The document describes a lesson plan for a digital communication course at Matrusri Engineering College. The lesson plan covers linear block codes, including their description, generation, syndrome detection, minimum distance, error correction capabilities, and decoding using standard arrays and Hamming codes over 10 class periods. The objectives are to distinguish different error control coding techniques and their encoding/decoding algorithms. Textbooks and references are also listed.
In digital communication system, the information bearing digital signal is processed such
that it can be represented by a sequence of binary digits (discrete messages). Then it is used for
ON/OFF keying of some characteristic of a high frequency sinusoidal carrier wave, such as
amplitude, phase or frequency. If the input message signal is in analog form, then it is converted
to digital form by the processes of sampling, quantizing and encoding. Computer data and
telegraph signals are some examples of digital signal. The key feature of a digital communication
system is that it deals with a finite set of discrete messages.
The document discusses the course objectives and outcomes for the Digital Communication subject at Matrusri Engineering College. It includes 5 course objectives related to familiarizing students with digital communication techniques like PCM, channel coding, modulation schemes, and spread spectrum communication. It also lists 5 course outcomes related to classifying modulation techniques, illustrating source coding methods, distinguishing error control codes, examining modulation scheme performance, and spread spectrum signal generation and acquisition. The document also provides a lesson plan and contents for the course's first unit on elements of digital communication systems.
The document provides information about the syllabus for the course "Information Theory & Error Correction Coding". It discusses the details of the final exam which has two parts worth 50 marks total. Part A is 20 marks and covers topics like channel capacity, coding models, error control types, and linear block codes. Part B is 30 marks and covers additional topics such as linear block codes, convolutional codes, decoding algorithms, and error correction capabilities. It also provides background information on discrete channels, channel capacity theorem, Shannon's channel coding theorem, and the purpose of channel coding. Key concepts discussed include linear codes, block codes, convolutional codes, encoding, decoding, and error detection/correction techniques.
This document provides information about the digital communication course PC601EC. It discusses the prerequisites, course objectives, and units that will be covered in the course. The course aims to familiarize students with digital communication system elements, waveform coding techniques, information theory, channel coding, baseband digital transmission, and spread spectrum communication. Key concepts that will be covered include PCM, source coding, error control codes, digital modulation schemes, and direct sequence and frequency hopping spread spectrum systems.
Noise Immune Convolutional Encoder Design and Its Implementation in Tanner ijcisjournal
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was
increasing at a very fast rate, with which interconnect density is increasing especially in functional logic
chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have
implemented a convolution encoder using a technique that provides higher noise immunity. The encoder
circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
NOISE IMMUNE CONVOLUTIONAL ENCODER DESIGN AND ITS IMPLEMENTATIONIN TANNERIJCI JOURNAL
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was increasing at a very fast rate, with which interconnect density is increasing especially in functional logic chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have implemented a convolution encoder using a technique that provides higher noise immunity. The encoder circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
This document provides an overview and outline of a course on digital communications. It begins with background information on the course, including the textbook and references. The document then outlines the main topics to be covered in the course, including probability review, signal and spectra, modulation and demodulation techniques, channel coding, spread spectrum techniques, synchronization, source coding, and fading channels. It also provides brief descriptions of digital communication basics like source, transmitter, receiver, and channel components. Overall, the document introduces the key concepts and topics to be covered in a digital communications course.
In digital communication system, the information bearing digital signal is processed such
that it can be represented by a sequence of binary digits (discrete messages). Then it is used for
ON/OFF keying of some characteristic of a high frequency sinusoidal carrier wave, such as
amplitude, phase or frequency. If the input message signal is in analog form, then it is converted
to digital form by the processes of sampling, quantizing and encoding. Computer data and
telegraph signals are some examples of digital signal. The key feature of a digital communication
system is that it deals with a finite set of discrete messages.
The document discusses the course objectives and outcomes for the Digital Communication subject at Matrusri Engineering College. It includes 5 course objectives related to familiarizing students with digital communication techniques like PCM, channel coding, modulation schemes, and spread spectrum communication. It also lists 5 course outcomes related to classifying modulation techniques, illustrating source coding methods, distinguishing error control codes, examining modulation scheme performance, and spread spectrum signal generation and acquisition. The document also provides a lesson plan and contents for the course's first unit on elements of digital communication systems.
The document provides information about the syllabus for the course "Information Theory & Error Correction Coding". It discusses the details of the final exam which has two parts worth 50 marks total. Part A is 20 marks and covers topics like channel capacity, coding models, error control types, and linear block codes. Part B is 30 marks and covers additional topics such as linear block codes, convolutional codes, decoding algorithms, and error correction capabilities. It also provides background information on discrete channels, channel capacity theorem, Shannon's channel coding theorem, and the purpose of channel coding. Key concepts discussed include linear codes, block codes, convolutional codes, encoding, decoding, and error detection/correction techniques.
This document provides information about the digital communication course PC601EC. It discusses the prerequisites, course objectives, and units that will be covered in the course. The course aims to familiarize students with digital communication system elements, waveform coding techniques, information theory, channel coding, baseband digital transmission, and spread spectrum communication. Key concepts that will be covered include PCM, source coding, error control codes, digital modulation schemes, and direct sequence and frequency hopping spread spectrum systems.
Noise Immune Convolutional Encoder Design and Its Implementation in Tanner ijcisjournal
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was
increasing at a very fast rate, with which interconnect density is increasing especially in functional logic
chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have
implemented a convolution encoder using a technique that provides higher noise immunity. The encoder
circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
NOISE IMMUNE CONVOLUTIONAL ENCODER DESIGN AND ITS IMPLEMENTATIONIN TANNERIJCI JOURNAL
With the rapid advances in integrated circuit(IC) technologies, number of functions on a chip was increasing at a very fast rate, with which interconnect density is increasing especially in functional logic chips. The on-chip noise affects are increasing and needs to be addressed. In this paper we have implemented a convolution encoder using a technique that provides higher noise immunity. The encoder circuit is simulated in Tanner 15.0 with data rate of 25Mbps and a clock frequency of 250MHz
This document provides an overview and outline of a course on digital communications. It begins with background information on the course, including the textbook and references. The document then outlines the main topics to be covered in the course, including probability review, signal and spectra, modulation and demodulation techniques, channel coding, spread spectrum techniques, synchronization, source coding, and fading channels. It also provides brief descriptions of digital communication basics like source, transmitter, receiver, and channel components. Overall, the document introduces the key concepts and topics to be covered in a digital communications course.
Performances Concatenated LDPC based STBC-OFDM System and MRC Receivers IJECEIAES
This document presents a study on the performance of a low density parity check (LDPC) coded orthogonal frequency division multiplexing (OFDM) system using space time block coding (STBC) under various digital modulations and channel conditions. The system incorporates a 3/4 rate convolutional encoder and a LDPC encoder. At the receiver, maximum ratio combining is implemented for channel equalization. Simulation results show that the LDPC coded OFDM system outperforms an uncoded system, and provides lower bit error rates under binary phase shift keying modulation in an additive white Gaussian noise channel.
Space time block coding is a technique used in wireless communication to transmit multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data transfer. The fact that the transmitted signal must traverse a potentially difficult environment with scattering, reflection, refraction and so on and may then be further corrupted by thermal noise in the receiver means that some of the received copies of the data may be closer to the original signal than others. This redundancy results in a higher chance of being able to use one or more of the received copies to correctly decode the received signal. In fact, space–time coding combines all the copies of the received signal in an optimal way to extract as much information from each of them as possible.
