverse frequency template has width d...
This document summarizes an article about implementing the RSA encryption/decryption algorithm on an FPGA. It begins with an overview of cryptography and the RSA algorithm. It then describes the key steps in RSA - key generation, encryption, and decryption. The main mathematical operations required for RSA are also summarized - modular addition, multiplication, and exponentiation. The document then presents the design of a 32-bit RSA decryption engine in VHDL, along with synthesis results showing its resource usage and maximum clock frequency on an FPGA. It concludes that an RSA decryption engine can be efficiently implemented on an FPGA using limited resources.
This document proposes and evaluates novel encoding and decoding algorithms for block turbo codes over Rayleigh fading channels. It describes block codes of different lengths and their error correction capabilities. Simulation results show that longer block codes provide higher gain and error correction compared to shorter codes, though complexity increases with length. When single block codes are used, error correction is lower, but using block turbo codes doubles the error correction capacity. Performance is evaluated for various block codes transmitting random data, voice signals, and images over additive white Gaussian noise channels. The proposed block turbo codes provide improved error correction compared to single block codes.
Error Detection and Correction in SRAM Cell Using Decimal Matrix Codeiosrjce
The document proposes a decimal matrix code (DMC) to improve memory reliability against multiple cell upsets. DMC uses a decimal algorithm for error detection that maximizes detection capability. It also proposes an encoder-reuse technique to minimize area overhead by reusing the encoder as part of the decoder. Simulation results show the DMC provides better error correction compared to Hamming and Reed-Solomon codes, with lower delay but higher area than Hamming code and lower power than Reed-Solomon code.
Evolution of Structure of Some Binary Group-Based N-Bit Compartor, N-To-2N De...VLSICS Design
Reversible logic has attracted substantial interest due to its low power consumption which is the main
concern of low power VLSI systems. In this paper, a novel 4x4 reversible gate called inventive gate has
been introduced and using this gate 1-bit, 2-bit, 8-bit, 32-bit and n-bit group-based reversible comparator
have been constructed with low value of reversible parameters. The MOS transistor realizations of 1-bit, 2-
bit, and 8-bit of reversible comparator are also presented and finding power, delay and power delay
product (PDP) with appropriate aspect ratio W/L. Novel inventive gate has the ability to use as an n-to-2n
decoder. Different novel reversible circuit design style is compared with the existing ones. The relative
results shows that the novel reversible gate wide utility, group-based reversible comparator outperforms
the present style in terms of number of gates, garbage outputs and constant input.
This document discusses Reed-Solomon error correcting codes. It begins with an introduction to Reed-Solomon codes and their use in communication and data storage. It then provides details on Reed-Solomon encoding and decoding. The decoding process involves calculating syndromes, finding error locations using the Chien search algorithm, and determining error values using Forney's algorithm. Extensions of the inversionless Massey-Berlekamp algorithm are also described, which can compute the error locator and evaluator polynomials simultaneously without field inversions.
Comparison of Turbo Codes and Low Density Parity Check CodesIOSR Journals
Abstract-The most powerful channel coding schemes, namely, those based on turbo codes and LPDC (Low density parity check) codes have in common principle of iterative decoding. Shannon’s predictions for optimal codes would imply random like codes, intuitively implying that the decoding operation on these codes would be prohibitively complex. A brief comparison of Turbo codes and LDPC codes will be given in this section, both in term of performance and complexity. In order to give a fair comparison of the codes, we use codes of the same input word length when comparing. The rate of both codes is R = 1/2. However, the Berrou’s coding scheme could be constructed by combining two or more simple codes. These codes could then be decoded separately, whilst exchanging probabilistic, or uncertainty, information about the quality of the decoding of each bit to each other. This implied that complex codes had now become practical. This discovery triggered a series of new, focused research programmes, and prominent researchers devoted their time to this new area.. Leading on from the work from Turbo codes, MacKay at the University of Cambridge revisited some 35 year old work originally undertaken by Gallagher [5], who had constructed a class of codes dubbed Low Density Parity Check (LDPC) codes. Building on the increased understanding on iterative decoding and probability propagation on graphs that led on from the work on Turbo codes, MacKay could now show that Low Density Parity Check (LDPC) codes could be decoded in a similar manner to Turbo codes, and may actually be able to beat the Turbo codes [6]. As a review, this paper will consider both these classes of codes, and compare the performance and the complexity of these codes. A description of both classes of codes will be given.
1) Reed-Solomon codes are a type of error-correcting code invented in 1960 that can detect and correct multiple symbol errors. They work by encoding data into redundant symbols that can be used to detect and locate errors.
2) Reed-Solomon codes are particularly good at correcting burst errors, where a block of symbols are corrupted together by noise. Even if an entire block of bits is corrupted, the code can still correct the errors by replacing the corrupted symbol.
3) The error correction capability of Reed-Solomon codes increases with larger block sizes, as noise is averaged over more symbols. However, implementing Reed-Solomon codes also becomes more complex with higher redundancy.
Justesen codes are created by tilting (n,k) Reed Solomon codes over GF(2^m) into (mn,mk) binary codes for multiple burst error correction. They are very good for long block lengths. Alternant codes are variation of BCH codes with fixed rate and large minimum distance.They are subfield-subcode of a Reed-Solomon codes over GF(q^m).Goppa codes are designed distance d have additional property over Alternant codes that inverse frequency template has width d...
This document summarizes an article about implementing the RSA encryption/decryption algorithm on an FPGA. It begins with an overview of cryptography and the RSA algorithm. It then describes the key steps in RSA - key generation, encryption, and decryption. The main mathematical operations required for RSA are also summarized - modular addition, multiplication, and exponentiation. The document then presents the design of a 32-bit RSA decryption engine in VHDL, along with synthesis results showing its resource usage and maximum clock frequency on an FPGA. It concludes that an RSA decryption engine can be efficiently implemented on an FPGA using limited resources.
This document proposes and evaluates novel encoding and decoding algorithms for block turbo codes over Rayleigh fading channels. It describes block codes of different lengths and their error correction capabilities. Simulation results show that longer block codes provide higher gain and error correction compared to shorter codes, though complexity increases with length. When single block codes are used, error correction is lower, but using block turbo codes doubles the error correction capacity. Performance is evaluated for various block codes transmitting random data, voice signals, and images over additive white Gaussian noise channels. The proposed block turbo codes provide improved error correction compared to single block codes.
Error Detection and Correction in SRAM Cell Using Decimal Matrix Codeiosrjce
The document proposes a decimal matrix code (DMC) to improve memory reliability against multiple cell upsets. DMC uses a decimal algorithm for error detection that maximizes detection capability. It also proposes an encoder-reuse technique to minimize area overhead by reusing the encoder as part of the decoder. Simulation results show the DMC provides better error correction compared to Hamming and Reed-Solomon codes, with lower delay but higher area than Hamming code and lower power than Reed-Solomon code.
Evolution of Structure of Some Binary Group-Based N-Bit Compartor, N-To-2N De...VLSICS Design
Reversible logic has attracted substantial interest due to its low power consumption which is the main
concern of low power VLSI systems. In this paper, a novel 4x4 reversible gate called inventive gate has
been introduced and using this gate 1-bit, 2-bit, 8-bit, 32-bit and n-bit group-based reversible comparator
have been constructed with low value of reversible parameters. The MOS transistor realizations of 1-bit, 2-
bit, and 8-bit of reversible comparator are also presented and finding power, delay and power delay
product (PDP) with appropriate aspect ratio W/L. Novel inventive gate has the ability to use as an n-to-2n
decoder. Different novel reversible circuit design style is compared with the existing ones. The relative
results shows that the novel reversible gate wide utility, group-based reversible comparator outperforms
the present style in terms of number of gates, garbage outputs and constant input.
