This document summarizes a research paper that proposes a new channel coding structure using serial concatenation of polar codes. The proposed method concatenates two polar codes in series with an interleaver in between to rearrange bits. This is done to improve the reliability and performance of polar codes at low error rates. Experimental results show that the proposed serial concatenation of polar codes achieves a lower bit error rate than standard polar codes alone for different block lengths and code rates.
CODING SCHEMES FOR ENERGY CONSTRAINED IOT DEVICESijmnct
This paper investigates the application of advanced forward error correction techniques mainly: lowdensity parity checks (LDPC) code and polar code for IoT networks. These codes are under consideration
for 5G systems. Different code parameters such as code rate and a number of decoding iterations are used
to show their effect on the performance of the network. LDPC is performed better than polar code, over the
IoT network scenario considered in the work, for the same coding rate and the number of decoding
iterations. Considering bit error rate (BER) performance, LDPC with rate1/3 provided an improvement of
up to 2.6 dB for additive white Gaussian noise (AWGN) channel, and 2 dB for SUI-3 (frequency selective
fading channel model). LDPC code gives an improvement in throughput of about 12% as compared to
polar code with a coding rate of 2/3 over AWGN channel. The corresponding values over SUI-3 channel
are about 10%. Finally, in comparison with LDPC, polar code shows better energy saving for large
number of decoding iterations and high coding rates.
CODING SCHEMES FOR ENERGY CONSTRAINED IOT DEVICESijmnct_journal
This paper investigates the application of advanced forward error correction techniques mainly: lowdensity parity checks (LDPC) code and polar code for IoT networks. These codes are under consideration for 5G systems. Different code parameters such as code rate and a number of decoding iterations are used
to show their effect on the performance of the network. LDPC is performed better than polar code, over the IoT network scenario considered in the work, for the same coding rate and the number of decoding iterations. Considering bit error rate (BER) performance, LDPC with rate1/3 provided an improvement of
up to 2.6 dB for additive white Gaussian noise (AWGN) channel, and 2 dB for SUI-3 (frequency selective fading channel model). LDPC code gives an improvement in throughput of about 12% as compared to polar code with a coding rate of 2/3 over AWGN channel. The corresponding values over SUI-3 channel
are about 10%. Finally, in comparison with LDPC, polar code shows better energy saving for large number of decoding iterations and high coding rates.
Simulation of Turbo Convolutional Codes for Deep Space MissionIJERA Editor
In satellite communication deep space mission are the most challenging mission, where system has to work at very low Eb/No. Concatenated codes are the ideal choice for such deep space mission. The paper describes simulation of Turbo codes in SIMULINK . The performance of Turbo code is depend upon various factor. In this paper ,we have consider impact of interleaver design in the performance of Turbo code. A details simulation is presented and compare the performance with different interleaver design .
An efficient reconfigurable code rate cooperative low-density parity check co...IJECEIAES
In recent days, extensive digital communication process has been performed. Due to this phenomenon, a proper maintenance of authentication, communication without any overhead such as signal attenuation code rate fluctuations during digital communication process can be minimized and optimized by adopting parallel encoder and decoder operations. To overcome the above-mentioned drawbacks by using proposed reconfigurable code rate cooperative (RCRC) and low-density parity check (LDPC) method. The proposed RCRC-LDPC is capable to operate over gigabits/sec data and it effectively performs linear encoding, dual diagonal form, widens the range of code rate and optimal degree distribution of LDPC mother code. The proposed method optimize the transmission rate and it is capable to operate on 0.98 code rate. It is the highest upper bounded code rate as compared to the existing methods. The proposed method optimizes the transmission rate and is capable to operate on a 0.98 code rate. It is the highest upper bounded code rate as compared to the existing methods. the proposed method's implementation has been carried out using MATLAB and as per the simulation result, the proposed method is capable of reaching a throughput efficiency greater than 8.2 (1.9) gigabits per second with a clock frequency of 160 MHz.
PERFORMANCE OF WIMAX PHYSICAL LAYER WITH VARIATIONS IN CHANNEL CODING AND DIG...ijistjournal
The aim of this paper is to analyze the bit error rate (BER) performance of WiMAX physical layer with the implementation of different concatenated channel coding schemes under QAM and 16QAM digital modulations over realistic channel conditions (i.e. noise and multipath fading). In concatenated channel coding, the WiMAX system incorporates CRC-CC (Cyclic Redundancy Check and Convolutional) or RSCC (Reed-Solomon and Convolutional) encoder over an additative white gaussian noise (AWGN) and other multipath fading (Raleigh and Rician) channels. A segment of synthetic data is used for the analysis. Computer simulation results based on BER and signal to noise ratio (SNR) demonstrate that the performance of concatenated CRC-CC coded WiMAX system under QAM modulation is better as compared to RS-CC coded system over noisy and fading environments.
PERFORMANCE OF WIMAX PHYSICAL LAYER WITH VARIATIONS IN CHANNEL CODING AND DIG...ijistjournal
The aim of this paper is to analyze the bit error rate (BER) performance of WiMAX physical layer with the implementation of different concatenated channel coding schemes under QAM and 16QAM digital modulations over realistic channel conditions (i.e. noise and multipath fading). In concatenated channel coding, the WiMAX system incorporates CRC-CC (Cyclic Redundancy Check and Convolutional) or RSCC (Reed-Solomon and Convolutional) encoder over an additative white gaussian noise (AWGN) and other multipath fading (Raleigh and Rician) channels. A segment of synthetic data is used for the analysis. Computer simulation results based on BER and signal to noise ratio (SNR) demonstrate that the performance of concatenated CRC-CC coded WiMAX system under QAM modulation is better as compared to RS-CC coded system over noisy and fading environments.
A new channel coding technique to approach the channel capacityijwmn
After Shannon’s 1948 channel coding theorem, we have witnessed many channel coding techniques developed to achieve the Shannon limit. A wide range of channel codes is available with different complexity levels and error correction performance. Many powerful coding schemes have been deployed in the power-limited Additive White Gaussian Noise (AWGN) channel. However, it seems like we have arrived at an end of advancement path, for most of the existing channel codes. This article introduces a new coding technique that can either be used as the last coding stage of concatenated coding scheme or in parallel configuration with other powerful channel codes to achieve reliable error performance with moderately complex decoding. We will go through an example to understand the overall approach of the proposed coding technique, and finally we will look at some simulation results over an AWGN channel to demonstrate its potential.