The document compares the performance of single stage and double stage interleavers in communication systems using turbo codes. A single stage interleaver uses one random interleaver between two convolutional encoders, while a double stage interleaver uses two interleavers in series. The document suggests that a double stage interleaver can improve the bit error rate (BER) of the system compared to a single stage interleaver by further scrambling the input bits. It also provides details on the components of a turbo code system such as convolutional encoders, interleavers, puncturing, and iterative decoding.
The Reliability in Decoding of Turbo Codes for Wireless CommunicationsIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
This document appears to be a student paper submission for a networking course. It discusses using a microwave backhaul link to connect two company branch offices located on different Greek islands. The paper will analyze how the bit error rate of the microwave link at different signal-to-noise ratios can impact the TCP throughput between the two branches. It will include simulations of the microwave link and the network implementation to examine this relationship and draw conclusions. The paper is divided into sections covering the theoretical background of the communication channel, analysis of error correction coding and modulation, and the planned simulations.
This document provides information on the course "Data Communication and Computer Networks" including the course code, credits, objectives, description, outcomes and syllabus. The main focus of the course is on local area network organization, implementation, and management. The course introduces computer network design, operations, and topics like the OSI model, error detection, local area networks, routing, and network protocols. Upon completion, students should be able to design, implement and maintain a typical computer network. The syllabus outlines 5 units that cover introductory concepts, data link layer, network layer, transport layer, and application layer. Assessment includes mid-term exams conducted by the college and a university end-term exam.
Today, communications is the largest sector of the electronics field. In addition, wireless, networking or other communications technologies are now contained in almost every electronic product. This makes a knowledge and understanding of communication a must rather than an option for every student. Without at least one course in communications, the student may graduate with an incomplete view of the products and systems so common today.
1) The document compares the performance of coded and uncoded MC-DS-CDMA systems using linear block codes. BCH codes are used as the outer code and convolutional codes are used as the inner code in a concatenated coding scheme.
2) Simulation results show that the coded system significantly outperforms the uncoded system, with a coding gain of around 4dB. Using error correction codes is especially beneficial when the number of users is increased, as it is not as severely impacted by multiple access interference.
3) Performance is better when using a decorrelating detector compared to a maximum ratio combiner. However, the benefit of the decorrelating detector is smaller when there are more users.
This document provides a detailed lesson plan for teaching a course on analog and digital communication. It includes 5 units: 1) Analog Communication, 2) Digital Communication, 3) Data and Pulse Communication, 4) Source and Error Control Coding, and 5) Multi-User Radio Communication. It outlines the topics, objectives, textbooks, reference books, weekly plan, and distribution of topics across weeks. The plan aims to help students understand various communication techniques, learn data and pulse communication, get familiar with source and error coding, and gain knowledge of multi-user radio systems.
Performance enhancement of audio transmission based on LMMSE methodnooriasukmaningtyas
The research in wireless communication has developed rapidly for the last
decades as a result of raising the demand for efficient data transmission with
more security and accuracy. This paper proposed a system based on the
special multiplexing (SM) technique and linear minimum mean square error
(LMMSE) detection method with the assistance of the hamming code as well
as the interleaving techniques for a better enhanced performance of an audio
transmission. Moreover, the comparison was done between the two systems
for different antenna configurations and with the presence of two types of
modulation: binary phase shift key and quateradure phase shift key. These
systems are employed by Matlab simulation to show significant results in
terms of enhancing the Rayleigh fading channel capacity, bit error rate
(BER) and security as well as in recovering the transmitting audio signals.
Each system has advantages than the others in one performance term respect
to the other terms. The simulation results have provided to prove and discuss
our analysis.
ESTIMATION AND COMPENSATION OF INTER CARRIER INTERFERENCE IN WIMAX PHYSICAL L...ijngnjournal
WiMAX is Wireless Interoperability for Microwave Access has emerged as a promising solution for transmission of higher data rates for fixed and mobile applications. IEEE 802.16d and e are the standards proposed by WiMAX group for fixed and mobile. As the wireless channel have so many limitation Such as Multipath, Doppler spread, Delay spread and Line Of Sight (LOS)/Non Line Of Sight (NLOS) components. To attain higher data rates the Multi Carrier System with Multiple Input and Multiple Output (MIMO) is incorporated in the WiMAX. The Orthogonal Frequency Division Multiplexing (OFDM) is a multi carrier technique used with the WiMAX systems. In OFDM the available spectrum is split into numerous narrow band channels of dissimilar frequencies to achieve high data rate in a multi path fading environment. And all these sub carriers are considered to be orthogonal to each other. As the number of sub carriers is increased there is no guarantee of sustained orthogonality, i.e. at some point the carriers are not
independent to each other, and hence where the orthogonality can be loosed which leads to interference and also owing to the synchronization between transmitter and receiver local oscillator, it causes interference known as Inter Carrier Interference (ICI). The systems uses MIMO-OFDM will suffer with the effects of ICI and Carrier Frequency Offset (CFO) “ε”. However these affect the power leakage in the midst of sub carriers, consequently degrading the system performance. In this paper a new approach is proposed in order to reduce the ICI caused in WiMAX and improve the system performance. In this scheme at the transmitter side the modulated data and a few predefined pilot symbols are mapped onto the non
neighboring sub carriers with weighting coefficients of +1 and -1. With the aid of pilot symbols the frequency offset is exactly estimated by using Maximum Likelihood Estimation (MLE) and hence can be minimized. At demodulation stage the received signals are linearly combined along with their weighted
coefficients and pilot symbols, called as Pilot Aided Self Cancellation Method (PASCS). And also to realize the various wireless environments the simulations are carried out on Stanford University Interim (SUI) channels. The simulation results shows that by incorporating this method into WiMAX systems it performs better when the Line Of Sight (LOS) component is present in the transmission and also it improves the Bit Error Rate (BER) and Carrier to Interference Ratio (CIR). The CIR can be improved 20 dB. In this paper the effectiveness of PASCS scheme is compared with the Self Cancellation Method (SCM). It provides accurate estimation of frequency offset and when residual CFO is less significant the ICI can be diminished successfully.
The document discusses digital communication systems and outlines topics that will be covered, including digital data communication, multiplexing techniques, digital modulation and demodulation, and performance comparisons of modulation schemes. The objectives are to provide an overview of communication systems and concepts, discuss digital transmission methods and modulation types, and enable students to design simple communication systems and discuss industry trends.
Utilise Multipath Propagation to Improve the performance of BCH and RS CodesALYAA AL-BARRAK
The document proposes utilizing multipath propagation to improve the performance of BCH and RS error correction codes without adding redundancy. It discusses using multipath signals as redundant copies, combining them using a Hamming weight combiner. Simulations showed combining 3 paths improved performance of BCH/RS codes with error correction capability t=1, outperforming codes with t=2. Future work includes analyzing performance with higher modulation schemes and wireless channel models.
The document summarizes a research paper that proposes a low density parity check (LDPC) algorithm for insertion/deletion channels. It begins by providing background on LDPC codes and how they are finding increasing use for reliable information transfer over bandwidth-constrained links with noise. It then describes the specific system model of a concatenated coding scheme using an outer error correcting code and inner marker code. The document analyzes the achievable transmission rates using this scheme through both bit-level and symbol-level maximum a posteriori probability (MAP) detection algorithms. It finds that the symbol-level approach confirms an advantage over codes optimized for additive white Gaussian noise channels.