A cornerstone of our digital society sytems from the explosive growth of multimedia traffic in general and video in particular. Video already accounts for over 50% of the internet traffic today and mobile video traffic is expected to grow by a factor of more than 20 in the next five years. This massive volume of data has resulted in a strong demand for implementing highly efficient approaches for video transmission. Error correcting codes for reliable communication have been studied for several decades. However, ideal coding techniques for video streaming are fundamentally different from the classical error corr ection codes. In order to be optimized they must operate under low latency, sequential encoding and decoding constrains, and as such they must inherently have a convolutional structure. Such unique constrains lead to fascinating new open problems in the de sign of error correction codes. In this talk we aim to look from a system theoretical perspective at these problems. In particular we propose the use of convolutional code.
The document provides a table of contents and questions on various technical aptitude topics such as data structures, C, C++, quantitative aptitude, UNIX concepts, RDBMS concepts, SQL, computer networks, and operating systems. It contains 35 questions related to data structures concepts like linked lists, trees, graphs, hashing etc. and their applications.
Richard Hamming developed Hamming codes in the late 1940s to enable error correction in computing. Hamming codes are perfect 1-error correcting codes that use parity checks to detect and correct single bit errors in binary data. The codes work by encoding k message bits into an n-bit codeword with additional parity check bits such that the minimum distance between any two codewords is 3, allowing correction of single bit errors. Hamming codes see widespread use and can be generalized to non-binary alphabets. Extended Hamming codes provide both single-error correction and double-error detection.
Direct Design of Reversible Combinational and Sequential Circuits Using PSDRM...IJRES Journal
Reversible logic will be a favourable logic by dissipating less heat than the thermo dynamic limit for
the emerging computing technologies. Also it has become very promising for low power designs. Reversible
designs of Combinational and Sequential circuits are built by replacing the latches, flip-flops and associated
combinational gates of the traditional irreversible designs by their reversible counter parts. But this replacement
technique is not very promising because it leads to high quantum cost and garbage outputs. So, in this paper we
presented both the direct design and replacement designs of 5-bit up down counter and universal shift register
which are practically important using reversible logic and PSDRM expressions. Replacement design is done by
replacing the RTL design using reversible designs. Direct design is done by representing the state transitions and
the output functions of the circuits using PSDRM expressions which are obtained from truth table or state
transition table. Thus my direct design of a 5-bit updown counter and universal shift register save 42.66%,
9.79% quantum cost and 93.75%, 40% garbage outputs respectively than the replacement design.
This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document discusses the implementation of Elliptic Curve Digital Signature Algorithm (ECDSA) using variable text message encryption methods. It begins with an abstract that outlines ECDSA, its advantages over other digital signature algorithms like smaller key size, and implementation of ECDSA over elliptic curves P-192 and P-256 with variable size text message, fixed size text message, and text based message encryption. It then provides details on elliptic curve cryptography, the elliptic curve discrete logarithm problem, finite fields, and domain parameters for ECDSA.
The document discusses the RSA cryptosystem. It begins by explaining that RSA is an important public-key cryptosystem based on the difficulty of factoring large integers. It then provides examples of how RSA works, including choosing prime numbers p and q to generate the public and private keys, and using modular exponentiation to encrypt and decrypt messages. The document also discusses the importance of integer factorization for the security of RSA, and considerations for designing a secure RSA system, such as choosing sufficiently large prime numbers.
Implementation of Elliptic Curve Digital Signature Algorithm Using Variable T...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document provides an overview of various channel coding techniques used in digital communication systems to combat noise and errors during transmission. It describes forward error correction methods like block codes, cyclic codes, convolutional codes and turbo codes. It also discusses error detection techniques like cyclic redundancy checks. Finally, it covers automatic repeat request protocols for retransmitting corrupted data packets.
The document contains questions and answers related to digital logic design concepts. Some key points:
- Karnaugh maps are used to minimize the number of gates and fan-in requirements in a digital circuit. Adjacent groups of 1s in a K-map correspond to terms in simplified Boolean expressions.
- Half adders and full adders are basic building blocks used to design multi-bit adders. A full adder can be realized using two half adders and two OR gates.
- Standard forms like SOP and POS are used to represent logic functions as sums of minterms or products of maxterms. Converting between forms allows implementing functions using different gate types like AND, OR,
Deep Recurrent Neural Networks with Layer-wise Multi-head Attentions for Punc...Seokhwan Kim
The document describes a deep recurrent neural network model with multi-head attention mechanisms for punctuation restoration. The model stacks multiple bidirectional recurrent layers to encode context and applies multi-head attention to each layer to capture hierarchical features. Evaluated on an English speech transcription dataset, the proposed model outperforms previous methods that use convolutional or recurrent neural networks alone or with single-head attention.
A method to determine partial weight enumerator for linear block codesAlexander Decker
This document presents a method to determine partial weight enumerators (PWE) for linear block codes using the error impulse technique and Monte Carlo method. The PWE can be used to compute an upper bound on the error probability of the maximum likelihood decoder. As an application, the document provides PWEs and analytical performances of shortened BCH codes, including BCH(130,66), BCH(103,47), and BCH(111,55). The full weight distributions of these codes are unknown. The proposed method estimates the PWE by drawing random codewords and computing the recovery rate of known-weight codewords, obtaining the PWE within a confidence interval.
A second important technique in error-control coding is that of convolutional coding . In this type of coding the encoder output is not in block form, but is in the form of an encoded
sequence generated from an input information sequence.
convolutional encoding is designed so that its decoding can be performed in some structured and simplified way. One of the design assumptions that simplifies decoding
is linearity of the code. For this reason, linear convolutional codes are preferred. The source alphabet is taken from a finite field or Galois field GF(q).
Convolution coding is a popular error-correcting coding method used in digital communications.
The convolution operation encodes some redundant information into the transmitted signal, thereby improving the data capacity of the channel.
Convolution Encoding with Viterbi decoding is a powerful FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by AWGN.
It is simple and has good performance with low implementation cost.
BCH codes, part of the cyclic codes, are very powerful error correcting codes widely used in the information coding techniques. This presentation explains these codes with an example.
This document provides information about getting fully solved assignments. It instructs students to send their semester and specialization name to the email address "help.mbaassignments@gmail.com" or call the phone number 08263069601. Mailing is preferred but calling can be done in an emergency. It then provides an example of an assignment for the subject "Logic Design" including questions about converting hexadecimal to other number systems, constructing logic gates from NAND gates, expanding Boolean functions, simplifying a Boolean function using a K-map, explaining differences between sequential and combinational circuits, and describing a serial in serial out shift register.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
This document presents a paper on implementing an image search firewall with content filtering. The paper proposes a system that uses one-click image searching to better understand user intent compared to text-based searches. It aims to restrict unauthorized users from overloading the server.
The system allows users to register and be allocated a time period by the admin to use the image search application. It provides directional image searching through categories instead of text queries. When a user clicks an image, similar images will be displayed. The admin can set permissions to allow or block users during certain sessions. Content filtering is used to remove negative images not aligned with user intentions. This is meant to improve search results and server speed by limiting traffic from unauthorized users.
A cornerstone of our digital society sytems from the explosive growth of multimedia traffic in general and video in particular. Video already accounts for over 50% of the internet traffic today and mobile video traffic is expected to grow by a factor of more than 20 in the next five years. This massive volume of data has resulted in a strong demand for implementing highly efficient approaches for video transmission. Error correcting codes for reliable communication have been studied for several decades. However, ideal coding techniques for video streaming are fundamentally different from the classical error corr ection codes. In order to be optimized they must operate under low latency, sequential encoding and decoding constrains, and as such they must inherently have a convolutional structure. Such unique constrains lead to fascinating new open problems in the de sign of error correction codes. In this talk we aim to look from a system theoretical perspective at these problems. In particular we propose the use of convolutional code.