CODING SCHEMES FOR ENERGY CONSTRAINED IOT DEVICESijmnct
This paper investigates the application of advanced forward error correction techniques mainly: lowdensity parity checks (LDPC) code and polar code for IoT networks. These codes are under consideration
for 5G systems. Different code parameters such as code rate and a number of decoding iterations are used
to show their effect on the performance of the network. LDPC is performed better than polar code, over the
IoT network scenario considered in the work, for the same coding rate and the number of decoding
iterations. Considering bit error rate (BER) performance, LDPC with rate1/3 provided an improvement of
up to 2.6 dB for additive white Gaussian noise (AWGN) channel, and 2 dB for SUI-3 (frequency selective
fading channel model). LDPC code gives an improvement in throughput of about 12% as compared to
polar code with a coding rate of 2/3 over AWGN channel. The corresponding values over SUI-3 channel
are about 10%. Finally, in comparison with LDPC, polar code shows better energy saving for large
number of decoding iterations and high coding rates.
CODING SCHEMES FOR ENERGY CONSTRAINED IOT DEVICESijmnct_journal
This paper investigates the application of advanced forward error correction techniques mainly: lowdensity parity checks (LDPC) code and polar code for IoT networks. These codes are under consideration for 5G systems. Different code parameters such as code rate and a number of decoding iterations are used
to show their effect on the performance of the network. LDPC is performed better than polar code, over the IoT network scenario considered in the work, for the same coding rate and the number of decoding iterations. Considering bit error rate (BER) performance, LDPC with rate1/3 provided an improvement of
up to 2.6 dB for additive white Gaussian noise (AWGN) channel, and 2 dB for SUI-3 (frequency selective fading channel model). LDPC code gives an improvement in throughput of about 12% as compared to polar code with a coding rate of 2/3 over AWGN channel. The corresponding values over SUI-3 channel
are about 10%. Finally, in comparison with LDPC, polar code shows better energy saving for large number of decoding iterations and high coding rates.
Simulation of Turbo Convolutional Codes for Deep Space MissionIJERA Editor
In satellite communication deep space mission are the most challenging mission, where system has to work at very low Eb/No. Concatenated codes are the ideal choice for such deep space mission. The paper describes simulation of Turbo codes in SIMULINK . The performance of Turbo code is depend upon various factor. In this paper ,we have consider impact of interleaver design in the performance of Turbo code. A details simulation is presented and compare the performance with different interleaver design .
An efficient reconfigurable code rate cooperative low-density parity check co...IJECEIAES
In recent days, extensive digital communication process has been performed. Due to this phenomenon, a proper maintenance of authentication, communication without any overhead such as signal attenuation code rate fluctuations during digital communication process can be minimized and optimized by adopting parallel encoder and decoder operations. To overcome the above-mentioned drawbacks by using proposed reconfigurable code rate cooperative (RCRC) and low-density parity check (LDPC) method. The proposed RCRC-LDPC is capable to operate over gigabits/sec data and it effectively performs linear encoding, dual diagonal form, widens the range of code rate and optimal degree distribution of LDPC mother code. The proposed method optimize the transmission rate and it is capable to operate on 0.98 code rate. It is the highest upper bounded code rate as compared to the existing methods. The proposed method optimizes the transmission rate and is capable to operate on a 0.98 code rate. It is the highest upper bounded code rate as compared to the existing methods. the proposed method's implementation has been carried out using MATLAB and as per the simulation result, the proposed method is capable of reaching a throughput efficiency greater than 8.2 (1.9) gigabits per second with a clock frequency of 160 MHz.
PERFORMANCE OF WIMAX PHYSICAL LAYER WITH VARIATIONS IN CHANNEL CODING AND DIG...ijistjournal
The aim of this paper is to analyze the bit error rate (BER) performance of WiMAX physical layer with the implementation of different concatenated channel coding schemes under QAM and 16QAM digital modulations over realistic channel conditions (i.e. noise and multipath fading). In concatenated channel coding, the WiMAX system incorporates CRC-CC (Cyclic Redundancy Check and Convolutional) or RSCC (Reed-Solomon and Convolutional) encoder over an additative white gaussian noise (AWGN) and other multipath fading (Raleigh and Rician) channels. A segment of synthetic data is used for the analysis. Computer simulation results based on BER and signal to noise ratio (SNR) demonstrate that the performance of concatenated CRC-CC coded WiMAX system under QAM modulation is better as compared to RS-CC coded system over noisy and fading environments.
PERFORMANCE OF WIMAX PHYSICAL LAYER WITH VARIATIONS IN CHANNEL CODING AND DIG...ijistjournal
The aim of this paper is to analyze the bit error rate (BER) performance of WiMAX physical layer with the implementation of different concatenated channel coding schemes under QAM and 16QAM digital modulations over realistic channel conditions (i.e. noise and multipath fading). In concatenated channel coding, the WiMAX system incorporates CRC-CC (Cyclic Redundancy Check and Convolutional) or RSCC (Reed-Solomon and Convolutional) encoder over an additative white gaussian noise (AWGN) and other multipath fading (Raleigh and Rician) channels. A segment of synthetic data is used for the analysis. Computer simulation results based on BER and signal to noise ratio (SNR) demonstrate that the performance of concatenated CRC-CC coded WiMAX system under QAM modulation is better as compared to RS-CC coded system over noisy and fading environments.
A new channel coding technique to approach the channel capacityijwmn
After Shannon’s 1948 channel coding theorem, we have witnessed many channel coding techniques developed to achieve the Shannon limit. A wide range of channel codes is available with different complexity levels and error correction performance. Many powerful coding schemes have been deployed in the power-limited Additive White Gaussian Noise (AWGN) channel. However, it seems like we have arrived at an end of advancement path, for most of the existing channel codes. This article introduces a new coding technique that can either be used as the last coding stage of concatenated coding scheme or in parallel configuration with other powerful channel codes to achieve reliable error performance with moderately complex decoding. We will go through an example to understand the overall approach of the proposed coding technique, and finally we will look at some simulation results over an AWGN channel to demonstrate its potential.
Turbo codes are error-correcting codes with performance that is close to the
Shannon theoretical limit (SHA). The motivation for using turbo codes is
that the codes are an appealing mix of a random appearance on the channel
and a physically realizable decoding structure. The communication systems
have the problem of latency, fast switching, and reliable data transfer. The
objective of the research paper is to design and turbo encoder and decoder
hardware chip and analyze its performance. Two convolutional codes are
concatenated concurrently and detached by an interleaver or permuter in the
turbo encoder. The expected data from the channel is interpreted iteratively
using the two related decoders. The soft (probabilistic) data about an
individual bit of the decoded structure is passed in each cycle from one
elementary decoder to the next, and this information is updated regularly.