Study of the operational SNR while constructing polar codes IJECEIAES
Channel coding is commonly based on protecting information to be communicated across an unreliable medium, by adding patterns of redundancy into the transmission path. Also referred to as forward error control coding (FECC), the technique is widely used to enable correcting or at least detecting bit errors in digital communication systems. In this paper we study an original FECC known as polar coding which has proven to meet the typical use cases of the next generation mobile standard. This work is motivated by the suitability of polar codes for the new coming wireless era. Hence, we investigate the performance of polar codes in terms of bit error rate (BER) for several codeword lengths and code rates. We first perform a discrete search to find the best operational signal-to-noise ratio (SNR) at two different code rates, while varying the blocklength. We find in our extensive simulations that the BER becomes more sensitive to operational SNR (OSNR) as long as we increase the blocklength and code rate. Finally, we note that increasing blocklength achieves an SNR gain, while increasing code rate changes the OSNR domain. This trade-off sorted out must be taken into consideration while designing polar codes for high-throughput application.
This document provides an overview of an EE 320 communication systems course. It outlines the course schedule, textbook, and assessments. It then summarizes key topics that will be covered, including the basic structure of a communication system, common system types, analog vs digital signals, information theory concepts like entropy and channel capacity, modulation techniques, and communication networks. The goal is to introduce students to fundamental concepts in communication systems engineering.
Effect of Interleaved FEC Code on Wavelet Based MC-CDMA System with Alamouti ...IJCSEIT Journal
In this paper, the impact of Forward Error Correction (FEC) code namely Trellis code with interleaver on
the performance of wavelet based MC-CDMA wireless communication system with the implementation of
Alamouti antenna diversity scheme has been investigated in terms of Bit Error Rate (BER) as a function of
Signal-to-Noise Ratio (SNR) per bit. Simulation of the system under proposed study has been done in M-ary
modulation schemes (MPSK, MQAM and DPSK) over AWGN and Rayleigh fading channel incorporating
Walsh Hadamard code as orthogonal spreading code to discriminate the message signal for individual
user. It is observed via computer simulation that the performance of the interleaved coded based proposed
system outperforms than that of the uncoded system in all modulation schemes over Rayleigh fading
channel.
New generation communication networks are moving towards autonomous wireless infrastructures which are very popular in the application of multimedia broadcasting and mobile communication where N numbers of data are transfer through the wireless network every day. In such applications security of transmitted signal is very important in wireless communication network. So the proposed work creates a methodology to increase the security of the data and communication using chaotic encryption algorithm to transfer the data from the wireless network. A proposed new structure is based on coupling of chaotic system. We combine the text message with the chaotic signals to reduce the attack and improve the security of the data. The performance of BER in AWGN channel are verified and analyzed with MATLAB toolbox.
This document discusses an iterative MMSE-PIC detection algorithm for MIMO-OFDM systems. It begins with an introduction to MIMO and OFDM technologies and how their combination can provide high spectrum efficiency and diversity gain against fading channels. It then describes the iterative MMSE-PIC detection algorithm, which utilizes parallel interference cancellation and iteration to improve detection performance compared to other detectors like ZF and MMSE in noisy environments. The document provides details on the system model and MIMO techniques like spatial multiplexing and diversity schemes before introducing the proposed iterative MMSE-PIC detection algorithm for MIMO-OFDM systems.
The document discusses the physical layer of the OSI model. It describes the role of the physical layer in encoding data bits into signals to transmit across network media like copper, fiber, and wireless. It explains physical layer elements, operations, standards, technologies, functions, signaling methods, encoding, data carrying capacity, and characteristics of different physical media like copper, fiber, and wireless networks.
This document provides an overview of spread spectrum communication. It discusses the advantages of spread spectrum such as interference suppression, multiple access capability, and message privacy. It describes the basic model of a spread spectrum system including pseudorandom sequence generation and synchronization. The two main types of spread spectrum modulation are direct sequence spread spectrum (DSSS) and frequency hopping spread spectrum (FHSS). Pseudorandom sequences are explained which are used to spread and later recover the signal. The document provides historical background on transmitted reference versus stored reference spread spectrum approaches.
This document discusses a digital communication course at Matrusri Engineering College. It outlines the course objectives, which include familiarizing students with digital communication systems, information theory, and channel coding techniques. It also lists the course outcomes, such as classifying modulation techniques and distinguishing error control codes. The document provides information on topics that will be covered, including spread spectrum communication, pseudorandom noise sequences, direct sequence spread spectrum, and frequency hopping spread spectrum.
Performances Concatenated LDPC based STBC-OFDM System and MRC Receivers IJECEIAES
This document presents a study on the performance of a low density parity check (LDPC) coded orthogonal frequency division multiplexing (OFDM) system using space time block coding (STBC) under various digital modulations and channel conditions. The system incorporates a 3/4 rate convolutional encoder and a LDPC encoder. At the receiver, maximum ratio combining is implemented for channel equalization. Simulation results show that the LDPC coded OFDM system outperforms an uncoded system, and provides lower bit error rates under binary phase shift keying modulation in an additive white Gaussian noise channel.
Space time block coding is a technique used in wireless communication to transmit multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data transfer. The fact that the transmitted signal must traverse a potentially difficult environment with scattering, reflection, refraction and so on and may then be further corrupted by thermal noise in the receiver means that some of the received copies of the data may be closer to the original signal than others. This redundancy results in a higher chance of being able to use one or more of the received copies to correctly decode the received signal. In fact, space–time coding combines all the copies of the received signal in an optimal way to extract as much information from each of them as possible.
The document compares the performance of single stage and double stage interleavers in communication systems using turbo codes. A single stage interleaver uses one random interleaver between two convolutional encoders, while a double stage interleaver uses two interleavers in series. The document suggests that a double stage interleaver can improve the bit error rate (BER) of the system compared to a single stage interleaver by further scrambling the input bits. It also provides details on the components of a turbo code system such as convolutional encoders, interleavers, puncturing, and iterative decoding.
The Reliability in Decoding of Turbo Codes for Wireless CommunicationsIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
This document appears to be a student paper submission for a networking course. It discusses using a microwave backhaul link to connect two company branch offices located on different Greek islands. The paper will analyze how the bit error rate of the microwave link at different signal-to-noise ratios can impact the TCP throughput between the two branches. It will include simulations of the microwave link and the network implementation to examine this relationship and draw conclusions. The paper is divided into sections covering the theoretical background of the communication channel, analysis of error correction coding and modulation, and the planned simulations.
This document provides information on the course "Data Communication and Computer Networks" including the course code, credits, objectives, description, outcomes and syllabus. The main focus of the course is on local area network organization, implementation, and management. The course introduces computer network design, operations, and topics like the OSI model, error detection, local area networks, routing, and network protocols. Upon completion, students should be able to design, implement and maintain a typical computer network. The syllabus outlines 5 units that cover introductory concepts, data link layer, network layer, transport layer, and application layer. Assessment includes mid-term exams conducted by the college and a university end-term exam.
Today, communications is the largest sector of the electronics field. In addition, wireless, networking or other communications technologies are now contained in almost every electronic product. This makes a knowledge and understanding of communication a must rather than an option for every student. Without at least one course in communications, the student may graduate with an incomplete view of the products and systems so common today.
1) The document compares the performance of coded and uncoded MC-DS-CDMA systems using linear block codes. BCH codes are used as the outer code and convolutional codes are used as the inner code in a concatenated coding scheme.
2) Simulation results show that the coded system significantly outperforms the uncoded system, with a coding gain of around 4dB. Using error correction codes is especially beneficial when the number of users is increased, as it is not as severely impacted by multiple access interference.