The document provides a table of contents and questions on various technical aptitude topics such as data structures, C, C++, quantitative aptitude, UNIX concepts, RDBMS concepts, SQL, computer networks, and operating systems. It contains 35 questions related to data structures concepts like linked lists, trees, graphs, hashing etc. and their applications.
Richard Hamming developed Hamming codes in the late 1940s to enable error correction in computing. Hamming codes are perfect 1-error correcting codes that use parity checks to detect and correct single bit errors in binary data. The codes work by encoding k message bits into an n-bit codeword with additional parity check bits such that the minimum distance between any two codewords is 3, allowing correction of single bit errors. Hamming codes see widespread use and can be generalized to non-binary alphabets. Extended Hamming codes provide both single-error correction and double-error detection.
Direct Design of Reversible Combinational and Sequential Circuits Using PSDRM...IJRES Journal
Reversible logic will be a favourable logic by dissipating less heat than the thermo dynamic limit for
the emerging computing technologies. Also it has become very promising for low power designs. Reversible
designs of Combinational and Sequential circuits are built by replacing the latches, flip-flops and associated
combinational gates of the traditional irreversible designs by their reversible counter parts. But this replacement
technique is not very promising because it leads to high quantum cost and garbage outputs. So, in this paper we
presented both the direct design and replacement designs of 5-bit up down counter and universal shift register
which are practically important using reversible logic and PSDRM expressions. Replacement design is done by
replacing the RTL design using reversible designs. Direct design is done by representing the state transitions and
the output functions of the circuits using PSDRM expressions which are obtained from truth table or state
transition table. Thus my direct design of a 5-bit updown counter and universal shift register save 42.66%,
9.79% quantum cost and 93.75%, 40% garbage outputs respectively than the replacement design.
This document presents the design and implementation of an FPGA-based BCH decoder. It discusses BCH codes, which are binary error-correcting codes used in wireless communications. The implemented decoder is for a (15, 5, 3) BCH code, meaning it can correct up to 3 errors in a block of 15 bits. The decoder uses a serial input/output architecture and is implemented using VHDL on a FPGA device. It performs BCH decoding through syndrome calculation, running the Berlekamp-Massey algorithm to solve the key equation, and using Chien search to find error locations. The simulation result verifies correct decoding operation.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document discusses the implementation of Elliptic Curve Digital Signature Algorithm (ECDSA) using variable text message encryption methods. It begins with an abstract that outlines ECDSA, its advantages over other digital signature algorithms like smaller key size, and implementation of ECDSA over elliptic curves P-192 and P-256 with variable size text message, fixed size text message, and text based message encryption. It then provides details on elliptic curve cryptography, the elliptic curve discrete logarithm problem, finite fields, and domain parameters for ECDSA.
The document discusses the RSA cryptosystem. It begins by explaining that RSA is an important public-key cryptosystem based on the difficulty of factoring large integers. It then provides examples of how RSA works, including choosing prime numbers p and q to generate the public and private keys, and using modular exponentiation to encrypt and decrypt messages. The document also discusses the importance of integer factorization for the security of RSA, and considerations for designing a secure RSA system, such as choosing sufficiently large prime numbers.
Implementation of Elliptic Curve Digital Signature Algorithm Using Variable T...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document provides an overview of various channel coding techniques used in digital communication systems to combat noise and errors during transmission. It describes forward error correction methods like block codes, cyclic codes, convolutional codes and turbo codes. It also discusses error detection techniques like cyclic redundancy checks. Finally, it covers automatic repeat request protocols for retransmitting corrupted data packets.
The document contains questions and answers related to digital logic design concepts. Some key points:
- Karnaugh maps are used to minimize the number of gates and fan-in requirements in a digital circuit. Adjacent groups of 1s in a K-map correspond to terms in simplified Boolean expressions.
- Half adders and full adders are basic building blocks used to design multi-bit adders. A full adder can be realized using two half adders and two OR gates.
- Standard forms like SOP and POS are used to represent logic functions as sums of minterms or products of maxterms. Converting between forms allows implementing functions using different gate types like AND, OR,
Deep Recurrent Neural Networks with Layer-wise Multi-head Attentions for Punc...Seokhwan Kim
The document describes a deep recurrent neural network model with multi-head attention mechanisms for punctuation restoration. The model stacks multiple bidirectional recurrent layers to encode context and applies multi-head attention to each layer to capture hierarchical features. Evaluated on an English speech transcription dataset, the proposed model outperforms previous methods that use convolutional or recurrent neural networks alone or with single-head attention.
A method to determine partial weight enumerator for linear block codesAlexander Decker
This document presents a method to determine partial weight enumerators (PWE) for linear block codes using the error impulse technique and Monte Carlo method. The PWE can be used to compute an upper bound on the error probability of the maximum likelihood decoder. As an application, the document provides PWEs and analytical performances of shortened BCH codes, including BCH(130,66), BCH(103,47), and BCH(111,55). The full weight distributions of these codes are unknown. The proposed method estimates the PWE by drawing random codewords and computing the recovery rate of known-weight codewords, obtaining the PWE within a confidence interval.
A second important technique in error-control coding is that of convolutional coding . In this type of coding the encoder output is not in block form, but is in the form of an encoded
sequence generated from an input information sequence.
convolutional encoding is designed so that its decoding can be performed in some structured and simplified way. One of the design assumptions that simplifies decoding
is linearity of the code. For this reason, linear convolutional codes are preferred. The source alphabet is taken from a finite field or Galois field GF(q).
Convolution coding is a popular error-correcting coding method used in digital communications.
The convolution operation encodes some redundant information into the transmitted signal, thereby improving the data capacity of the channel.
Convolution Encoding with Viterbi decoding is a powerful FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by AWGN.
It is simple and has good performance with low implementation cost.
BCH codes, part of the cyclic codes, are very powerful error correcting codes widely used in the information coding techniques. This presentation explains these codes with an example.
This document provides information about getting fully solved assignments. It instructs students to send their semester and specialization name to the email address "help.mbaassignments@gmail.com" or call the phone number 08263069601. Mailing is preferred but calling can be done in an emergency. It then provides an example of an assignment for the subject "Logic Design" including questions about converting hexadecimal to other number systems, constructing logic gates from NAND gates, expanding Boolean functions, simplifying a Boolean function using a K-map, explaining differences between sequential and combinational circuits, and describing a serial in serial out shift register.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
This document presents a paper on implementing an image search firewall with content filtering. The paper proposes a system that uses one-click image searching to better understand user intent compared to text-based searches. It aims to restrict unauthorized users from overloading the server.
The system allows users to register and be allocated a time period by the admin to use the image search application. It provides directional image searching through categories instead of text queries. When a user clicks an image, similar images will be displayed. The admin can set permissions to allow or block users during certain sessions. Content filtering is used to remove negative images not aligned with user intentions. This is meant to improve search results and server speed by limiting traffic from unauthorized users.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
The document summarizes a study determining atmospheric stability classes in Mazoe, Zimbabwe over two years. Neutral stability class D was found to be most prevalent, occurring over 60% of the time. Moderate to strong winds with slight solar radiation and over 50% cloud cover were common. Stability classes A, B, and C indicating unstable conditions occurred up to 20% of the time. Very stable classes E and F were rare or did not occur. In general, neutral stability dominated, meaning the atmosphere neither enhanced nor resisted vertical air movement.
This document describes the creation of a geographic information systems (GIS) database for Keelaiyur Block in Nagappattinam District, Tamil Nadu. Specifically:
1) The database includes demographic, land use, rural electrification, and agricultural implements data for the block collected from secondary sources.
2) GIS techniques are used to analyze and interpret the data to create spatially referenced information to support planning and sharing information with various organizations.
3) Examples of changes in land use classification, rural electrification infrastructure, and agricultural machinery ownership in the block are presented from 2001-2002 to 2005-2006 based on the database.