The performance of the chip is also verified using the maximum a posteriori
(MAP) method in the decoder chip. The performance of field-programmable
gate array (FPGA) hardware is evaluated using hardware and timing
parameters extracted from Xilinx ISE 14.7. The parallel concatenation offers
a better global rate for the same component code performance, and reduced
delay, low hardware complexity, and higher frequency support.
Implementation of a bit error rate tester of a wireless communication system ...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Iterative network channel decoding with cooperative space-time transmissionijasuc
One of the most efficient methods of exploiting space diversity for portable wireless devices is cooperative
communication utilizing space-time block codes. In cooperative communication, users besides
communicating their own information, also relay the information of other users. In this paper we
investigate a scheme where cooperation is achieved using two methods, namely, distributed space-time
coding and network coding. Two cooperating users utilize Alamouti space time code for inter-user
cooperation and in addition utilize a third relay which performs network coding. The third relay does not
have any of its information to be sent. In this paper we propose a scheme utilizing convolutional code based
network coding, instead of conventional XOR based network code and utilize iterative joint networkchannel
decoder for efficient decoding. Extrinsic information transfer (EXIT) chart analysis is performed to
investigate the convergence property of the proposed decoder.
A New Bit Split and Interleaved Channel Coding for MIMO DecoderIJARBEST JOURNAL
Authors:-C. Amar Singh Feroz1, S. Karthikeyan2, K. Mala3
Abstract– In wireless communications, the use of multiple antennas at both the
transmitter and receiver is a key technology to enable high data transmission without
additional bandwidth or transmit power. MIMO schemes are widely used in many
wireless standards, allowing higher throughput using spatial multiplexing techniques.
Bit split mapping based on JDD is designed. Here ETI coding is used for encoding and
Viterbi is used for decoding. Experimental results for 16-QAM and 64 QAM with the
code rate of ½ and 1/3 codes are shown to verify the proposed approach and to elucidate
the design tradeoffs in terms the BER performance. This bit split mapping based JDD
algorithm can greatly improve BER performance with different system settings.
Fpga implementation of (15,7) bch encoder and decoder for text messageeSAT Journals
Abstract In a communication channel, noise and interferences are the two main sources of errors occur during the transmission of the message. Thus, to get the error free communication error control codes are used. This paper discusses, FPGA implementation of (15, 7) BCH Encoder and Decoder for text message using Verilog Hardware Description Language. Initially each character in a text message is converted into binary data of 7 bits. These 7 bits are encoded into 15 bit codeword using (15, 7) BCH encoder. If any 2 bit error in any position of 15 bit codeword, is detected and corrected. This corrected data is converted back into an ASCII character. The decoder is implemented using the Peterson algorithm and Chine’s search algorithm. Simulation was carried out by using Xilinx 12.1 ISE simulator, and verified results for an arbitrarily chosen message data. Synthesis was successfully done by using the RTL compiler, power and area is estimated for 180nm Technology. Finally both encoder and decoder design is implemented on Spartan 3E FPGA. Index Terms: BCH Encoder, BCH Decoder, FPGA, Verilog, Cadence RTL compiler
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
A NOVEL APPROACH FOR LOWER POWER DESIGN IN TURBO CODING SYSTEMVLSICS Design
Low Power is an extremely important issue for future mobile communication systems; The focus of this paper is to implementat turbo codes for low power solutions. The effect on performance due to variation in parameters like frame length, number of iterations, type of encoding scheme and type of the interleave in the presence of additive white Gaussian noise is studied with the floating point model. In order to obtain the effect of quantization and word length variation, a fixed point model of the application is also developed.. The application performance measure, namely bit-error rate (BER) is used as a design constraint while optimizing for power and area coverage. Low power Optimization is Performed on Implementation levels by the use of Voltage scaling. With those Techniques we can reduced the power 98.5%and Area(LUT) is 57% and speed grade is Increased .This type of Power maneger is proposed and implemented based on the timing details of the turbo decoder in the VHDL model.
Lightweight hamming product code based multiple bit error correction coding s...journalBEEI
In this paper, we present multiple bit error correction coding scheme based on extended Hamming product code combined with type II HARQ using shared resources for on chip interconnect. The shared resources reduce the hardware complexity of the encoder and decoder compared to the existing three stages iterative decoding method for on chip interconnects. The proposed method of decoding achieves 20% and 28% reduction in area and power consumption respectively, with only small increase in decoder delay compared to the existing three stage iterative decoding scheme for multiple bit error correction. The proposed code also achieves excellent improvement in residual flit error rate and up to 58% of total power consumption compared to the other error control schemes. The low complexity and excellent residual flit error rate make the proposed code suitable for on chip interconnection links.
Performances Concatenated LDPC based STBC-OFDM System and MRC Receivers IJECEIAES
This paper presents the bit error rate performance of the low density parity check (LDPC) with the concatenation of convolutional channel coding based orthogonal frequency-division-multiplexing (OFDM) using space time block coded (STBC). The OFDM wireless communication system incorporates 3/4rated convolutional encoder under various digital modulations (BPSK, QPSK and QAM) over an additative white gaussian noise (AWGN) and fading (Raleigh and Rician) channels. At the receiving section of the simulated system, Maximum Ratio combining (MRC) channel equalization technique has been implemented to extract transmitted symbols without enhancing noise power.
Centrality-Based Network Coder Placement For Peer-To-Peer Content DistributionIJCNCJournal
Network coding has been shown to achieve optimal multicast throughput, yet at an expensive computation
cost: every node in the network has to code. Interested in minimizing resource consumption of network
coding while maintaining its performance, in this paper, we propose a practical network coder placement
algorithm which achieves comparable content distribution time as network coding, and at the same time,
substantially reduces the number of network coders compared to a full network coding solution in which all
peers have to encode, i.e. become encoders. Our algorithm is derived from two key elements. First, it is
based on the insight that coding at upstream peers eliminates information duplication to downstream peers,
which results in efficient content distribution. Second, our placement strategy exploits centrality
characteristics of the network topology to quickly determine key positions to place encoders. Performance
evaluation using various topology and algorithm parameters confirms the effectiveness of our proposed
method.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
In code division multiple access (CDMA) code construction and analysis, the bit error rate due to multiple access interference is an important performance parameter which is overcome to some extent by generating almost orthogonal codes. Ideal orthogonal code families should have zero autocorrelation and no crosscorrelation. The building of fiber-optic CDMA (FOCDMA) is based on binary, unipolar spreading codes, which in turn requires considerably longer length of spreading codes in order to satisfy these constraints. Spreading an optical bit in wavelength, time and multiple fibers is observed to satisfy the constraints for accommodating sufficiently large number of users with a comparatively smaller spreading code length. Various optical code families of different dimensions have been proposed for FOCDMA. The performance of the code families varies under different conditions. In this research, some aspects of the performance issues have been considered.
