Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

A new iterative decoder for product codes

K Kapustin Alexey, Iitp Ras, Zyablov Victor, Ryabinkin Eygene, Nrc Ki

Published Jan 1, 2014• 3 citations
OpenAlex

Abstract

The most popular decoder for product codes is an iterative decoder. It has low complexity and can correct many errors in average case, but it also has an uncorrectable errors of weight equal to one quoter code distance. To overcome this limitation we propose a new decoder algorithm, that utilizes iterative decoder, but has better error correction efficiency at low error rates. Thecomputer simulation showed that the increase in error correction efficiency is larger for high-rate codes.

Related papers

The Decoding Algorithms For Error-Correcting Product Codes Based On Project Geometry Low-Density Parity-Check Codes

Назаров Лев Евгеньевич

The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block product-codes (block turbo-codes) which enable to reliable information transfer at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated product codes is construction with usage of low-density parity-check codes (LDPC) and these code constructions are in the class of LDPC too. According to this fact the considered code constructions have symbol-by-symbol decoding algorithms developed for total class LDPC codes, namely BP (belief propagation) and its modification MIN_SUM_BP. The BP decoding algorithm is iterative and for implementation the signal/noise is required, for implementation of MIN_SUM_BP decoding algorithm the signal/noise is not required. The resulted characteristics of product codes constructed with usage of LDPC based on project geometry (length of code words, information volume, code rate, error performances) are presented in this paper. These component LDPC codes are cyclic and have encoding and decoding algorithms with low complexity implementation. The computer simulations for encoding and iterative symbol-by-symbol decoding algorithms for the number of turbo-codes with different code rate and information volumes are performed. The results of computer simulations have shown that MIN_SUM_BP decoding algorithm is more effective than BP decoding algorithm for channel with additive white gaussian noise concerning error-performances.

Radioelectronics Nanosystems Information Technologies•Oct 30, 2020•0 citations

Iterative Soft-Decision Decoding of Binary Cyclic Codes

Marco Baldi, Giovanni Cancellieri, Franco Chiaraluce

Binary cyclic codes achieve good error correction performance and allow the implementation of very simpleencoder and decoder circuits. Among them, BCH codesrepresent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that softdecision decoding algorithms can produce significant coding gain with respect to hard-decision techniques. Several approaches have been proposed to implement iterative soft-decision decoding of binary cyclic codes. We study the technique based on “extended parity-check matrices”, and show that such method is not suitable for high rates or long codes. We propose a new approach, based on “reduced parity-check matrices” and “spread parity-check matrices”, that can achieve better correction performance in many practical cases, without increasing the complexity.

Journal of Communications Software and Systems•Jun 22, 2008•3 citations

Iterative Decoding of High Dimensionality Parity Code

Toshio Fukuta

Given the importance of the traffic on modern communication networks, advanced error correction methods are needed to overcome the changes expected in channel quality.Conventional countermeasures that use high dimensionality parity codes often fail to provide sufficient error correction capability.We propose a parity code with high dimensionality that is iteratively decoded.It provides better error correcting capability than conventional decoding methods.The proposal uses the steepest descent method to increase code bit reliability and the coherency between parities and code bits gradually.Furthermore, the quantization of the decoding algorithm is discussed.It is found that decoding with quantization can keep the error correcting capability high.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Oct 1, 2003•2 citations

ITERATIVE DECODING OF GEOMETRIC PRODUCT CODES

Gökmen Altay, Osman Nuri UCAN

We present iterative decoding process of Geometric Product codes that is a newly proposed linear block code construction technique. We also report the bit error performances for one of the constructed code of the technique utilising our iterative decoding approach.

IU-Journal of Electrical & Electronics Engineering•Jan 1, 2005•0 citations

Düşük yoğunluklu eşlik denetim kodları için kod çözme algoritmalarının karşılaştırılması.

Kolaylı, Mert

Low-density parity-check (LDPC) codes are a subclass of linear block codes. These codes have parity-check matrices in which the ratio of the non-zero elements to all elements is low. This property is exploited in defining low complexity decoding algorithms. Low-density parity-check codes have good distance properties and error correction capability near Shannon limits. In this thesis, the sum-product and the bit-flip decoding algorithms for low-density parity-check codes are implemented on Intel Pentium M 1,86 GHz processor using the software called MATLAB. Simulations for the two decoding algorithms are made over additive white gaussian noise (AWGN) channel changing the code parameters like the information rate, the blocklength of the code and the column weight of the parity-check matrix. Performance comparison of the two decoding algorithms are made according to these simulation results. As expected, the sum-product algorithm, which is based on soft-decision decoding, outperforms the bit-flip algorithm, which depends on hard-decision decoding. Our simulations show that the performance of LDPC codes improves with increasing blocklength and number of iterations for both decoding algorithms. Since the sum-product algorithm has lower error-floor characteristics, increasing the number of iterations is more effective for the sum-product decoder compared to the bit-flip decoder. By having better BER performance for lower information rates, the bit-flip algorithm performs according to the expectations; however, the performance of the sum-product decoder deteriorates for information rates below 0.5 instead of improving. By irregular construction of LDPC codes, a performance improvement is observed especially for low SNR values.