3) Performance is better when using a decorrelating detector compared to a maximum ratio combiner. However, the benefit of the decorrelating detector is smaller when there are more users.
This document provides a detailed lesson plan for teaching a course on analog and digital communication. It includes 5 units: 1) Analog Communication, 2) Digital Communication, 3) Data and Pulse Communication, 4) Source and Error Control Coding, and 5) Multi-User Radio Communication. It outlines the topics, objectives, textbooks, reference books, weekly plan, and distribution of topics across weeks. The plan aims to help students understand various communication techniques, learn data and pulse communication, get familiar with source and error coding, and gain knowledge of multi-user radio systems.
Performance enhancement of audio transmission based on LMMSE methodnooriasukmaningtyas
The research in wireless communication has developed rapidly for the last
decades as a result of raising the demand for efficient data transmission with
more security and accuracy. This paper proposed a system based on the
special multiplexing (SM) technique and linear minimum mean square error
(LMMSE) detection method with the assistance of the hamming code as well
as the interleaving techniques for a better enhanced performance of an audio
transmission. Moreover, the comparison was done between the two systems
for different antenna configurations and with the presence of two types of
modulation: binary phase shift key and quateradure phase shift key. These
systems are employed by Matlab simulation to show significant results in
terms of enhancing the Rayleigh fading channel capacity, bit error rate
(BER) and security as well as in recovering the transmitting audio signals.
Each system has advantages than the others in one performance term respect
to the other terms. The simulation results have provided to prove and discuss
our analysis.
ESTIMATION AND COMPENSATION OF INTER CARRIER INTERFERENCE IN WIMAX PHYSICAL L...ijngnjournal
WiMAX is Wireless Interoperability for Microwave Access has emerged as a promising solution for transmission of higher data rates for fixed and mobile applications. IEEE 802.16d and e are the standards proposed by WiMAX group for fixed and mobile. As the wireless channel have so many limitation Such as Multipath, Doppler spread, Delay spread and Line Of Sight (LOS)/Non Line Of Sight (NLOS) components. To attain higher data rates the Multi Carrier System with Multiple Input and Multiple Output (MIMO) is incorporated in the WiMAX. The Orthogonal Frequency Division Multiplexing (OFDM) is a multi carrier technique used with the WiMAX systems. In OFDM the available spectrum is split into numerous narrow band channels of dissimilar frequencies to achieve high data rate in a multi path fading environment. And all these sub carriers are considered to be orthogonal to each other. As the number of sub carriers is increased there is no guarantee of sustained orthogonality, i.e. at some point the carriers are not
independent to each other, and hence where the orthogonality can be loosed which leads to interference and also owing to the synchronization between transmitter and receiver local oscillator, it causes interference known as Inter Carrier Interference (ICI). The systems uses MIMO-OFDM will suffer with the effects of ICI and Carrier Frequency Offset (CFO) “ε”. However these affect the power leakage in the midst of sub carriers, consequently degrading the system performance. In this paper a new approach is proposed in order to reduce the ICI caused in WiMAX and improve the system performance. In this scheme at the transmitter side the modulated data and a few predefined pilot symbols are mapped onto the non
neighboring sub carriers with weighting coefficients of +1 and -1. With the aid of pilot symbols the frequency offset is exactly estimated by using Maximum Likelihood Estimation (MLE) and hence can be minimized. At demodulation stage the received signals are linearly combined along with their weighted
coefficients and pilot symbols, called as Pilot Aided Self Cancellation Method (PASCS). And also to realize the various wireless environments the simulations are carried out on Stanford University Interim (SUI) channels. The simulation results shows that by incorporating this method into WiMAX systems it performs better when the Line Of Sight (LOS) component is present in the transmission and also it improves the Bit Error Rate (BER) and Carrier to Interference Ratio (CIR). The CIR can be improved 20 dB. In this paper the effectiveness of PASCS scheme is compared with the Self Cancellation Method (SCM). It provides accurate estimation of frequency offset and when residual CFO is less significant the ICI can be diminished successfully.
The document discusses digital communication systems and outlines topics that will be covered, including digital data communication, multiplexing techniques, digital modulation and demodulation, and performance comparisons of modulation schemes. The objectives are to provide an overview of communication systems and concepts, discuss digital transmission methods and modulation types, and enable students to design simple communication systems and discuss industry trends.
Utilise Multipath Propagation to Improve the performance of BCH and RS CodesALYAA AL-BARRAK
The document proposes utilizing multipath propagation to improve the performance of BCH and RS error correction codes without adding redundancy. It discusses using multipath signals as redundant copies, combining them using a Hamming weight combiner. Simulations showed combining 3 paths improved performance of BCH/RS codes with error correction capability t=1, outperforming codes with t=2. Future work includes analyzing performance with higher modulation schemes and wireless channel models.
The document summarizes a research paper that proposes a low density parity check (LDPC) algorithm for insertion/deletion channels. It begins by providing background on LDPC codes and how they are finding increasing use for reliable information transfer over bandwidth-constrained links with noise. It then describes the specific system model of a concatenated coding scheme using an outer error correcting code and inner marker code. The document analyzes the achievable transmission rates using this scheme through both bit-level and symbol-level maximum a posteriori probability (MAP) detection algorithms. It finds that the symbol-level approach confirms an advantage over codes optimized for additive white Gaussian noise channels.
Study of the operational SNR while constructing polar codes IJECEIAES
Channel coding is commonly based on protecting information to be communicated across an unreliable medium, by adding patterns of redundancy into the transmission path. Also referred to as forward error control coding (FECC), the technique is widely used to enable correcting or at least detecting bit errors in digital communication systems. In this paper we study an original FECC known as polar coding which has proven to meet the typical use cases of the next generation mobile standard. This work is motivated by the suitability of polar codes for the new coming wireless era. Hence, we investigate the performance of polar codes in terms of bit error rate (BER) for several codeword lengths and code rates. We first perform a discrete search to find the best operational signal-to-noise ratio (SNR) at two different code rates, while varying the blocklength. We find in our extensive simulations that the BER becomes more sensitive to operational SNR (OSNR) as long as we increase the blocklength and code rate. Finally, we note that increasing blocklength achieves an SNR gain, while increasing code rate changes the OSNR domain. This trade-off sorted out must be taken into consideration while designing polar codes for high-throughput application.
This document provides an overview of an EE 320 communication systems course. It outlines the course schedule, textbook, and assessments. It then summarizes key topics that will be covered, including the basic structure of a communication system, common system types, analog vs digital signals, information theory concepts like entropy and channel capacity, modulation techniques, and communication networks. The goal is to introduce students to fundamental concepts in communication systems engineering.
Effect of Interleaved FEC Code on Wavelet Based MC-CDMA System with Alamouti ...IJCSEIT Journal
In this paper, the impact of Forward Error Correction (FEC) code namely Trellis code with interleaver on
the performance of wavelet based MC-CDMA wireless communication system with the implementation of
Alamouti antenna diversity scheme has been investigated in terms of Bit Error Rate (BER) as a function of
Signal-to-Noise Ratio (SNR) per bit. Simulation of the system under proposed study has been done in M-ary
modulation schemes (MPSK, MQAM and DPSK) over AWGN and Rayleigh fading channel incorporating
Walsh Hadamard code as orthogonal spreading code to discriminate the message signal for individual
user. It is observed via computer simulation that the performance of the interleaved coded based proposed
system outperforms than that of the uncoded system in all modulation schemes over Rayleigh fading
channel.