Performance Comparision of Coded and Un-Coded OFDM for Different Fic CodeIJERA Editor
Error correction and detection in digital communication is used to compensate the bit error rate introduced during transmission of data. In this paper the investigation has been made to the performance of some error detecting and correcting coding algorithm for OFDM system. Convolution code, RS code and linear block code based OFDM system has been implemented, studied and analyzed. Simulation is performed in MATLAB environment.
More Related Content
Similar to New Structure of Channel Coding: Serial Concatenation of Polar Codes
Turbo codes are error-correcting codes with performance that is close to the
Shannon theoretical limit (SHA). The motivation for using turbo codes is
that the codes are an appealing mix of a random appearance on the channel
and a physically realizable decoding structure. The communication systems
have the problem of latency, fast switching, and reliable data transfer. The
objective of the research paper is to design and turbo encoder and decoder
hardware chip and analyze its performance. Two convolutional codes are
concatenated concurrently and detached by an interleaver or permuter in the
turbo encoder. The expected data from the channel is interpreted iteratively
using the two related decoders. The soft (probabilistic) data about an
individual bit of the decoded structure is passed in each cycle from one
elementary decoder to the next, and this information is updated regularly.
The performance of the chip is also verified using the maximum a posteriori
(MAP) method in the decoder chip. The performance of field-programmable
gate array (FPGA) hardware is evaluated using hardware and timing
parameters extracted from Xilinx ISE 14.7. The parallel concatenation offers
a better global rate for the same component code performance, and reduced
delay, low hardware complexity, and higher frequency support.
Implementation of a bit error rate tester of a wireless communication system ...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Iterative network channel decoding with cooperative space-time transmissionijasuc
One of the most efficient methods of exploiting space diversity for portable wireless devices is cooperative
communication utilizing space-time block codes. In cooperative communication, users besides
communicating their own information, also relay the information of other users. In this paper we
investigate a scheme where cooperation is achieved using two methods, namely, distributed space-time
coding and network coding. Two cooperating users utilize Alamouti space time code for inter-user
cooperation and in addition utilize a third relay which performs network coding. The third relay does not
have any of its information to be sent. In this paper we propose a scheme utilizing convolutional code based
network coding, instead of conventional XOR based network code and utilize iterative joint networkchannel
decoder for efficient decoding. Extrinsic information transfer (EXIT) chart analysis is performed to
investigate the convergence property of the proposed decoder.
A New Bit Split and Interleaved Channel Coding for MIMO DecoderIJARBEST JOURNAL
Authors:-C. Amar Singh Feroz1, S. Karthikeyan2, K. Mala3
Abstract– In wireless communications, the use of multiple antennas at both the
transmitter and receiver is a key technology to enable high data transmission without
additional bandwidth or transmit power. MIMO schemes are widely used in many
wireless standards, allowing higher throughput using spatial multiplexing techniques.
Bit split mapping based on JDD is designed. Here ETI coding is used for encoding and
Viterbi is used for decoding. Experimental results for 16-QAM and 64 QAM with the
code rate of ½ and 1/3 codes are shown to verify the proposed approach and to elucidate
the design tradeoffs in terms the BER performance. This bit split mapping based JDD
algorithm can greatly improve BER performance with different system settings.
Fpga implementation of (15,7) bch encoder and decoder for text messageeSAT Journals
Abstract In a communication channel, noise and interferences are the two main sources of errors occur during the transmission of the message. Thus, to get the error free communication error control codes are used. This paper discusses, FPGA implementation of (15, 7) BCH Encoder and Decoder for text message using Verilog Hardware Description Language. Initially each character in a text message is converted into binary data of 7 bits. These 7 bits are encoded into 15 bit codeword using (15, 7) BCH encoder. If any 2 bit error in any position of 15 bit codeword, is detected and corrected. This corrected data is converted back into an ASCII character. The decoder is implemented using the Peterson algorithm and Chine’s search algorithm. Simulation was carried out by using Xilinx 12.1 ISE simulator, and verified results for an arbitrarily chosen message data. Synthesis was successfully done by using the RTL compiler, power and area is estimated for 180nm Technology. Finally both encoder and decoder design is implemented on Spartan 3E FPGA. Index Terms: BCH Encoder, BCH Decoder, FPGA, Verilog, Cadence RTL compiler
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
A NOVEL APPROACH FOR LOWER POWER DESIGN IN TURBO CODING SYSTEMVLSICS Design
Low Power is an extremely important issue for future mobile communication systems; The focus of this paper is to implementat turbo codes for low power solutions. The effect on performance due to variation in parameters like frame length, number of iterations, type of encoding scheme and type of the interleave in the presence of additive white Gaussian noise is studied with the floating point model. In order to obtain the effect of quantization and word length variation, a fixed point model of the application is also developed.. The application performance measure, namely bit-error rate (BER) is used as a design constraint while optimizing for power and area coverage. Low power Optimization is Performed on Implementation levels by the use of Voltage scaling. With those Techniques we can reduced the power 98.5%and Area(LUT) is 57% and speed grade is Increased .This type of Power maneger is proposed and implemented based on the timing details of the turbo decoder in the VHDL model.
Lightweight hamming product code based multiple bit error correction coding s...journalBEEI
In this paper, we present multiple bit error correction coding scheme based on extended Hamming product code combined with type II HARQ using shared resources for on chip interconnect. The shared resources reduce the hardware complexity of the encoder and decoder compared to the existing three stages iterative decoding method for on chip interconnects. The proposed method of decoding achieves 20% and 28% reduction in area and power consumption respectively, with only small increase in decoder delay compared to the existing three stage iterative decoding scheme for multiple bit error correction. The proposed code also achieves excellent improvement in residual flit error rate and up to 58% of total power consumption compared to the other error control schemes. The low complexity and excellent residual flit error rate make the proposed code suitable for on chip interconnection links.
Performances Concatenated LDPC based STBC-OFDM System and MRC Receivers IJECEIAES
This paper presents the bit error rate performance of the low density parity check (LDPC) with the concatenation of convolutional channel coding based orthogonal frequency-division-multiplexing (OFDM) using space time block coded (STBC). The OFDM wireless communication system incorporates 3/4rated convolutional encoder under various digital modulations (BPSK, QPSK and QAM) over an additative white gaussian noise (AWGN) and fading (Raleigh and Rician) channels. At the receiving section of the simulated system, Maximum Ratio combining (MRC) channel equalization technique has been implemented to extract transmitted symbols without enhancing noise power.
Centrality-Based Network Coder Placement For Peer-To-Peer Content DistributionIJCNCJournal
Network coding has been shown to achieve optimal multicast throughput, yet at an expensive computation
cost: every node in the network has to code. Interested in minimizing resource consumption of network
coding while maintaining its performance, in this paper, we propose a practical network coder placement
algorithm which achieves comparable content distribution time as network coding, and at the same time,
substantially reduces the number of network coders compared to a full network coding solution in which all
peers have to encode, i.e. become encoders. Our algorithm is derived from two key elements. First, it is
based on the insight that coding at upstream peers eliminates information duplication to downstream peers,
which results in efficient content distribution. Second, our placement strategy exploits centrality
characteristics of the network topology to quickly determine key positions to place encoders. Performance
evaluation using various topology and algorithm parameters confirms the effectiveness of our proposed
method.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
In code division multiple access (CDMA) code construction and analysis, the bit error rate due to multiple access interference is an important performance parameter which is overcome to some extent by generating almost orthogonal codes. Ideal orthogonal code families should have zero autocorrelation and no crosscorrelation. The building of fiber-optic CDMA (FOCDMA) is based on binary, unipolar spreading codes, which in turn requires considerably longer length of spreading codes in order to satisfy these constraints. Spreading an optical bit in wavelength, time and multiple fibers is observed to satisfy the constraints for accommodating sufficiently large number of users with a comparatively smaller spreading code length. Various optical code families of different dimensions have been proposed for FOCDMA. The performance of the code families varies under different conditions. In this research, some aspects of the performance issues have been considered.
Performance Comparision of Coded and Un-Coded OFDM for Different Fic CodeIJERA Editor
Error correction and detection in digital communication is used to compensate the bit error rate introduced during transmission of data. In this paper the investigation has been made to the performance of some error detecting and correcting coding algorithm for OFDM system. Convolution code, RS code and linear block code based OFDM system has been implemented, studied and analyzed. Simulation is performed in MATLAB environment.
Similar to New Structure of Channel Coding: Serial Concatenation of Polar Codes (20)
Performance Comparision of Coded and Un-Coded OFDM for Different Fic Code
New Structure of Channel Coding: Serial Concatenation of Polar Codes
1. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
DOI:10.5121/ijwmn.2023.15501 1
NEW STRUCTURE OF CHANNEL CODING: SERIAL
CONCATENATION OF POLAR CODES
Mohammed Mensouri and Mustapha Eddahibi
IMIS Laboratory, Ibn Zohr University, Agadir, Morocco
ABSTRACT
In this paper, we introduce a new coding and decoding structure for enhancing the reliability and
performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar
codes in series to create robust error-correcting codes. The primary objective here is to optimize the
behavior of individual elementary codes within polar codes. In this structure, we incorporate interleaving,
a technique that rearranges bits to maximize the separation between originally neighboring symbols. This
rearrangement is instrumental in converting error clusters into distributed errors across the entire
sequence. To evaluate their performance, we proposed to model a communication system with seven
components: an information source, a channel encoder, a modulator, a channel, a demodulator, a channel
decoder, and a destination. This work focuses on evaluating the bit error rate (BER) of codes for different
block lengths and code rates. Next, we compare the bit error rate (BER) performance between our
proposed method and polar codes.
KEYWORDS
Polar codes, Concatenated codes, Serial, Interleaver, Deinterleaver, Successive Cancellation Algorithm,
Coding, Decoding, Channel coding
1. INTRODUCTION
Error correction codes are considered one of the most important elements of the 5G technology.
The 5G standardization process selected two new channel coding schemes. Low Density Parity
Codes (LDPC) have been adopted as a data coding scheme[1].They are designed to support high
throughput, variables code rate and code length, in addition to very good error correction
capability. Conversely, polar codes have been embraced as a novel coding technique for control
information. Their design focuses on achieving effective error correction performance with
concise block lengths and accommodating a wide range of code rates, all while maintaining
stringent decoding latency requirements [2][3]. Polar codes are one of the latest additions to the
family of error-correcting codes . They have been selected as the encoding method for the control
channel in the fifth-generation cellular mobile communications network.
Large capacity, low latency, increased dependability, high data rates, and improved quality of
services (QoS) are all features of the new 5G technology [4]. 5G technology is expected to
significantly improve service quality given the volume of data on the network and the diversity
of services. The performance seen by the user can be increased by reducing the BER (Bit Error
Rate), i.e. by combining appropriate encoding and decoding schemes. When data is transmitted
over a link, errors are introduced into the system. These errors reduce system performance.
Therefore, the errors are calculated using BER. This value is calculated by dividing the number
of bits received in error by the total number of bits transmitted during the same time period. This
is the rate at which errors occur during transmission. Bit Error Rate (BER) and signal-to-noise
2. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
2
ratio (SNR) are inversely proportional to each other. A BER of 10−9 is typically regarded as an
acceptable level for telecommunications, whereas a minimum BER of 10−13 is considered more
appropriate for data transmission.
In the present work, we harken back to the classical notion of code concatenation, a strategy that
involves the sequential connection of two Polar Codes. These Polar Codes are interlinked in a
series configuration, complemented by an interleaver structure. This interleaver orchestrates the
permutation of bits within the outer codewords, and an inner encoder subsequently processes
these permuted outer codewords, collectively contributing to the efficiency of the concatenated
codes.
The structure of this paper is as follows. In Section 2, we will present the principles of
concatenated codes, which form the foundation of our work. In Section 3, we describe the
encoding and the decoding of Polar codes. The main contribution of the paper is Section 4, where
we have developed a new coding and decoding structure which consists of concatenating two
polar codes in series to build powerful error-correcting codes. Experimental results are given in
section 5 that compares the error performance of serial concatenation Polar Codes for different
block lengths and code rates. Finally, the conclusion is given in Section 6.
2. RELATED WORKS
The concept of concatenated codes, which encompass error-correcting codes constructed by
amalgamating two or more simpler codes, represents a powerful approach that offers impressive
performance while maintaining a manageable level of complexity. These codes were originally
introduced by Forney in 1965 [5] as a solution to address theoretical challenges. By the 1970s,
they had already found widespread utilization, particularly in the domain of space
communications [6]. Subsequent developments in the realm of concatenated codes have given
rise to the emergence of turbo codes and other modern, near-capacity codes, marking a
significant evolution of this coding approach [7]. The fundamental premise behind code
concatenation is to leverage the performance benefits of multiple codes, whether through a serial
or parallel architecture, thereby ushering in a multitude of advanced code concatenation
techniques that transcend the simplicity of a basic coding system.
One notable outcome of code concatenation is the potential to enhance the bit error probability.