•Jan 1, 2006•0 citations

Modified algorithm for hard decision decoding of product codes

Ali Al‐Shaikhi, M.A. Kousa

Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels.

IEEE Wireless Communications and Networking Conference•Oct 19, 2004•4 citations
The most popular decoder for product codes is an iterative decoder. It has low complexity and can correct many errors in average case, but it also has an uncorrectable errors of weight equal to one quoter code distance. To overcome this limitation we propose a new decoder algorithm, that utilizes iterative decoder, but has better error correction efficiency at low error rates. Thecomputer simulation showed that the increase in error correction efficiency is larger for high-rate codes.
The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block product-codes (block turbo-codes) which enable to reliable information transfer at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated product codes is construction with usage of low-density parity-check codes (LDPC) and these code constructions are in the class of LDPC too. According to this fact the considered code constructions have symbol-by-symbol decoding algorithms developed for total class LDPC codes, namely BP (belief propagation) and its modification MIN_SUM_BP. The BP decoding algorithm is iterative and for implementation the signal/noise is required, for implementation of MIN_SUM_BP decoding algorithm the signal/noise is not required. The resulted characteristics of product codes constructed with usage of LDPC based on project geometry (length of code words, information volume, code rate, error performances) are presented in this paper. These component LDPC codes are cyclic and have encoding and decoding algorithms with low complexity implementation. The computer simulations for encoding and iterative symbol-by-symbol decoding algorithms for the number of turbo-codes with different code rate and information volumes are performed. The results of computer simulations have shown that MIN_SUM_BP decoding algorithm is more effective than BP decoding algorithm for channel with additive white gaussian noise concerning error-performances.
Binary cyclic codes achieve good error correction performance and allow the implementation of very simpleencoder and decoder circuits. Among them, BCH codesrepresent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that softdecision decoding algorithms can produce significant coding gain with respect to hard-decision techniques. Several approaches have been proposed to implement iterative soft-decision decoding of binary cyclic codes. We study the technique based on “extended parity-check matrices”, and show that such method is not suitable for high rates or long codes. We propose a new approach, based on “reduced parity-check matrices” and “spread parity-check matrices”, that can achieve better correction performance in many practical cases, without increasing the complexity.
Given the importance of the traffic on modern communication networks, advanced error correction methods are needed to overcome the changes expected in channel quality.Conventional countermeasures that use high dimensionality parity codes often fail to provide sufficient error correction capability.We propose a parity code with high dimensionality that is iteratively decoded.It provides better error correcting capability than conventional decoding methods.The proposal uses the steepest descent method to increase code bit reliability and the coherency between parities and code bits gradually.Furthermore, the quantization of the decoding algorithm is discussed.It is found that decoding with quantization can keep the error correcting capability high.
Low-density parity-check (LDPC) codes are a subclass of linear block codes. These codes have parity-check matrices in which the ratio of the non-zero elements to all elements is low. This property is exploited in defining low complexity decoding algorithms. Low-density parity-check codes have good distance properties and error correction capability near Shannon limits. In this thesis, the sum-product and the bit-flip decoding algorithms for low-density parity-check codes are implemented on Intel Pentium M 1,86 GHz processor using the software called MATLAB. Simulations for the two decoding algorithms are made over additive white gaussian noise (AWGN) channel changing the code parameters like the information rate, the blocklength of the code and the column weight of the parity-check matrix. Performance comparison of the two decoding algorithms are made according to these simulation results. As expected, the sum-product algorithm, which is based on soft-decision decoding, outperforms the bit-flip algorithm, which depends on hard-decision decoding. Our simulations show that the performance of LDPC codes improves with increasing blocklength and number of iterations for both decoding algorithms. Since the sum-product algorithm has lower error-floor characteristics, increasing the number of iterations is more effective for the sum-product decoder compared to the bit-flip decoder. By having better BER performance for lower information rates, the bit-flip algorithm performs according to the expectations; however, the performance of the sum-product decoder deteriorates for information rates below 0.5 instead of improving. By irregular construction of LDPC codes, a performance improvement is observed especially for low SNR values.
Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels.