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

IEEE Communications Letters

Density evolution for two improved BP-Based decoding algorithms of LDPC codes

J. Chen, M.P.C. Fossorier

Published May 1, 2002• 438 citations
Publisher

Abstract

In this letter, we analyze the performance of two improved belief propagation (BP) based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization.

DOI
10.1109/4234.1001666

Related papers

Density evolution for BP-based decoding algorithms of LDPC codes and their quantized versions

Jinghu Chen, P.M.C. Fossorier

In this paper, we analyze the performance of two improved BP-based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization. Finite quantization effects on the BP-based and the offset BP-based decoding algorithms are evaluated.

Globecom•Mar 22, 2004•51 citations

A high‐performance belief propagation decoding algorithm for codes with short cycles

Ali Karimi-lenji, Monireh Houshmand, Fahimeh Zarmehi

Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.

International Journal of Communication Systems•Feb 28, 2017•2 citations

Reduced-Complexity Decoding of LDPC Codes

J. Chen, Ajay Dholakia, Evangelos S. Eleftheriou +2 more

Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.

IEEE Transactions on Communications•Aug 1, 2005•952 citations

Simulation-Based Validation of Improved BP-Based Decoding Algorithms of LDPC codes

Manel Abdelhedi, Fethi Tlili, Larbi Ben Hadj Slama

Low-density parity-check (LDPC) codes deliver very good performance when decoded with the BP algorithm. Unfortunately, this algorithm has the disadvantage to be complex for implementation. In this paper, we investigate the BP algorithm and its simplifications (BP-Based, normalized BP-Based, offset BP-Based). Previous works on normalized and offset BP-Based proposed theoretical values for the offset and normalization factors, we perform simulations which allow to validate these theoretical results.

International Symposium on Communications, Control and Signal Processing•Mar 1, 2008•4 citations

An improved normalized BP based decoding algorithm for LDPC codes

Haigang Zhang, Dongfeng Yuan, Cheng‐Xiang Wang

A uniformly most powerful (UMP) belief propagation (BP) based algorithm is referred to as a simplified version of a BP algorithm with reduced complexity but performance loss for low density parity check (LDPC) codes. To compensate the performance loss, the normalized BP based algorithm was proposed, where the normalization factor was derived by mean ratio or by minimizing the mean square error. In this paper, an improved novel normalized BP based algorithm is proposed. The normalization uses multiplicative factor instead of divisional factor. The novel scheme shows better performance than the existing normalized BP based algorithms while keeping the same implementation complexity. The simulation is done for two kinds of LDPC codes: random constructed codes and finite geometry codes. At high signal-to-noise ratio (SNR) region, the proposed scheme can achieve even better performance than BP algorithm for short length random constructed LDPC codes.

IET International Conference on Wireless, Mobile and Multimedia Networks (ICWMMN)•Jan 1, 2008•5 citations

Improved Belief Propagation (BP) Decoding for LDPC Codes with a large number of short cycles

Kyuhyuk Chung, Jun Heo

In this paper, we improve performance of Low Density Parity Check (LDPC) codes by adding a large number of short cycles. Short cycles, especially cycles of length 4, degrade performance of LDPC codes if the standard BP (Belief Propagation) decoding is used. Therefore current researches have focused on removing cycles of length 4 for designing good performance LDPC codes. We found that a large number of cycles of length 4 improve performance of LDPC codes if a modified BP decoding is used. We present the modified BP decoding algorithm for LDPC codes with a large number of short cycles. We show that the modified BP decoding performance of LDPC codes with a large number of short cycles is better than the standard BP decoding performance of LDPC codes designed by avoiding short cycles.

IEEE Vehicular Technology Conference•Sep 8, 2006•16 citations
In this letter, we analyze the performance of two improved belief propagation (BP) based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization.
In this paper, we analyze the performance of two improved BP-based decoding algorithms for LDPC codes, namely the normalized BP-based and the offset BP-based algorithms, by means of density evolution. The numerical calculations show that with one properly chosen parameter for each of these two improved BP-based algorithms, performances very close to that of the BP algorithm can be achieved. Simulation results for LDPC codes with code length moderately long validate the proposed optimization. Finite quantization effects on the BP-based and the offset BP-based decoding algorithms are evaluated.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
Low-density parity-check (LDPC) codes deliver very good performance when decoded with the BP algorithm. Unfortunately, this algorithm has the disadvantage to be complex for implementation. In this paper, we investigate the BP algorithm and its simplifications (BP-Based, normalized BP-Based, offset BP-Based). Previous works on normalized and offset BP-Based proposed theoretical values for the offset and normalization factors, we perform simulations which allow to validate these theoretical results.
A uniformly most powerful (UMP) belief propagation (BP) based algorithm is referred to as a simplified version of a BP algorithm with reduced complexity but performance loss for low density parity check (LDPC) codes. To compensate the performance loss, the normalized BP based algorithm was proposed, where the normalization factor was derived by mean ratio or by minimizing the mean square error. In this paper, an improved novel normalized BP based algorithm is proposed. The normalization uses multiplicative factor instead of divisional factor. The novel scheme shows better performance than the existing normalized BP based algorithms while keeping the same implementation complexity. The simulation is done for two kinds of LDPC codes: random constructed codes and finite geometry codes. At high signal-to-noise ratio (SNR) region, the proposed scheme can achieve even better performance than BP algorithm for short length random constructed LDPC codes.
In this paper, we improve performance of Low Density Parity Check (LDPC) codes by adding a large number of short cycles. Short cycles, especially cycles of length 4, degrade performance of LDPC codes if the standard BP (Belief Propagation) decoding is used. Therefore current researches have focused on removing cycles of length 4 for designing good performance LDPC codes. We found that a large number of cycles of length 4 improve performance of LDPC codes if a modified BP decoding is used. We present the modified BP decoding algorithm for LDPC codes with a large number of short cycles. We show that the modified BP decoding performance of LDPC codes with a large number of short cycles is better than the standard BP decoding performance of LDPC codes designed by avoiding short cycles.