This enhancement stems from the synergistic combination of two or more codes, culminating in
the creation of robust, higher block-length codes that are often accompanied by the incorporation
of interleavers [8]. These interleavers serve to optimize the arrangement of bits within the
codewords, facilitating reliable data transmission at rates that approach the channel capacity. It is
important to note, however, that this gain in performance may be offset by an increase in decoder
complexity.
Here are some common examples of code concatenation in the field of digital communications:
• Reed-Solomon and Convolutional Code Concatenation: As explained earlier, Reed-Solomon
codes are often used as inner codes to correct random errors, while convolutional codes are
used as outer codes to correct burst errors.
• LDPC and Convolutional Code Concatenation: LDPC (Low-Density Parity-Check) codes are
error correction codes effective for burst error correction. They are often used in conjunction
with convolutional codes to enhance error correction performance.
• Turbo Code: Turbo codes are a form of code concatenation. They consist of two separate
convolutional codes with an interleaver in between. Data is first encoded by one convolutional
3. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
3
code, interleaved, and then encoded again by another convolutional code. This significantly
improves error correction performance.
These examples demonstrate how code concatenations are used to combine the advantages of
different types of codes to achieve optimal error correction performance.
3. POLAR CODES
3.1. Polar Coding
Polar Codes are linear block codes. Their invention was proposed in [9]. Polar Codes apply
channel polarization transformation to divide binary channels into perfect or completely noisy
channels [2]. They then assign the information bits to the 𝐾most reliable binary channels while
the remaining bits are frozen, i.e., they are all set to a known value, usually “0”. Similarly, for
codeword length 𝑁 , The polar code (𝑁, 𝐾) is characterized as a block code
comprising 𝐾 input bits and 𝑁 output bits, featuring the generation matrix G, which is formed by
taking the 𝑛𝑡ℎ Kronecker power of the matrix F, as follows:
The encoding procedure is executed through matrix multiplication, denoted as 𝑋 = 𝑈. 𝐺, wherein
𝑈 represents the input vector sequence 𝑈 = (𝑢0,𝑢1,. . . , 𝑢𝑁−1) comprising both information bits
and frozen bits, while 𝑋signifies the resulting encoded vector 𝑋 = (𝑥0, 𝑥1,. . . , 𝑥𝑁−1).
For example, the Polar Code (8,4) and 𝑈 = [0, 0,0, 𝑢3,0, 𝑢5,𝑢6,𝑢7] the corresponding
codeword is:
𝑋 = 𝑈. 𝐺 3
4. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
4
The codeword obtained by multiplying 𝑈 and 𝐺, as shown in this example, is non-systematic
because information bits are not part of the codeword. A forward error correction code is
considered systematic when it allows for a clear differentiation between information bits and
parity bits. The key advantage of systematic codes lies in the straightforward appending of parity
data to the source block. In cases where received data is correct, receivers are not required to
retrieve the original source symbols. A block code can be represented in the form of a factor
graph as explained in [10]. In the context of Polar Codes, we've noted that the generator matrix is
constructed through a recursive process. It is then feasible to illustrate that the formation of the
graph similarly follows a recursive pattern.
In this example, two generating matrices and their representation graph are shown. In figure 1 the
generator matrix and the coding graph of a Polar Code of size 𝑁 = 2 and message 𝑈 = [𝑢0,𝑢1]
are presented.
Figure 1. Generator matrix and graphical representation of the encoder for a Polar Code (2,2)
More generally, the factor graph of a Polar Code, as described in [11], with a size of N = 2n, is
structured into n stages. Each stage consists of N/2 parity nodes with a degree of 3 and N/2
variable nodes, also with a degree of 3. The degree of a node signifies the number of its
connections to other nodes. The factor graph can be used for encoding and decoding. For coding,
the input vector 𝑈, on the left side, is propagated in the graph in order to generate the code word
X, on the right. An illustration of a Polar Code with an efficiency of 𝑅 = 0.5 is provided in
Figure 2. This implies that half of the vector 𝑈 comprises frozen bits, while the other half
consists of information bits.
Figure 2 : Factor graph of a non-systematic CP(8;4) Polar Code encoder
3.2. Decoding Algorithms of Polar Codes
Decoding algorithms, as a general concept, represent a procedure through which the data
received at the channel's output is analyzed and processed to retrieve the originally transmitted
information while minimizing errors. The complexity, speed, and efficiency of decoding
algorithms can vary significantly. Up to now, many efficient polar code decoding algorithms
have been reported since the first polar code decoding algorithm was proposed in [2], Successive
Cancellation decoder (SC). Although Successive Cancellation (SC) exhibits excellent
performance with extremely long polar codes, it experiences a notable decline in maximum-
5. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
5
likelihood decoding performance when dealing with short to medium block lengths. In an effort
to address this problem, several variants of SC decoders, such as Successive Cancellation List
(SCL) [11], Fli Successive Cancellation (SCF) [12], and Stack Successive Cancellation (SCS)
[13], have been introduced, albeit at the expense of increased complexity.
Nonetheless, owing to the inherent serial processing of SC-based decoding algorithms, all of the
previously mentioned approaches encounter notable drawbacks including substantial decoding
latency and reduced throughput, thus impacting their practical usability. These algorithms yield
hard outputs, meaning they produce binary results. On the other hand, fully parallel decoding
algorithms, like the belief propagation (BP) method with soft output, have garnered considerable
interest. The performance of BP decoding, based on Forney's factor graph representation, has
been extensively examined in [14] [15].
The primary decoding algorithm for these codes is the hard decision method, commonly known
as Successive Cancellation (SC). It stands as the most commonly utilized approach, and we will
delve into its details in the following sections.
3.3. Decoding of the Polar Codes by Successive Cancellation
After the message has traversed the communication channel, the received noisy version Y =
(y0, y1, … , yN−1 of code word X = (x0,x1, . . . , xN−1) is received. The aim of the decoding is to
estimate the vector U = (u0, u1, . . . , uN−1) from the noisy version of the code word Y. In Arıkan's
work presented in [9], it was demonstrated that Polar Codes can achieve the channel capacity
when decoded using the successive cancellation algorithm. This decoding process involves the
estimation of a bit 𝑢𝑖 based on observations from the channel and the information about
previously estimated bits. The value of the estimated bit is denoted 𝑢𝑖 with 𝑈 =
(𝑢0,𝑢1,. . . , 𝑢𝑁−1).
Figure 3. Error correcting communication over a noisy channel.
The decoding can be represented as a factorization graph. During the encoding process depicted
in Figure 2, the information bits and the frozen bits are positioned on the left side of the graph.