El documento anuncia un desfile para celebrar la Semana del Ambiente en el estado Falcón de Venezuela. Se invita a todas las escuelas a asistir con cinco docentes y un grupo de niños ambientalistas con trajes alusivos al medio ambiente. El desfile se llevará a cabo el miércoles 5 de mayo en la Zona Educativa de Falcón.
El estacionamiento de un bloque de apartamentos fue diseñado para un número limitado de vehículos y no consideró el aumento de residentes y vehículos. Actualmente hay una falta de espacio para estacionamiento que se vuelve crítica en horas pico. Mientras que el consejo comunal y la alcaldía alegan falta de fondos para ayudar, los residentes proponen una estructura elevada financiada por cuotas de residentes y colaboración de las autoridades para solucionar el problema a largo plazo.
* Erdi Mailako Heziketa Zikloak, Miguel Altuna Bergara: Mekanizazioa, Administrazio Kudeaketa, Instalazio Elektriko eta Automatikoak.
* Ciclos Formativos de Grado Medio, Miguel Altuna Bergara: Mecanizado, Gestión Administrativa y Instalaciones Eléctricas y Automáticas.
O autor critica os defeitos do povo brasileiro, como a esperteza, a falta de honestidade e de valores, que prejudicam o desenvolvimento do país. Ele argumenta que os problemas não estão nos políticos, mas sim na "matéria prima defeituosa" que somos enquanto povo, e que será necessária uma mudança interna antes que o país possa progredir.
The document appears to be lyrics for a song that describe an intense dance battle or "slam" between two groups. The lyrics mention shoving, elbowing, headbutts, bruises, bloody noses, and intense dancing. They encourage the reader to get rowdy, bloody, and sweaty during the dense and intense dancing. The lyrics repeat refrains telling the reader to "dance and dense, denso".
1) Reed-Solomon codes are a type of error-correcting code invented in 1960 that can detect and correct multiple symbol errors. They work by encoding data into redundant symbols that can be used to detect and locate errors.
2) Reed-Solomon codes are particularly good at correcting burst errors, where a block of symbols are corrupted together by noise. Even if an entire block of bits is corrupted, the code can still correct the errors by replacing the corrupted symbol.
3) The error correction capability of Reed-Solomon codes increases with larger block sizes, as noise is averaged over more symbols. However, implementing Reed-Solomon codes also becomes more complex with higher redundancy.
1) Reed-Solomon codes are a type of error-correcting code invented in 1960 that can detect and correct multiple symbol errors. They work by encoding data into redundant symbols that can be used to detect and locate errors.
2) Reed-Solomon codes are particularly good at correcting burst errors, where a run of symbols are corrupted together, because they can correct a set number of errors regardless of where in the codeword they occur.
3) The error correction capability increases with lower code rates (more redundant symbols) and longer block lengths, as this averages the noise over more symbols and makes it less likely for a noise burst to corrupt too many consecutive symbols.
The International Journal of Engineering and Science (The IJES)theijes
This document summarizes a research paper that presents a unified hybrid Reed-Solomon decoder architecture capable of correcting both burst errors and random errors/erasures. The architecture combines low-complexity algorithms for correcting burst errors and random errors. It first provides background on Reed-Solomon codes, including their encoding and standard decoding process. It then describes the proposed unified hybrid decoding architecture, which uses a reformulated inversionless algorithm for burst error correction and integrates it with standard algorithms like Berlekamp-Massey for random error correction. The architecture is the first to allow multi-mode Reed-Solomon decoding to handle different error types.
The document outlines Reed-Solomon error correction codes. It discusses how Reed-Solomon codes encode data using a generator polynomial to produce parity check symbols. The document then describes how Reed-Solomon codes can decode errors using syndrome calculation, error location polynomials, and finding the error positions and values through algorithms like Forney's method and Chien search. Reed-Solomon codes are widely used in applications like CDs, DVDs, wireless communications and digital television for their ability to efficiently correct both random and burst errors.
Reed Solomon Coding For Error Detection and Correctioninventionjournals
This document discusses Reed-Solomon coding for error detection and correction. It provides an overview of Reed-Solomon codes, including that they are a type of linear block code well-suited for correcting burst errors. The encoding and decoding processes are described at a high-level, involving the generation and root-finding of polynomials over Galois fields. Applications mentioned include data storage, satellite communications, barcodes, and CD audio. In summary, the document provides a technical introduction to Reed-Solomon coding, the encoding and decoding algorithms, and common uses in digital communication and storage systems.
Fixed Point Realization of Iterative LR-Aided Soft MIMO Decoding AlgorithmCSCJournals
Multiple-input multiple-output (MIMO) systems have been widely acclaimed in order to provide high data rates. Recently Lattice Reduction (LR) aided detectors have been proposed to achieve near Maximum Likelihood (ML) performance with low complexity. In this paper, we develop the fixed point design of an iterative soft decision based LR-aided K-best decoder, which reduces the complexity of existing sphere decoder. A simulation based word-length optimization is presented for physical implementation of the K-best decoder. Simulations show that the fixed point result of 16 bit precision can keep bit error rate (BER) degradation within 0.3 dB for 8×8 MIMO systems with different modulation schemes.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document summarizes a proposed design for a radix-8 Booth encoded modulo 2n-1 multiplier that can adapt its delay to match the critical path delay of a residue number system (RNS) multiplier. The design represents the hard multiple (3X) in a partially redundant form using a k-bit ripple carry adder to reduce carry propagation length. It also represents other partial products in a partially redundant, biased form. This allows the delay to be controlled by varying k. For a given n, valid values of k exist where the bias can be compensated by a single precomputed constant without affecting correctness.
A High Throughput CFA AES S-Box with Error Correction CapabilityIOSR Journals
The document describes a proposed method for implementing a fault tolerant Advanced Encryption Standard (AES) using a Hamming error correction code. AES operates by performing rounds of transformations on blocks of data, with the most complex step being the SubBytes transformation which involves calculating multiplicative inverses in GF(28). The proposed method uses composite field arithmetic to more efficiently calculate these inverses. It also applies a (12,8) Hamming error correction code to each byte before and after processing to detect and correct single bit errors caused by radiation events, improving reliability for satellite communications. The parity check bits for the Hamming code are precalculated and stored for the AES S-box lookup tables.
This document summarizes a research paper that proposes a new binary tree algorithm for implementing a Huffman decoder. It begins by explaining the disadvantages of using an array data structure to represent the Huffman decoding tree and how the proposed binary tree method requires less memory. The proposed decoder is then implemented using ASIC and FPGA design tools. Performance metrics like power, area, and number of registers are obtained and compared between the ASIC and FPGA implementations. Simulation results show that the ASIC implementation has lower power consumption than the FPGA version. In conclusion, the binary tree algorithm is shown to improve memory usage for Huffman decoding.
This document proposes and evaluates several designs for implementing the AES encryption algorithm in hardware. It presents new composite field constructions for the AES S-box that improve on prior work in terms of implementation area and speed. It also introduces a novel fault-tolerant AES model that incorporates Hamming error correction codes to detect and correct single event upsets, making it suitable for use in space-based applications. The designs are implemented on an FPGA and evaluation shows improvements in area requirements, timing, and power consumption compared to previous implementations.
Performance Study of RS (255, 239) and RS (255.233) Used Respectively in DVB-...IJERA Editor
The error correction codes have a wide range of applications in digital communication (satellite, wireless) and digital data storage. This paper presents a comparative study of performance between RS (255, 239) and RS (255.233) used respectively in the Digital Video Broadcasting – Terrestrial (DVB-T) and National Aeronautics and Space Administration (NASA). The performances were evaluated by applying modulation scheme in additive white Gaussian noise (AWGN) channel. Performances of modulation with RS codes are evaluated in bit error rate (BER) and signal energy -to- noise power density ratio (Eb / No). The analysis is studied with the help of MATLAB simulator to analyze a communication link with AWGN Channel, and different modulations.