New generation communication networks are moving towards autonomous wireless infrastructures which are very popular in the application of multimedia broadcasting and mobile communication where N numbers of data are transfer through the wireless network every day. In such applications security of transmitted signal is very important in wireless communication network. So the proposed work creates a methodology to increase the security of the data and communication using chaotic encryption algorithm to transfer the data from the wireless network. A proposed new structure is based on coupling of chaotic system. We combine the text message with the chaotic signals to reduce the attack and improve the security of the data. The performance of BER in AWGN channel are verified and analyzed with MATLAB toolbox.
This document discusses an iterative MMSE-PIC detection algorithm for MIMO-OFDM systems. It begins with an introduction to MIMO and OFDM technologies and how their combination can provide high spectrum efficiency and diversity gain against fading channels. It then describes the iterative MMSE-PIC detection algorithm, which utilizes parallel interference cancellation and iteration to improve detection performance compared to other detectors like ZF and MMSE in noisy environments. The document provides details on the system model and MIMO techniques like spatial multiplexing and diversity schemes before introducing the proposed iterative MMSE-PIC detection algorithm for MIMO-OFDM systems.
The document discusses the physical layer of the OSI model. It describes the role of the physical layer in encoding data bits into signals to transmit across network media like copper, fiber, and wireless. It explains physical layer elements, operations, standards, technologies, functions, signaling methods, encoding, data carrying capacity, and characteristics of different physical media like copper, fiber, and wireless networks.
This document provides an overview of spread spectrum communication. It discusses the advantages of spread spectrum such as interference suppression, multiple access capability, and message privacy. It describes the basic model of a spread spectrum system including pseudorandom sequence generation and synchronization. The two main types of spread spectrum modulation are direct sequence spread spectrum (DSSS) and frequency hopping spread spectrum (FHSS). Pseudorandom sequences are explained which are used to spread and later recover the signal. The document provides historical background on transmitted reference versus stored reference spread spectrum approaches.
This document discusses a digital communication course at Matrusri Engineering College. It outlines the course objectives, which include familiarizing students with digital communication systems, information theory, and channel coding techniques. It also lists the course outcomes, such as classifying modulation techniques and distinguishing error control codes. The document provides information on topics that will be covered, including spread spectrum communication, pseudorandom noise sequences, direct sequence spread spectrum, and frequency hopping spread spectrum.
This document discusses digital carrier modulation schemes. It begins with an introduction to digital modulation, describing how digital data is mapped to modulated waveforms that differ in amplitude, frequency, phase, or combinations of these. It then describes various digital modulation techniques including coherent (ASK, FSK, BPSK) and non-coherent. It provides details on BPSK, BFSK, and BASK modulation including block diagrams, waveform diagrams, and merits and demerits. The goals of digital communication systems are also summarized.
This document discusses channel coding. It defines linear block codes, which encode k information bits into n codeword bits through the addition of n-k check bits. The generator matrix defines the mapping of k message bits to n-bit codewords. Linear block codes have the property that the modulo-2 sum of any two codewords is also a valid codeword. Channel coding introduces redundancy to enable error detection and correction at the receiver. Common channel coding techniques include linear block codes, cyclic codes, and convolutional codes.
This document describes a digital communication course outline at Matrusri Engineering College. It includes 5 objectives focused on digital modulation techniques, information theory, channel coding, and spread spectrum communication. It also lists 5 course outcomes related to classifying modulation techniques, source coding methods, error control codes, analyzing digital modulation schemes, and spread spectrum signal generation and acquisition. The document provides a lesson plan and contents for a unit on information theory and source coding covering concepts like uncertainty, entropy, source coding techniques, and channel capacity.
This document provides an overview of information theory and source coding. It defines key information theory concepts like entropy, which is a measure of uncertainty or average information content. Entropy is calculated based on the probabilities of different messages from an information source. The document also discusses discrete memoryless sources, which independently and identically generate discrete symbols. The entropy of a discrete memoryless source represents the average information per message. Extended entropy is defined as the entropy of blocks of symbols from the source.
The document discusses various digital communication techniques including:
- Elements of a digital communication system such as source encoding, channel encoding, modulation, and demodulation.
- Types of channels for digital communication including telephone channels, optical fiber channels, and satellite channels.
- Key aspects of telephone channels including a bandwidth of 300Hz to 3400Hz and support for transmission rates up to 16.8 kbps. Optical fiber channels use light signals transmitted through fiber optic cables while overcoming noise from photodiodes and amplifiers.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
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Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
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1. MATRUSRI ENGINEERING COLLEGE
DEPARTMENT OF ELECTRONICS COMMUNICATION
AND ENGINEERING
SUBJECT NAME: DIGITAL COMMUNICATION(PC601EC)-VI SEM
FACULTY NAME: Mr.A.ABHISHEK Reddy,Asst.Prof.
MATRUSRI
ENGINEERING COLLEGE
2. DIGITAL COMMUNICATION
COURSE OBJECTIVES:
1. Familiarize the students with elements of digital communication system and
waveform coding techniques like PCM, DPCM, DM and ADM.
2. Introduce the concepts of information theory and source coding
3. Familiarize the students with channel coding techniques such as LBC, BCC and
convolution codes
4. Introduce the concepts of baseband digital data transmission and analyze the
error performance of different digital carrier modulation schemes like ASK, FSK,
PSK etc.
5. Familiarize the students with the concepts of spread spectrum communication
with emphasis on DSSS and FHSS.
COURSE OUTCOMES:
CO1: Classify the different types of digital modulation techniques PCM, DPCM, DM
and ADM and compare their performance by SNR.
CO2: Illustrate the classification of channels and Source coding methods.
CO3:Distinguish different types of Error control codes along with their
encoding/decoding algorithms.
CO4: Examine the Performance of different Digital Carrier Modulation schemes of
Coherent and Non-coherent type based on Probability of error.
CO5:Generation of PN sequence using Spread Spectrum and characterize the
Acquisition Schemes for Receivers to track the signals.
MATRUSRI
ENGINEERING COLLEGE
3. LESSON PLAN:
UNIT III- Channel Coding
MATRUSRI
ENGINEERING COLLEGE
S. No. Topic(S)
No.
of Hrs
Relevant
COs
Text Book/
Reference
Book
1. Types of transmission errors, need for error control
coding
01 CO3 T2,R1,R3
2. Linear Block Codes (LBC): description of LBC, generation 01 CO3 T2,R1,R3
3. Syndrome and error detection, Minimum distance of
Linear block code
02 CO3 T2,R1,R3
4. error correction and error detection capabilities,
Standard array and syndrome decoding, Hamming codes.
02 CO3 T2,R1,R3
5. Binary cyclic codes (BCC): Description of cyclic codes,
encoding
01 CO3 T2,R1,R3
6. decoding and error correction using shift registers 01 CO3 T2,R1,R3
7 Convolution codes: description, encoding 01 CO3 T2,R1,R3
8 code tree, state diagram 01 CO3 T2,R1,R3
TOTAL 10
4. TEXT BOOKS /REFERENCES
TEXT BOOKS:
1. Simon Haykin, “Communication systems” 4/e, Wiley India 2011
2. Sam Shanmugam K, “Digital and Analog Communication systems”,
Wiley 1979.
3. B.P.Lathi, “Modern digital and analog communication systems” 3/e,
OxfordUniversityPress. 1998.
4. Leon W.Couch II., Digital and Analog Communication Systems, 6th Edn,
Pearson Education inc., New Delhi, 2001.