The progression from the left to the right of the graph is employed to compute the code word
bits. During decoding, dual operation of encoding, the direction of the path is reversed. Channel
information comes from the right (Figure 3). They represent the estimates of the bits of the code
word. The steps for decoding the size 2 elementary kernel are detailed in Figure 2.4. The input
data of the decoding algorithms presented here are therefore LLRs, contained in the vector 𝐿of
size 𝑁, taken out of the composite channel. The output data of the algorithm decoding are bits
contained in the vector 𝑈 of size 𝐾. During the polar code decoding process, both data formats,
LLRs and partial sums (PS), are used. The LLRs denoted 𝐿𝑖,𝑗 are the estimates of the bit value at
the position (𝑖,𝑗) of the factorization graph. The partial sums noted 𝑠𝑖,𝑗 correspond to the hard
decision of this same bit of the graph of factorization.
The first step(a) of the decoding is the loading of the LLRs of the L-channel: LLR 𝐿0,0 and 𝐿1,0
take the value of the LLRs of the channel. The LLRs and partial sums of each point in the
6. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
6
factorization graph are then calculated via the operations𝑓,𝑅0,g,𝑅1 and ℎ symbolized in Figure
2.4 by arrows. They correspond to the following equations:
𝑓(𝐿𝑎, 𝐿𝑏) = 𝑠𝑖𝑔𝑛(𝐿𝑎, 𝐿𝑏). 𝑚𝑖𝑛 (|𝐿𝑎|, |𝐿𝑏|) 6
𝑔(𝐿𝑎, 𝐿𝑏, 𝑠𝑎) = (1 − 2 𝑠𝑎)𝐿𝑎+ 𝐿𝑏7ℎ(𝑠𝑎, 𝑠𝑏) = (𝑠𝑎⨁𝑠𝑏, 𝑠𝑏) 8
𝑅0(𝐿𝑎) = 0 9
The function f is applied in step(b). It allows the calculation of 𝐿1,0. Step(c) is the application of
the 𝑅0 function on the top node. The 𝑅0 function is applied assuming that the 𝑢0 bit is a frozen
bit. The function g then allows, in step (d), the calculation of 𝐿1,1. Step (e) is the calculation of
s1;1 by the corresponding R1 operation This operation is a thresholding of the LLR to obtain the
partial sum. When the threshold is applied, the reliability information is lost. After decoding the
partial sum 𝑠1,1, the function ℎ is applied in order to propagate the partial sums, in step (f).
4. SERIAL CONTINUATION OF POLARCODES
4.1. Encoding
A serial concatenation of Polar Codes is obtained by the combination of two Polar codes in a
serial way and they are separated by interlevaer π as shown in figure 4. The first polar code C1 is
called external code, while the second polare code C2 is internal code. The information bits are
encoded by the external code, interleaved through an interleaver (𝜋) and then re-encoded by the
internal code. The interleaver rearranges the order of the bits transmitted, while the
corresponding deinterleaver restores the original order. Deinterlacing can thus disperse a burst of
errors associated with isolated errors so that these individual errors may be easier to correct by
the second decoder.
Figure 4. Series concatenation of polar codes
Considering that 𝑅1 = 𝑁𝐾11 and 𝑅1 = 𝑁𝐾22 are the respective rate of the polar code C1 and the polar
code C2. The overall rate of the code built is directly related to the rate 𝑅1 and 𝑅2 of the two
Polar Codes C1 and Polar Codes C2 by the relation:
𝑅𝑠 = 𝑅1 × 𝑅2 11
7. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
7
If 𝑅1 and 𝑅2 are identical, the preceding relation becomes:
𝑅𝑠 = 𝑅12 12
4.2. Decoding the Concatenated Polar Codes
At the decoding level, there are two Polar Decoders 1 and Polar Decoders 2 concatenated in
series and separated by a deinterleaver π−1 as shown in figure 4 part decoding. In fact, decoder
2 receives as input the sequences generated by encoder 2. The Polar decoder 2 generates at
output a sequence which has many grouped errors. The purpose of the deinterleaver 𝜋−1 then is
to disperse these errors to increase the correction efficiency of the Polar decoder 1.
4.3. Interleaver and Deinterleaver
Interleaving involves reorganizing a sequence of bits in a way that maximizes the separation
between symbols that were initially located close to one another, as explained in reference [16].
This makes it possible in particular to transform an error relating to grouped bits into an error
distributed over the whole of the sequence. He There are several types of interleavers. An
interleaver is a device that reorders a data sequence using a deterministic bijective mapping. Let
C = (c0, c1,. . . , cN−1) be a sequence of length N. An interleaver transforms 𝐶 into a sequence X =
(x0, x1,. . . , xN−1) in such a way that 𝑋 represents a permutation of the elements in 𝐶. When we
treat 𝐶 and 𝑋 as a pair of N-dimensional vectors, there is a one-to-one correspondence, denoted
as 𝑐𝑖 → 𝑥𝑗, between each element in 𝐶 and each element in 𝑋, as illustrated in Figure 5.
Let 𝐼 = {0, 1 … 𝑁 − 1}. An interleaving operation can be characterized through the one-to-one
index mapping function:
𝜋: 𝐼 → 𝐼 13
𝑖 → 𝑗 = 𝜋(𝑖)
In this context, "𝑖" denotes the index of an element within the original sequence 𝐶, while "𝑗"
corresponds to the index of the corresponding element in the interleaved sequence 𝑋. This
mapping function can be represented as an ordered set known as the interleaving vector 𝜋 =
(𝜋(0), 𝜋(1), … , 𝜋(𝑁 − 1)).. The 𝑘𝑡ℎ element of the permuted sequence 𝑋 is given by:
𝑥𝑘 = 𝑐𝜋(𝑘) 14
Figure 5. Mechanism of data interleaving
8. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
8
The deinterleaver, often referred to as the inverse interleaver, reverses the permutation, restoring
the permuted sequence to its original order. In this paper, we employ 𝜋 to represent the
interleaving vector and 𝜋−1 for the deinterleaving vector. With the appropriate deinterleaver, the
permuted elements can be repositioned to their original locations:
𝜋−1: 𝐼 → 𝐼 15
𝑗 → 𝑖 = 𝜋−1(𝑗)
𝜋−1(𝜋(𝑘)) = 𝜋(𝜋−1(𝑘)) = 𝑘 If
we replace 𝑘 by 𝜋−1(𝑛) in equation 14, we get:
16
𝑥𝜋−1(𝑛) = 𝑐𝜋(𝜋−1(𝑛)) = 𝑐𝑛
17
5. PERFORMANCE EVALUATION
In the current section, several performance curves are presented. These curves show the impact
of parameters on decoding performance of the concatenated coding scheme described in the
previous subsection for serial continuation of Polar codes . These parameters and their effects
are important, as they are the levers used in communication standards to adapt to system
constraints. The axes of the various curves are always the same. On the x-axis is the signal-to-
noise ratio, Eb/N0. On the y-axis is the BER (Bit Error Rate). The simulations are executed to
evaluate the system's behavior when data is transmitted through an AWGN channel, making use
of Binary Phase Shift Keying (BPSK) modulation.