Design and Implementation of Variable Radius Sphere Decoding Algorithmcsandit
Sphere Decoding (SD) algorithm is an implement deco
ding algorithm based on Zero Forcing
(ZF) algorithm in the real number field. The classi
cal SD algorithm is famous for its
outstanding Bit Error Rate (BER) performance and de
coding strategy. The algorithm gets its
maximum likelihood solution by recursive shrinking
the searching radius gradually. However, it
is too complicated to use the method of shrinking t
he searching radius in ground
communication system. This paper proposed a Variabl
e Radius Sphere Decoding (VR-SD)
algorithm based on ZF algorithm in order to simplif
y the complex searching steps. We prove the
advantages of VR-SD algorithm by analyzing from the
derivation of mathematical formulas and
the simulation of the BER performance between SD an
d VR-SD algorithm.
Hardware Implementations of RS Decoding Algorithm for Multi-Gb/s Communicatio...RSIS International
In this paper, we have designed the VLSI hardware for a novel RS decoding algorithm suitable for Multi-Gb/s Communication Systems. Through this paper we show that the performance benefit of the algorithm is truly witnessed when implemented in hardware thus avoiding the extra processing time of Fetch-Decode-Execute cycle of traditional microprocessor based computing systems. The new algorithm with less time complexity combined with its application specific hardware implementation makes it suitable for high speed real-time systems with hard timing constraints. The design is implemented as a digital hardware using VHDL
An Efficient Interpolation-Based Chase BCH Decoderijsrd.com
This document describes an efficient interpolation-based Chase decoder for Bose-Chaudhuri-Hocquenghem (BCH) codes. BCH codes are error-correcting codes commonly used in applications such as flash memory and digital video broadcasting. The proposed Chase decoder uses an interpolation-based approach inspired by Chase decoders for Reed-Solomon codes but modified to leverage the binary properties of BCH codes. This allows it to correct up to t + η errors, where t is the number of errors the underlying BCH code can correct and η is the number of bits flipped in the Chase algorithm. The decoder consists of syndrome calculation, key equation solving, error location via Chien search, and error correction
Design and Implementation of Encoder for (15, k) Binary BCH Code Using VHDL a...IOSR Journals
Abstract: In this paper we have designed and implemented(15, k) a BCH Encoder on FPGA using VHDL for reliable data transfers in AWGN channel with multiple error correction control. The digital logic implementation of binary encoding of multiple error correcting BCH code (15, k) of length n=15 over GF (24) with irreducible primitive polynomial x4+x+1 is organized into shift register circuits. Using the cyclic codes, the reminder b(x) can be obtained in a linear (15-k) stage shift register with feedback connections corresponding to the coefficients of the generated polynomial. Three encoder are designed using VHDL to encode the single, double and triple error correcting BCH code (15, k) corresponding to the coefficient of generated polynomial. Information bit is transmitted in unchanged form up to k clock cycles and during this period parity bits are calculated in the LFSR then the parity bits are transmitted from k+1 to 15 clock cycles. Total 15-k numbers of parity bits with k information bits are transmitted in 15 code word. Here we have implemented (15, 5, 3), (15, 7, 2) and (15, 11, 1) BCH code encoder on Xilinx Spartan 3 FPGA using VHDL and the simulation & synthesis are done using Xilinx ISE 13.3. BCH encoders are conventionally implemented by linear feedback shift register architecture. Encoders of long BCH codes may suffer from the effect of large fan out, which may reduce the achievable clock speed. The data rate requirement of optical applications require parallel implementations of the BCH encoders. Also a comparative performance based on synthesis & simulation on FPGA is presented. Keywords: BCH, BCH Encoder, FPGA, VHDL, Error Correction, AWGN, LFSR cyclic redundancy checking, fan out .
This document presents an overview of low density parity check (LDPC) codes. It discusses the need for coding to achieve lower bit error rates at smaller signal-to-noise ratios. LDPC codes can provide coding gains close to the Shannon limit and outperform convolutional codes. The document explains the characteristics of LDPC codes such as their sparse parity check matrix and graphical representation using Tanner graphs. It also provides examples of encoding LDPC codes using techniques like matrix triangulation to solve for the parity bits. Decoding of LDPC codes uses iterative algorithms to converge to the most likely codeword.
The document describes Reed-Solomon error correcting codes. It begins by defining error correcting codes and their use of redundancy to recover corrupted data. It then discusses encoding messages into codewords by evaluating polynomials over finite fields and transmitting the codewords. The relationship between code rate, relative distance and error correction capability is also covered, along with the Singleton bound. Reed-Solomon codes specifically encode messages as polynomial coefficients and evaluate the polynomials at predefined points to generate codewords.
This document discusses widelinearly minimum mean square error (WLMMSE) estimation for unique word orthogonal frequency-division multiplexing (UW-OFDM). It first provides background on UW-OFDM and describes the system model. It then discusses the WLMMSE estimator and how it can outperform the linear MMSE estimator for improper constellations like binary phase-shift keying (BPSK). Simulation results are presented showing the WLMMSE estimator achieves around 1 dB gain over the LMMSE estimator for BPSK. The document concludes the WLMMSE/UW-OFDM scheme can achieve up to 1.9 dB gain over conventional IEEE 802.11 schemes.
Review paper on Reed Solomon (204,188) Decoder for Digital Video Broadcasting...IRJET Journal
This document discusses a review paper on a (204,188) Reed Solomon decoder used for digital video broadcasting terrestrial applications. It provides an overview of Reed Solomon codes, how they are used for error correction, and their applications in areas like data storage and digital video broadcasting. It then describes the encoding and decoding process for a (204,188) Reed Solomon code in detail, including how the encoder works, syndrome calculation, error location and evaluation, and Chien search decoding. Digital video broadcasting standards that use concatenated Reed Solomon codes for error protection are also discussed.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
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yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
Monitoring and Managing Anomaly Detection on OpenShift.pdfTosin Akinosho
Monitoring and Managing Anomaly Detection on OpenShift
Overview
Dive into the world of anomaly detection on edge devices with our comprehensive hands-on tutorial. This SlideShare presentation will guide you through the entire process, from data collection and model training to edge deployment and real-time monitoring. Perfect for those looking to implement robust anomaly detection systems on resource-constrained IoT/edge devices.
Key Topics Covered
1. Introduction to Anomaly Detection
- Understand the fundamentals of anomaly detection and its importance in identifying unusual behavior or failures in systems.
2. Understanding Edge (IoT)
- Learn about edge computing and IoT, and how they enable real-time data processing and decision-making at the source.
3. What is ArgoCD?
- Discover ArgoCD, a declarative, GitOps continuous delivery tool for Kubernetes, and its role in deploying applications on edge devices.
4. Deployment Using ArgoCD for Edge Devices
- Step-by-step guide on deploying anomaly detection models on edge devices using ArgoCD.
5. Introduction to Apache Kafka and S3
- Explore Apache Kafka for real-time data streaming and Amazon S3 for scalable storage solutions.
6. Viewing Kafka Messages in the Data Lake
- Learn how to view and analyze Kafka messages stored in a data lake for better insights.
7. What is Prometheus?
- Get to know Prometheus, an open-source monitoring and alerting toolkit, and its application in monitoring edge devices.
8. Monitoring Application Metrics with Prometheus
- Detailed instructions on setting up Prometheus to monitor the performance and health of your anomaly detection system.
9. What is Camel K?
- Introduction to Camel K, a lightweight integration framework built on Apache Camel, designed for Kubernetes.
10. Configuring Camel K Integrations for Data Pipelines
- Learn how to configure Camel K for seamless data pipeline integrations in your anomaly detection workflow.
11. What is a Jupyter Notebook?
- Overview of Jupyter Notebooks, an open-source web application for creating and sharing documents with live code, equations, visualizations, and narrative text.