5. R.E.Zimer&R.L.Peterson : Introduction to Digital Communication, PHI,
2001.
REFERENCES:
1. P. Ramakrishna Rao, “Digital Communication”, TMH, 2011.
2. Dr. Sanjay Sharma, “Digital and Analog Communication”, Mc Graw
Hill Publication, 2009.
3. Bernard Sklar “Digital Communications – Fundamentals and
Applications” / 2nd Edition, Prentice Hall.
4. John G. Proakis” Digital Communications” Fourth Edition (textbook)
McGraw Hill.
MATRUSRI
ENGINEERING COLLEGE
5. UNITIII-Channel Coding:
types of transmission errors, need for error control coding, linear
block codes (LBC): description of LBC, generation, syndrome and
error detection, minimum distance of linear block code, error
correction and error detection capabilities, standard array and
syndrome decoding, hamming codes. binary cyclic codes (bcc):
description of cyclic codes, encoding, decoding and error
correction using shift registers. convolution codes: description,
encoding – code tree, state diagram.
UNIT-III
OUTCOMES:
Distinguish different types of Error control codes along with their
encoding/decoding algorithms.
MATRUSRI
ENGINEERING COLLEGE
6. CONTENTS:
- Channel Coding: Introduction
- Types Of Transmission Errors
- Need For Error Control Coding
-Classification of codes
OUTCOMES:
Understanding the need for error control coding techniques with
block diagram and different types of codes.
MODULE-I
MATRUSRI
ENGINEERING COLLEGE
7. INTRODUCTION
In any digital communication system, the two important desirable features are the
higher transmission rate and good reliability (i.e., Low probability of error).
To achieve these features baseband coding techniques are used.
There are two types of baseband coding.
Source coding and
channel coding.
Source coding is used for an efficient representation of data generated by a
discrete source.
Channel coding is used for the reliable transmission of digital
information over the channel. Channel coding methods introduce controlled
redundancy in order to provide error detecting and correcting capability to the
data being transmitted. Hence channel coding is also called as error control
coding.
Channel Coding
MATRUSRI
ENGINEERING COLLEGE
8. Depending upon the nature of the noise, the codewords transmitted
through the channel is affected differently.
There are mainly two types of errors introduced during data transmission.
1) Random error
2) Burst error.
Both random error and burst errors occur in the contents of a message.
Hence they may also be referred to as “content errors”.
Alternatively, it is possible that a data block may be lost in the network as
it has been delivered to a wrong destination. It is referred as the “flow
integrity error”.
Types of Transmission errors
MATRUSRI
ENGINEERING COLLEGE
9. * The primary communication resources are the transmitted signal power
and channel bandwidth.
* These two parameters, together with the power spectral density of
receiver noise, determine the signal energy per bit-to-noise power density
ratio, Eb/No.
* This ratio Eb/No uniquely determines the probability of error (Pe) or bit
error rate (BER), for a particular modulation scheme.
* The channel induced noise can introduce errors in the transmitted
binary data. i.e., A bit 0 may change to bit 1 or a bit 1 may change to bit 0.
The reliability of data transmission gets severely affected because of these
errors.
Need for Error Control Coding
MATRUSRI
ENGINEERING COLLEGE
10. The channel encoder adds extra bits (redundancy) to the message bits in a
controlled manner. The encoded signal is modulated and then transmitted over
the noisy channel.
After demodulation, the channel decoder identifies the redundant bits
and uses them to detect and correct the errors in the message bits. Thus the
errors introduced due to channel noise are minimized by channel coding.
Drawbacks of channel coding
* The addition of redundant bits in the coded messages, increases the required
transmission bandwidth.
* The use of coding adds complexity to the communication system.
Therefore, the design trade-offs in the use of error control coding to
achieve acceptable error performance must include consideration of bandwidth
and system complexity.
Digital Communication System with Channel Coding
MATRUSRI
ENGINEERING COLLEGE
12. 1. Why coding of information required?
2. Define “error”. Write the cause for its occurrences in digital
communication systems with different types.
3. Explain the block diagram of Digital communication system with
channel coding.
Questions & Answers
MATRUSRI
ENGINEERING COLLEGE
13. CONTENTS:
Error control coding methods
Important terms used in Error Control Coding
Linear Block Codes (LBC): description of LBC,
Generation, syndrome and error detection,
Minimum distance of linear block code,
OUTCOMES:
Understanding Error Control Coding methods and generation &
detection of linear block codes along with Hamming codes.
MODULE-II
MATRUSRI
ENGINEERING COLLEGE
14. - The redundant bits added to the message are called check bits. Errors can be
detected and corrected with the help of these bits.
- The check bits reduce the data rate through the channel.
- It is not possible to detect and correct all the error in the received message.
Errors upto certain limit can only be detected and corrected.
There are two main methods used for error control coding. They are
1) Forward acting Error Correction (FEC)
2) Error detection with retransmission or Automatic Repeat Request (ARQ)
ERROR CONTROL CODING METHODS
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ENGINEERING COLLEGE
18. Codeword:
the encoded block of ‘n’ bits is called a codeword. It contains message bits (k) and
redundant check bits (q).
Block length: the number of bits ‘n’ after coding is called the block length of the
code.
Code rate: the code rate ‘r’ is defined as the ratio of message bits (k) and the
encoder output bits (n). Hence,
code rate, where 0 < r < 1 (3.1)
code vector: an ‘n’ bit code word can be visualized in an n-dimensional space as a
vector whose elements or co-ordinates are the bits in the code word.
TERMINOLOGIES
MATRUSRI
ENGINEERING COLLEGE
19. Code efficiency: the code efficiency is the ratio of the message bits to the
transmitted bits for that block by the encoder. Hence,
Weight of the code: the number of non-zero elements in the transmitted code
vector is called code vector weight.
Hamming distance: the hamming distance (d) between the two code vectors is
equal to the number of elements in which they differ. Eg. Let X = 101 and Y = 110.
Then hamming distance (d) between X and Y code vectors is 2.
Minimum hamming distance:
the smallest hamming distance between the valid code vectors is termed as the
minimum hamming distance (dmin).
MATRUSRI
ENGINEERING COLLEGE
21. FUNCTIONAL DIAGRAM OF BLOCK CODER:
An (n, k) LBC is a said to be systematic if the k-message bits either appear at the
beginning of the codeword or at the end of the code word.