Figure 6. Decoding performance of the concatenated Polar Codes for different values of N With
𝑅 = 1/2
Figure 6 illustrates the decoding performance of concatenated Polar codes as codeword size
increases. While it is clear that the bit error rate decreases for a given signal-to-noise ratio, the
Shannon limit is a little far away for the codeword sizes shown.
Error-correcting codes are based on the notion of redundancy, quantified by the performance of
the code. The lower the efficiency, the higher the redundancy. This is illustrated in Figure 7,
again considering the SC algorithm. The observed trend is that the lower the yield, the lower the
9. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
9
error rate. Figure 7 shows the performance of theconcatenated Polar Codes. The code considered
is a code with a codeword size of 2048.
Figure 8 allows to compare the performances in BER between our proposed method and the polar
code. According to this figure, we can see that the BER of our method is better than the simple
polar code. Note that the length of the information sequence is K = 1723 bits and N = 2048 to do
this simulation.
In this section, we discussed the simulation results of our method for different parameters. In the
future works, we will compare the simulation results of our method against various
errorcorrecting codes, such as LDPC and Turbo Codes.
Figure 7. Decoding performance of theconcatenated Polar Codes for different values of R With N= 2048
Figure 8. Comparison of decoding performance between concatenated series of Polar codes and
Polar code with N= 2048
10. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
10
6. CONCLUSION
In this paper, we provide a comprehensive overview of polar codes, including their construction.
Then, we presented the main algorithms for decoding polar codes. The decoding algorithm used,
called SC, was detailed because it was used in the new encoding and decoding scheme. Through
the various simulations presented in this paper, we noticed that this new coding and decoding
structure by using polar codes has good performance of point of view BER. This structure
consists of two concatenated polar codes in series, separated by an interleaver, in order to
develop a highly efficient code suitable for use in 5G technology. The interleaver and
deinterleaver play crucial roles in this coding and decoding structure. A well-designed
permutation should enable us to achieve good performance in terms of Bit Error Rate (BER).
Investigating the impact of the interleaver and deinterleaver on this structure will be the focus of
future work.
ACKNOWLEDGEMENTS
We would like to thank all authors for their contributions and the success of this manuscript and
all editors and anonymous reviewers of this manuscript.
REFERENCES
[1] R.G. Gallager (1963), Low Density Parity Check Code, MIT Press, Combridge.
[2] E. Arikan, (2009) "Channel polarization: A method for constructing capacity achieving codes for
symmetric binary-input memoryless channels”, IEEE Trans. Information Theory, Vol. 55, No. 7, pp.
3051–3073.
[3] Y. Fan et al., (2015) "Low-latency list decoding of polar codes with double thresholding," 2015
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South
Brisbane, QLD, Australia, pp. 1042-1046, doi: 10.1109/ICASSP.2015.7178128
[4] Hani Attar, Haitham Issa, Jafar Ababneh, Mahdi Abbasi, Ahmed A. A. Solyman, Mohammad
Khosravi, Ramy Said Agieb, (2022) "5G System Overview for Ongoing Smart Applications:
Structure, Requirements, and Specifications", Computational Intelligence and Neuroscience, vol.
2022, pages 11. https://doi.org/10.1155/2022/2476841
[5] G. D. Forney, Jr, (1966) Concatenated Codes, MIT Press, Cambridge, MA.
[6] D. J. Costello & G. D. Forney, (2007 ) "Channel coding: The road to channel capacity," in
Proceedings of the IEEE, Vol. 95, No. 6, pp. 1150-1177. Doi: 10.1109/JPROC.2007.895188.
[7] C.Berrou, A.Glavieux, P.Thitimajshima, (1993) “Near shannon limit errorcorrecting coding
anddecoding: turbo-codes”, in: IEEE International Conferenceon Communication, pp.1064– 1070.
[8] H, P. ao, D., & Hoeher (2008), “Helical interleaver set design for interleave-division multiplexing
and related techniques”, IEEE Communications Letters, 12(11), pp. 843–845.
doi:10.1109/LCOMM.2008.080990
[9] E.Arikan (2008) “Channel polarization: a method for constructing capacity-achieving codes”, In
IEEE International Symposium on Information Theory (ISIT 2008), pp. 1173–1177.
[10] H. Aurora, C. Condo & W. J. Gross (2018) “Low-Complexity Software Stack Decoding of Polar
Codes”, In IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5.
[11] I. Tal & A. Vardy , (2011 ) “List Decoding of Polar Codes”, In IEEE International Symposium on
Information Theory (ISIT), pages 1–5.
[12] Orion Afisiadis, Alexios Balatsoukas-Stimming & Andreas Burg, (2014) “A low-complexity
improved successive cancellation decoder for polar codes”, 48th Asilomar Conference on Signals,
Systems and Computers, IEEE, pp. 2116–2120.
[13] Kai Niu and Kai Chen, (2012) “Stack decoding of polar codes”, Electronics letters 48.12, pp. 695–
697.
[14] Erdal Arıkan ,(2010) “Polar codes: A pipelined implementation”, Proc. 4th ISBC, pp. 11–14.
11. International Journal of Wireless & Mobile Networks (IJWMN), Vol.15, No.5, October 2023
11
[15] Nadine Hussami, Satish Babu Korada, & Rudiger Urbanke (2009) “Performance of polar codes for
channel and source coding” IEEE International Symposium on Information Theory, IEEE, pp.
1488–1492.
[16] C. Berrou, Y. Saouter, C. Douillard, S. Kerouedan,& M. Jezequel , (2004) “Designing good
permutations for turbo codes : towards a single model”, in IEEE International Conference on
Communications (ICC), vol. 1, pp. 341–345.
AUTHORS
Prof. Mohammed Mensouri received the M.S degree in Networks and
Telecommunication in 2008, from Faculty of Sciences and Technology, Cadi Ayyad
University, Marrakech, Morocco. In 2015, He received Ph.D of Computer Science in
Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco. He is professor
at Ibn Zohr University, Agadir, Moroc. His research interest information theory and
channel coding , especially error correction codes.
Prof. Mustapha Eddahibi received his PhD from Unversity Cadi Ayyad Marrakech in
2007. He is currently computer science teacher researcher in University Ibn Zohr. He is a
former head of the decisional expert systems research team. His research interests are in
the area of intelligent computing, information engineering, digital Information Encoding
and Processing.