12. Jupyter Notebooks with Code Examples
- Hands-on examples and code snippets in Jupyter Notebooks to help you implement and test anomaly detection models.
5th LF Energy Power Grid Model Meet-up SlidesDanBrown980551
5th Power Grid Model Meet-up
It is with great pleasure that we extend to you an invitation to the 5th Power Grid Model Meet-up, scheduled for 6th June 2024. This event will adopt a hybrid format, allowing participants to join us either through an online Mircosoft Teams session or in person at TU/e located at Den Dolech 2, Eindhoven, Netherlands. The meet-up will be hosted by Eindhoven University of Technology (TU/e), a research university specializing in engineering science & technology.
Power Grid Model
The global energy transition is placing new and unprecedented demands on Distribution System Operators (DSOs). Alongside upgrades to grid capacity, processes such as digitization, capacity optimization, and congestion management are becoming vital for delivering reliable services.
Power Grid Model is an open source project from Linux Foundation Energy and provides a calculation engine that is increasingly essential for DSOs. It offers a standards-based foundation enabling real-time power systems analysis, simulations of electrical power grids, and sophisticated what-if analysis. In addition, it enables in-depth studies and analysis of the electrical power grid’s behavior and performance. This comprehensive model incorporates essential factors such as power generation capacity, electrical losses, voltage levels, power flows, and system stability.
Power Grid Model is currently being applied in a wide variety of use cases, including grid planning, expansion, reliability, and congestion studies. It can also help in analyzing the impact of renewable energy integration, assessing the effects of disturbances or faults, and developing strategies for grid control and optimization.
What to expect
For the upcoming meetup we are organizing, we have an exciting lineup of activities planned:
-Insightful presentations covering two practical applications of the Power Grid Model.
-An update on the latest advancements in Power Grid -Model technology during the first and second quarters of 2024.
-An interactive brainstorming session to discuss and propose new feature requests.
-An opportunity to connect with fellow Power Grid Model enthusiasts and users.
What is an RPA CoE? Session 1 – CoE VisionDianaGray10
In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems
Freshworks Rethinks NoSQL for Rapid Scaling & Cost-EfficiencyScyllaDB
Freshworks creates AI-boosted business software that helps employees work more efficiently and effectively. Managing data across multiple RDBMS and NoSQL databases was already a challenge at their current scale. To prepare for 10X growth, they knew it was time to rethink their database strategy. Learn how they architected a solution that would simplify scaling while keeping costs under control.
How information systems are built or acquired puts information, which is what they should be about, in a secondary place. Our language adapted accordingly, and we no longer talk about information systems but applications. Applications evolved in a way to break data into diverse fragments, tightly coupled with applications and expensive to integrate. The result is technical debt, which is re-paid by taking even bigger "loans", resulting in an ever-increasing technical debt. Software engineering and procurement practices work in sync with market forces to maintain this trend. This talk demonstrates how natural this situation is. The question is: can something be done to reverse the trend?
Your One-Stop Shop for Python Success: Top 10 US Python Development Providersakankshawande
Simplify your search for a reliable Python development partner! This list presents the top 10 trusted US providers offering comprehensive Python development services, ensuring your project's success from conception to completion.
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor IvaniukFwdays
At this talk we will discuss DDoS protection tools and best practices, discuss network architectures and what AWS has to offer. Also, we will look into one of the largest DDoS attacks on Ukrainian infrastructure that happened in February 2022. We'll see, what techniques helped to keep the web resources available for Ukrainians and how AWS improved DDoS protection for all customers based on Ukraine experience
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/temporal-event-neural-networks-a-more-efficient-alternative-to-the-transformer-a-presentation-from-brainchip/
Chris Jones, Director of Product Management at BrainChip , presents the “Temporal Event Neural Networks: A More Efficient Alternative to the Transformer” tutorial at the May 2024 Embedded Vision Summit.
The expansion of AI services necessitates enhanced computational capabilities on edge devices. Temporal Event Neural Networks (TENNs), developed by BrainChip, represent a novel and highly efficient state-space network. TENNs demonstrate exceptional proficiency in handling multi-dimensional streaming data, facilitating advancements in object detection, action recognition, speech enhancement and language model/sequence generation. Through the utilization of polynomial-based continuous convolutions, TENNs streamline models, expedite training processes and significantly diminish memory requirements, achieving notable reductions of up to 50x in parameters and 5,000x in energy consumption compared to prevailing methodologies like transformers.
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1. Md. Taj, P Srinivas, S. Nagaraju / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.1607-1612
1607 | P a g e
Design and Implementation of FPGA System to Reduce Reed-
Solomon Errors
Md. Taj1
, P Srinivas2
, S. Nagaraju3
1
Dept.of ECE Nimra College of Engineering & Technology, Jupudi, Vijayawada-India.
2
Assistant Professor Dept.of ECE Nimra College of Engineering & Technology, Vijayawada, India.
3
Assistant Professor Dept.of ECE VLITS Vadlamdui Guntur, India.
ABSTRACT
The data reliability has become an
important issue in most communication and storage
systems for high speed operation and mass data
process. Various error correction code are provided
for improving data reliability. A Reed-Solomon code
is quite suitable for burst errors, but in case of
random errors, it has some difficulty. For MLC
NAND flash memories, Bose- Chaudhuri-
Hocquenghem (BCH) codes are frequently used.
BCH codes provide flexible code length and
variable range of error correcting capability.
However, NAND flash memory systems process with
the large size of data such as a page or a block unit.
Hence, BCH codes may not be appropriate for a
NAND flash controller.
We propose product Reed- Solomon (RS) code for
non-volatile NAND flash memory systems. Reed-
Solomon codes are the most diversely used in data
storage systems, but powerful for burst errors only.
In order to correct multiple random errors and
burst errors, another efficient decoding algorithm is
required. The product code composing of column-
wise Reed-Solomon codes and row-wise Reed-
Solomon codes may allow decoding multiple errors
beyond their error correction capability. The
proposed code consists of two shortened Reed-
Solomon codes and a conventional Reed- Solomon
code. We implement the proposed coding scheme on
a FPGA-based simulator with using an FPGA
device. The proposed code can correct 16 symbol
errors.
KEY WORDS: Bose-Chaudhuri-Hocquenghem
(BCH), Reed-Solomon codes, Berlekamp-Massey
Algorithm, flipped, Euclid's Algorithm, mass data
process, decoding, FPGA-based simulator, NAND
flash controller, and Altera.
I. INTRODUCTION
The data reliability has become an important
issue in most communication and storage systems for
high speed operation and mass data process. Various
error correction code are provided for improving data
reliability. A Reed-Solomon code is quite suitable for
burst errors, but in case of random errors, it has some
difficulty. For MLC NAND flash memories, Bose-
Chaudhuri-Hocquenghem (BCH) codes are
frequently used. BCH codes provide flexible code
length and variable range of error correcting
capability. However, NAND flash memory systems
process with the large size of data such as a page or a
block unit. Hence, BCH codes may not be
appropriate for a NAND flash controller.
The Reed- Solomon (RS) code for non-
volatile NAND flash memory systems. Reed-
Solomon codes are the most diversely used in data
storage systems, but powerful for burst errors only. In
order to correct multiple random errors and burst
errors, another efficient decoding algorithm is
required. The product code composing of column-
wise Reed-Solomon codes and row-wise Reed-
Solomon codes may allow to decoding multiple
errors beyond their error correction capability. The
proposed code consists of two shortened Reed-
Solomon codes and a conventional Reed- Solomon
code. We implement the proposed coding scheme on
a FPGA-based simulator with using an FPGA device.
The proposed code can correct 16 symbol errors.