Linear Block Codes (LBC): Description of LBC
MATRUSRI
ENGINEERING COLLEGE
22. Message bits :
Parity bits:
Code Vector :
Generation of Linear Block Codes (LBC)
MATRUSRI
ENGINEERING COLLEGE
0 1 2 3 1 1
[ ] [m ,m ,m ,m ,......,m ]
k k
M
0 1 2 3 1 1 ( )
[B] [b ,b ,b ,b ,......,b ]
n k n k
[ ]
C b m
0 1 2 3 1 0 1 2 3 1
[b ,b ,b ,b ,......,b ,m ,m ,m ,m ,......,m ]
n k k
23. Predetermined rule for finding parity bits :
P-matrix:
Generation of Linear Block Codes (LBC)
MATRUSRI
ENGINEERING COLLEGE
0 0 0,0 1 1,0 2 2,0 1 k 1,0
1 0 0,1 1 1,1 2 2,1 1 k 1,1
1 0 0,n k 1 1 1,n k 1 2 2,n k 1 1 k 1,n k 1
b m m m m
b m m m m
b m m m m
k
k
n k k
p p p p
p p p p
p p p p
0,0 0,1 0,n k 1
1,0 1,1 1,n k 1
( )
k 1,0 k 1,1 k 1,n k 1
[ ]k n k
p p p
p p p
P
p p p
24. Generator Matrix :
Generation of Linear Block Codes (LBC)
MATRUSRI
ENGINEERING COLLEGE
[ ] [ ] [ ]
k
C m P I m G
[G] [ ] [ ] [ ]
k k n k n k
P I or G I P
0,0 0,1 0,n k 1
0
1,0 1,1 1,n k 1
1
k 1,0 k 1,1 k 1,n k 1
1
1 0 0
0 1 0
[G]
0 0 1
k
k k identity matrix
P matrix
p p p
g
p p p
g
p p p
g
25. The H-matrix is useful at the decoder of the receiver.
Parity Check Matrix[H]
MATRUSRI
ENGINEERING COLLEGE
( )
[ ] [ ]or[ ]
T T
n k n n k n k
H I P P I
( )
[H]
n k
T
n n k
I
P
[ ] [ ]or[ ]
k n k k
G P I I P
. 0
T
C H
27. EXAMPLE 1
The generator matrix for a block code is given below. Find all code vectors of this
code.
G =
Questions & Answers
MATRUSRI
ENGINEERING COLLEGE
28. CONTENTS:
-Syndrome and error detection,
-Minimum distance of linear block code,
-Error correction and error detection capabilities,
-Standard array and syndrome decoding,
-Hamming codes.
OUTCOMES:
Estimate the error using syndrome and correct .
MODULE-III
MATRUSRI
ENGINEERING COLLEGE
29. When R is received, the decoder computes the following operation.
Syndrome,
SYNDROME DECODING
MATRUSRI
ENGINEERING COLLEGE
0 1 2 1
. [s ,s ,s ,......,s ]
T
n k
S R H
30. The error detection and correction capabilities of a coding technique
depend on the minimum hamming distance dmin
Error control capabilities
Error detection and correction capability of block codes
MATRUSRI
ENGINEERING COLLEGE
S.No.
Name of errors detected /
corrected
Distance requirement
1.
Detect upto ‘s’ errors per code
word
dmin ≥ s + 1
2.
Correct upto ‘t’ errors per code
word
dmin ≥ 2t + 1
3.
Correct upto ‘t’ errors and
detect s > t errors per code
word
dmin ≥ t + s+ 1
31. 1. Determine the syndrome of the received vector R
2. Identify the coset with this syndrome and let its coset leader be an error
pattern e
3. Decode the received vector R into the code vector C =R+ e.
STANDARD ARRAY DECODING
MATRUSRI
ENGINEERING COLLEGE
T
S RH
2.
32. Hamming codes are (n, k) linear block codes. They can be generated either
systematically or non-systematically.
Systematic form of hamming codes
the systematic form of hamming codes satisfy the following conditions.
1) Number of check bits, q ≥ 3
2) Code word length, n = 2q – 1
3) Number of message bits, k = n – q
4) Minimum hamming distance, dmin = 3
5) since dmin = 3,
The error detection capability is
dmin ≥ s + 1 → 3 ≥ s + 1 → s ≤ 3 – 1 → s ≤ 2
The error correction capability is
dmin ≥ 2t + 1 → 3 ≥ 2t + 1 → 2t ≤ 2 → t ≤ 1
Hence by using hamming code, we can correct single bit errors and detect errors
in two bits.
Hamming Codes
MATRUSRI
ENGINEERING COLLEGE
33. 1. The parity check matrix of a (7, 4) linear block code is given by
H =
i. Find the generator matrix (G).
ii. List all the code vectors.
iii. How many errors can be detected?
iv. How many errors can be corrected?
v. Draw the encoder circuit.
TRY IT?
MATRUSRI
ENGINEERING COLLEGE
34. 2. Consider a data (message) block of 1 1 0 1. The hamming code adds three parity
bits to the message bits in such a way that both message bits and check bits get
mixed. The check bit locations are as shown below.
Here p1, p2 and p3 represent the parity check bits to be added. D represents the
data (message) bits.
MATRUSRI
ENGINEERING COLLEGE
1 2 3 4 5 6 7 ---> Bit location
P1 P2 D P3 D D D
35. CONTENTS:
- Binary cyclic codes (BCC): description of cyclic codes
- Encoding, decoding and
- Error correction using shift registers.
OUTCOMES:
Understanding generation & detection of Binary cyclic codes (BCC)
MODULE-IV
MATRUSRI
ENGINEERING COLLEGE
36. A cyclic code exhibits the following two properties.
(I) linearity property: A code is said to be linear if modulo-2 addition of any two
code words will produce another valid codeword.
(Ii) cyclic property: A code is said to be cyclic if every cyclic shift of a code word
produces another valid code word.
For example, consider the n-bit code word, X = (xn-1, xn-2, ….. x1, x0).
Binary Cyclic Codes (BCC)
MATRUSRI
ENGINEERING COLLEGE
37. Cyclically shifting ‘C’ ‘i’ places to the right is equivalent to cyclically
shifting C, (n-i) places to left. This property of cyclic codes allows us to
treat the elements of each code-vector as the coefficients of a polynomial
of degree (n-1) or less.
Representation of code words by a polynomial
MATRUSRI
ENGINEERING COLLEGE
0 1 2 3 1
C = (C ,C ,C ,C ,......,C )
n
(i)
1 1 0 1 1
C = [C ,C ,.....,C ,C ,C ,......,C ]
n i n i n n i
2 1
0 1 2 1
( ) C +C X+C X +.......+C n
n
C X X
38. Systematic Encoding :
because X cannot be a factor of and minimum factor is (1+X)
Non-systematic :
C(X)=M(X)G(X).
MATRUSRI
ENGINEERING COLLEGE
Re ( )
( ) b( )
a( )
( ) ( )
n k
Quotient
mainder PARITY
X m X X
X
g X g X
( ) ( ) ( )
n k
C X b X X m X
2
0 1 2
g( ) +g X+g X +.......+g n k
n k
X g X
0 g 1
n k
g
1
n
X
40. Syndrome and Error Correction Using (n-k) shift register
MATRUSRI
ENGINEERING COLLEGE
41. Advantages of cyclic codes
- Cyclic codes can correct burst errors that span many successive bits.
- They have an excellent mathematical structure. This makes the design of error
correcting codes with multiple-error correction capability relatively easier.
- The encoding and decoding circuits for cyclic codes can be easily implemented
using shift registers.
- The error correcting and decoding methods of cyclic codes are simpler and easy
to implement. These methods eliminate the storage (large memories) needed for
lookup table decoding. Therefore the codes become powerful and efficient.
Disadvantages of cyclic codes
- Even though the error detection is simpler, the error correction is slightly more
complicated. This is due to the complexity of the combinational logic circuit used for
error correction.
Advantages & Disadvantages of cyclic codes
MATRUSRI
ENGINEERING COLLEGE
42. EXAMPLE 1
The generator polynomial of a (7, 4) cyclic code is g(p) = p3 + p + 1. Find all the
code vectors for the code in non-systematic form.
(i) consider any message vector as
M = (m3 m2 m1 m0) = (1 0 0 1)
(ii) consider another message vector as
M = (m3 m2 m1 m0) = ( 0 1 1 0 )
Questions & Answers
MATRUSRI
ENGINEERING COLLEGE
Example 2
The generator polynomial of a (7, 4) cyclic code is g(p) = p3 + p + 1. Find all the
code vectors for the code in systematic form by considering any message
vector as
M = (m3 m2 m1 m0) = (1 1 1 0 )
43. CONTENTS:
- Convolution codes: description
- Encoding – code tree
- State diagram.