Fig.1 Concept of forward error correction
II. Reed Solomon Encoder
The encoder is the easy bit. Since the code is
systematic, the whole of the block can be read into the
encoder, and then output the other side without
alteration. Once the kith data symbol has been read in,
the parity symbol calculation is finished, and the
parity symbols can be output to give the full n
symbols. Gross simplification coming up. The idea of
the parity words is to create a long polynomial (n
coefficients long it contains the message and the
parity) which can be divided exactly by the RS
generator polynomial. That way, at the decoder the
received message block can be divided by the RS
generator polynomial. If the remainder of the division
is zero, then no errors are detected.
If there is a remainder, then there are errors.
Dividing a polynomial by another is not conceptually
easy, but if you follow the maths in some of the
references its not too hard to understand. The encoder
acts to divide the polynomial represented by the k
message symbols d(x) by the RS generator
polynomial g(x). This generator polynomial is not the
same as the Galois Field generator polynomial, but is
derived from it
x(n-k).d(x)/g(x) = q(x) + r(x)/g(x) (1)
The term x(n-k) is a constant power of x,
which is simply a shift upwards n-k places of all the
2. Md. Taj, P Srinivas, S. Nagaraju / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.1607-1612
1608 | P a g e
polynomial coefficients in d(x). It happens as part of
the shifting process in the architecture below. The
remainder after the division r(x) becomes the parity.
By concatenating the parity symbols on to the end of
the k message symbols, an n coefficient polynomial is
created which is exactly divisible by g(x).
The encoder is a 2t tap shift register, where
each register is m bits wide. The multiplier
coefficients g0 to g (2t-1) are coefficients of the RS
generator polynomial. The coefficients are fixed,
which can be used to simplify the multipliers if
required. The only hard bit is working out the
coefficients, and for hardware implementations the
values can often be hard coded.
At the beginning of a block all the registers
are set to zero. From then on, at each clock cycle the
symbol in each register is added to the product of the
feedback symbol and the fixed coefficient for that tap,
and passed on to the next register. The symbol in the
last register becomes the feedback value on the next
cycle. When all n input symbols have been read in,
the parity symbols are sitting in the register, and it just
remains to shift them out one by one.
Equation(2),expresses the most conventional
form of Reed-Solomon (R-S) codes in terms of the
parameters n, k, t, and any positive integer m > 2.
(n, k) = (2m
- 1, 2m
- 1 - 2t) (2)
where n - k = 2t is the number of parity symbols, and
t is the symbol-error correcting capability of the code.
The generating polynomial for an R-S code takes the
following form
g(X ) = g0 + g1 X + g2 X2
+ … + g2t - 1 X2t - 1
+ X2t
(3)
The degree of the generator polynomial is
equal to the number of parity symbols. R-S codes are
a subset of the Bose, Chaudhuri, and Hocquenghem
(BCH) codes; hence, it should be no surprise that this
relationship between the degree of the generator
polynomial and the number of parity symbols holds,
just as for BCH codes.
Since the generator polynomial is of degree
2t, there must be precisely 2t successive powers of α
that are roots of the polynomial. We designate the
roots of g(X) as α, α2
, …, α2t
. It is not necessary to
start with the root α; starting with any power of α is
possible. Consider as an example the (7, 3) double-
symbol-error correcting R-S code. We describe the
generator polynomial in terms of its 2t = n - k = 4
roots, as follows
g(X) = ( X – α ) ( X – α2
) ( X – α3
)( X – α4
)
= ( X2
- ( α + α2
) X + α3
) ( X2
- ( α3
+ α4
) X + α7
)
= ( X2
– α4
X + α3
) ( X2
- α6
X + α0
)
= X4
- ( α4
+ α6
) X3
+ ( α3
+ α10
+ α0
) X2
- ( α4
+
α9
) X + α3
= X4
– α3
X3
+ α0
X2
– α1
X + α3
Following the low order to high order
format, and changing negative signs to positive, since
in the binary field +1 = –1, g(X ) can be expressed as
follows:
g(X ) = α3
+ α1
X + α0
X2
+ α3 X3
+ X4
(4)
III. Encoding in Systematic Form
Since R-S codes are cyclic codes, encoding
in systematic form is analogous to the binary
encoding procedure. We can think of shifting a
message polynomial, m(X ), into the rightmost k
stages of a codeword register and then appending a
parity polynomial, p(X ), by placing it in the leftmost
n - k stages. Therefore we multiply m(X ) by Xn-k
,
thereby manipulating the message polynomial
algebraically so that it is right-shifted n - k positions.
Next, we divide Xn-k
m(X ) by the generator
polynomial g(X ), which is written in the following
form
Xn-k
m(X ) = q(X ) g(X ) + p(X ) (5)
where q(X ) and p(X ) are quotient and remainder
polynomials, respectively. As in the binary case, the
remainder is the parity. Equation (23) can also be
expressed as follows
p(X ) = Xn-k
m(X ) modulo g(X ) (6)
The resulting codeword polynomial, U(X ) can be
written as
U(X ) = p(X ) + Xn-k
m(X ) (7)
We demonstrate the steps implied by Equations (5)
and (6) by encoding the following three-symbol
message:
with the (7, 3) R-S code whose generator polynomial
is given in Equation (5). We first multiply (upshift)
the message polynomial α1
+ α3
X + α5
X2
by X n - k
= X4
, yielding α1
X4
+ α3
X5
+ α5
X6
. We next divide
this upshifted message polynomial by the generator
polynomial in Equation (5), α3
+ α1
X + α0
X2
+ α3
X3
+ X4
. Polynomial division with nonbinary
coefficients is more tedious than its binary
counterpart, because the required operations of
addition (subtraction) and multiplication (division). It
is left as an exercise for the reader to verify that this
polynomial division results in the following
remainder (parity) polynomial.
p(X ) = α0
+ α2
X + α4
X2
+ α6
X3
(8)
Then, from Equation (7), the codeword polynomial
can be written as follows
U(X ) = α0
+ α2
X + α4
X2
+ α6
X3
+ α1
X4
+ α3
X5
+
α5
X6
(9)
Systematic Encoding with an (n - k)–Stage
Shift Register Using circuitry to encode a three-
symbol sequence in systematic form with the (7, 3)
R-S code described by g(X ) in Equation (4) requires
the implementation of a linear feedback shift register
(LFSR) circuit, as shown in Figure 6. It can easily be
verified that the multiplier terms in Figure 6, taken
from left to right, correspond to the coefficients of
the polynomial in Equation (4) (low order to high
order). This encoding process is the nonbinary
equivalent of cyclic encoding. Here,the (7, 3) R-S
nonzero codewords are made up of 2m - 1 = 7
symbols, and each symbol is made up of m = 3 bits.
IV. Reed Solomon Decoder
3. Md. Taj, P Srinivas, S. Nagaraju / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.1607-1612
1609 | P a g e
Earlier, a test message encoded in
systematic form using a (7, 3) R-S code resulted in a
codeword polynomial described by Equation (7).
Now, assume that during transmission this codeword
becomes corrupted so that two symbols are received
in error. (This number of errors corresponds to the
maximum error-correcting capability of the code.)
For this seven-symbol codeword example, the error
pattern, e(X), can be described in polynomial form as
follows
Fig2. Encoder with LFSR
e( X ) = ∑ en Xn
, (10) Where n = 0, 1, 2, 3, 4, 5, 6
For this example, let the double-symbol error be such
that
e ( X ) = 0 + 0X + 0X2
+ α2
X3
+ α5
X4
+ 0X5
+ 0X6
= (0 0 0)+(0 0 0)X+(0 0 0)X2
+(0 0 1)X3
+(1 1
1)X4
+(0 0 0)X5
+(0 0 0)X6
(11)
In other words, one parity symbol has been corrupted
with a 1-bit error (seen as α2
), and one data symbol
has been corrupted with a 3-bit error (seen as α5
). The
received corrupted-codeword polynomial, r(X), is
then represented by the sum of the transmitted-
codeword polynomial and the error-pattern
polynomial as follows
r(X) = U(X) + e(X) (12)
Following Equation (12), we add U(X ) from
Equation (11) to e(X ) and r(X ), as follows
r(X) = (100) + (001)X + (011)X2
+ (100)X3
+
(101)X4
+ (110)X5
+ (111)X6
α α2
Xα4
X2
α0
X3
α6
X4
α3
X5
α5
X6
(13)
In this example, there are four unknowns—two error
locations and two error values. Notice an important
difference between the non binary decoding of r(X )
that we are faced with in Equation (13) and binary
decoding; in binary decoding, the decoder only needs
to find the error locations. Knowledge that there is an
error at a particular location dictates that the bit must
be “flipped” from 1 to 0 or vice versa. But here, the
nonbinary symbols require that we not only learn the
error locations, but also determine the correct symbol
values at those locations. Since there are four
unknowns in this example, four equations are
required for their solution.
Decoding is a far harder task than encoding. Typically
about ten times more resources (be it logic, memory
or processor cycles) are required to decode and
correct the corrupted data The decode operation takes
several stages. There are plenty of sources available
for software implementations of the various
algorithms required. Hardware implementations
(FPGA or ASIC) are a little harder to come by,
especially those with parameterised specifications.
Texas Instruments give their software decoder away
for free, whilst by comparison FPGA manufacturers
such as Xilinx or Altera can charge many thousands
of dollars for their hardware implementation.
V. Berlekamp-Massey
The second step is to find the error
polynomial lambda. This requires solving 2t
simultaneous equations, one for each syndrome. The
2t syndromes form a simultaneous equation with t
unknowns. The unknowns are the locations of the
errors. In general there are many possible solutions to
the set of equations, but we assume that the one with
the least number of errors is the correct one.
This assumption is the reason that more than t errors
can actually cause the decoder to corrupt the received
signal further (if allowed to). If more than t errors
occur, then there will exist a possible solution to the
equations with less than t errors. Unfortunately this
solution is unlikely to correct the right symbols. The
process of solving the simultaneous equations is
usually split into two stages. First, an error location
polynomial is found.
This Polynomial has roots which give the
error locations. Then the roots of the error polynomial
are found. There are several methods of finding the
error polynomial lambda, the two most popular are
Euclid's Algorithm (easier to implement) and the
Berlekamp-Massey Algorithm (more efficient use of
hardware resources). The algorithm iteratively solves
the error locator polynomial by solving one equation
after another and updating the error locator
polynomial. If it turns out that it cannot solve the
equation at some step, then it computes the error and
weights it, increases the size of the error polynomial,
and does another iteration.
Fig3.Flow chart for Reed Solomon Decoder
4. Md. Taj, P Srinivas, S. Nagaraju / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.1607-1612
1610 | P a g e
A maximum of 2t iterations are required.
For n symbol errors, the algorithm gives a
polynomial with n coefficients. At this point the
decoder fails if there are more than t errors, and no
corrections can be made. Doing so might actually
introduce more errors than there were originally
Suppose there are ν errors in the codeword
at location X j1 , X j2 , ... , X j. Then, the error
polynomial e(X ) shown in Equations (10) and (11)
can be written as follows
e(X) = ej1Xj1
+ ej2Xj2
+ … + ejvXjv
(14)
The indices 1, 2, … ν refer to the first, second, …, νth
errors, and the index j refers to the error location. To
correct the corrupted codeword, each error value ejl
and its location Xjl
, where l = 1, 2, ..., ν, must be
determined. We define an error locator number as jl l.
Next, we obtain the n - k = 2t syndrome symbols by
substituting αi into the received polynomial for i = 1,
2, … 2t.
S1 = r(α) = ej1β1 + ej2β2 + … + ejvβv
S2 = r(α2
) = ej1β1
2
+ ej2β2
2
+ … + ejvβv
2
S2t = r(α2t
) = ej1β1
2t
+ ej2β2
2t
+ … + ejvβv
2t
(15)
There are 2t unknowns (t error values
and t locations), and 2t simultaneous equations.
However, these 2t simultaneous equations cannot be
solved in the usual way because they are nonlinear
(as some of the unknowns have exponents). Next, it
is necessary to learn the location of the error or
errors. An error-locator polynomial, σ(X ), can be
defined as follows
σ(X) = ( 1 + β1X ) ( 1 + β2X ) . . . ( 1 + βvX)
= 1 + σ1X + σ2X2
+ . . . + σvXv
(16)
The roots of σ(X ) are 1/β1, 1/β2, … ,1/βν.
The reciprocal of the roots of σ(X) are the error-
location numbers of the error pattern e(X). Then,
using autoregressive modeling techniques, we form a
matrix from the syndromes, where the first t
syndromes are used to predict the next syndrome.
That is,
(17)
We apply the autoregressive model of Equation (17)
by using the largest dimensioned matrix that has a
nonzero determinant. For the (7, 3) double-symbol
error correcting R-S code, the matrix size is 2 × 2,
and the model is written as follows
(18)
To solve for the coefficients σ1 and σ2 and
of the error-locator polynomial, σ(X ), we first take
the inverse of the matrix in Equation (18). The
inverse of a matrix [A] is found as follows
Fig4. Berlekamp-Massey Algorithm
Therefore
Cofactor (19)
(20)
VI. Design Summery Report
Number of errors: 0
Number of warnings: 257
1. Number of Slice
Registers
4,737 out of
28,800 16%
2. Number of Slice
LUTs
6,302 out of
28,800 21%
3. Number used as
logic
6,261 out of
28,800 21%
4. Number of route-
thrus
53 out of 57,600
1%
5. Md. Taj, P Srinivas, S. Nagaraju / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.1607-1612
1611 | P a g e
Table 5.2 Logic Utilization
1. Number of occupied
Slices
2,502 out of 7,200
34%
2. Number with an unused
Flip Flop
2,949 out of 7,686
38%
3. Number with an unused
LUT
1,384 out of 7,686
18%
4. Number of fully used
LUT-FF pairs
3,353 out of 7,686
43%
Table5.3 Logic Distribution
VII. 6. RESULTS
Fig5. Generation Of code words
Fig6. Generation Of Parity Bits
Fig 7. Adding Noise
Fig8. Detection of Error Values
Fig8.Decoded Symbols
VIII. Conclusion
This paper proposes a product Reed-
Solomon code for multiple random errors and burst
errors. The proposed code takes two dimensional
array data consisted of two shortened Reed-Solomon
codes in a column-wise and a conventional Reed-
Solomon code in a row-wise. The proposed code
becomes powerful against multiple random errors
and burst errors. The proposed code can corrects 16
symbol errors. The code has the coding gain of 1.8
dB and the bandwidth of 1.07 Gbps when operated at
290 MHz with the power consumption of 26.4 mW.
Future Scope of the project is to provide effective
code for detecting 20 error symbols in 255 code
words. Code can implement with low area and low
power
References
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Fields by Reed, I. S. and Solomon, G.
SIAM Journal of Applied Math.
[2] Information Theory and Reliable
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[3] Digital Communications: Fundamentals and
Applications, Second Edition by Sklar, B.
[4] The Application of Error Control to
Communications by Berlekamp, E. R., Peile,
R. E., and Pope, S. P.
[5] Forward Error Correction Coding for Fading
Compensation in Mobile Satellite Channels
by Hagenauer, J., and Lutz, E.
6. Md. Taj, P Srinivas, S. Nagaraju / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 4, Jul-Aug 2013, pp.1607-1612
1612 | P a g e
[6] Theory and Practice of Error Control Codes
by Blahut, R. E.
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Kang, C. G. Kim, S. W. Rhee, and Y. Jee.
[9] X., Yang, “Industrial Data Communication
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[10] C. E. Cummings, “Simulation and Synthesis
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