OUTCOMES:
Understanding generation of Convolution codes with graphical
representations like code tree, state diagram etc.
MODULE-V
MATRUSRI
ENGINEERING COLLEGE
44. - In block coding, the encoder accepts a k-bit message block and
generates an n-bit code word. Thus code words are produced on a block-
by-block basis.
- Therefore, a buffer is required in the encoder to place the message
block.
- A subclass of tree codes is convolutional codes.
- The convolutional encoder accepts the message bits continuously and
generates the encoded codeword sequence continuously. Hence there is no
need for buffer.
-But in convolutional codes, memory is required to implement the encoder.
CONVOLUTIONAL CODES
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ENGINEERING COLLEGE
46. Consider that the current message bit is shifted to position m0. Then m1 and m2 store
the previous two message bits. Now, by mod-2 adders 1 and 2 we get the new values of X1
and X2. We can write
X1 = m0 + m1 + m2 and X2 = m0 + m2
Convolutional Encoder redrawn alternatively
MATRUSRI
ENGINEERING COLLEGE
47. In this convolutional encoder, for every input message bit, two encoded
output bits X1 and X2 are transmitted. Hence number of message bits,
k = 1. The number of encoded output bits for one message bit, n = 2.
Code rate:
The code rate of this convolutional encoder is given by
Code rate, r =
where 0 < r < 1
Convolutional Encoder
MATRUSRI
ENGINEERING COLLEGE
48. Constraint length:
The constraint length (K) of a convolution code is defined as the number
of shifts over which a single message bit can influence the encoder
output. It is expressed in terms of message bits.
Convolutional Encoder
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ENGINEERING COLLEGE
For the above convolutional encoder, constraint length is K = 3 bits.
Whenever a particular message bit enters the shift register, it remains in
the shift register for three shifts i.e.,
First shift → message bit is entered in position m0.
Second shift → message bit is shifted in position m1.
Third shift → message bit is shifted in position m2.
Constraint length ‘K’ is also equal to one plus the number of shift registers
required to implement the encoder.
49. Dimension of the code:
The code dimension of a convolutional code depends on the number of message
bits ‘k’, the number of encoder output bits, ‘n’ and its constraint length ‘K’. The
code dimension is therefore represented by (n, k, K).
For the encoder shown above, the code dimension is given by (2, 1, 3)
where n = 2, k = 1 and constraint length K = 3.
Graphical representation of convolutional codes
Convolutional code structure is generally presented in graphical form by the
following three equivalent ways.
1. By means of the state diagram
2. By drawing the code trellis
3. By drawing the code tree
These methods can be better explained by using an example.
Convolutional Encoder
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50. Example problem
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For the convolutional encoder given below in Figure,
determine the following.
a) Code rate b) Constraint length c) Dimension of the code
d) Represent the encoder in graphical form.
51. a) code rate:
the code rate, r = k/n
the number of message bits, k = 1.
The number of encoder output bits, n = 2.
Hence code rate, r = 1/2
b) constraint length:
constraint length, k = 1 + number of shift registers.
Hence k = 1 + 2 = 3
c) code dimension:
code dimension = (n, k, K) = (2, 1, 3)
hence the given encoder is of ½ rate convolutional encoder of dimension (2, 1, 3).
Solution
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52. D) graphical form representation
The encoder output is X = (X1 X2 X1 X2 X1 X2….. And so on)
the mod-2 adder 1 output is x1 = m0 + m1 + m2
the mod-2 adder 2 output is x2 = m0 + m2.
We can represent the encoder output for possible input message bits in the form
of a logic table.
Solution
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Input
Messag
e bit
Present State Next State
Encoder
Output
m0 m1 m2 m1 m2 X1 X2
A
0 0 0 0 0 0 0
1 0 0 1 0 1 1
B
0 1 0 0 1 1 0
1 1 0 1 1 0 1
C
0 0 1 0 0 1 1
1 0 1 1 0 0 0
D
0 1 1 0 1 0 1
1 1 1 1 1 1 0
53. - The encoder output depends on the current input message bit and the
contents in the shift register i.E., The previous two bits.
- The present condition of the previous two bits in the shift register may
be in four combinations. Let these combinations 00, 10, 01 and 11 be
corresponds to the states A, B, C and D respectively.
- For each input message bit, the present state of the m1 and m2 bits will
decide the encoded output.
- The logic table presents the encoded output X1 and X2 for the possible ‘0’
or ‘1’ bit input if the present state is A or B or C or D.
Solution
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54. The state of a convolutional encoder is defined by the contents of the shift
register. The number of states is given by 2 k-1 = 23-1 = 22 = 4. Here K represents the
constraint length.
Let the four states be A = 00, B = 10, C = 01 and D = 11 as per the logic table. A
state diagram as shown in the figure 3.9 illustrates the functioning of the encoder.
1. State Diagram Representation
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55. Suppose in the state A = 00.
i. At this state, if the incoming message bit is 0, the encoder output is X = (X1 X2) =
00. Then if the m0, m1 and m2 bits are shifted, the contents of the shift register will
also be in state A = 00. This is represented by a solid line path starting from A and
ending at A itself.
Ii. At the ‘A’ state, if the incoming message bit is 1, then the encoder output is X =
11. Now if the m0, m1 and m2 bits are shifted, the contents of the shift register will
become the state B = 10. This is represented by a dashed line path starting from A
and ending at B.
Similarly we can draw line paths for all other states, as shown in the above figure.
2. Code tree representation
•The code tree diagram is a simple way of describing the encoding procedure.
By traversing the diagram from left to right, each tree branch depicts the
encoder output codeword.
•Figure below shows the code representation for this encoder.
Continued with state diagram representation
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56. 2. Code Tree Representation
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57. Advantages of convolutional codes:
- The convolutional codes operate on smaller blocks of data. Hence decoding
delay is small.
- The storage hardware required is less.
Disadvantages of convolutional codes:
- Due to complexity, the convolutional codes are difficult to analyze.
- These codes are not developed much as compared to block codes.
Advantages & Disadvantages of Convolutional Codes
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58. Comparison between
Linear Block codes and Convolutional codes
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Sl. No. Linear Block Codes Convolutional Codes
1. Block codes are generated by
X = MG (or)
X(p) = M(p) .G(p)
Convolutional codes are generated by
convolution between message sequencing and
generating sequence.
2. For a block of message bits, encoded
block (code vector) is generated
Each message bit is encoded separately. For
every message bit, two or more encoded bits
are generated.
3. Coding is block by block. Coding is bit by bit.
4. Syndrome decoding is used for most
liklihood decoding.
Viterbi decoding is used for most liklihood
decoding.
5. Generator matrices, parity check
matrices and syndrome vectors are
used for analysis.
Code tree, code trellis and state diagrams are
used for analysis.
6. Generating polynomial and generator
matrix are used to get code vectors.
Generating sequences are used to get code
vectors.
7. Error correction and detection
capability depends upon minimum
distance dmin.
Error correction and detection capability
depends upon free distance dmin.
59. Example 1
For the convolutional encoder given below in figure, determine the
following.
A) code rate b) constraint length c) dimension of the code d)
represent the encoder in graphical form.
Questions & Answers
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60. Example 2
Explain tree diagram, trellis diagram and state transition diagram of
convolution codes.
Questions & Answers
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