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 International Symposium on Information Theory (ISIT)

Iterative reliability based decoding of LDPC codes

M.P.C. Fossorier

Published Nov 13, 2002• 4 citations
Publisher

Abstract

In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.

DOI
10.1109/isit.2001.936096

Related papers

Iterative reliability-based decoding of low-density parity check codes

M.P.C. Fossorier

In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.

IEEE Journal on Selected Areas in Communications•May 1, 2001•167 citations

Efficient Near Maximum-Likelihood Reliability-Based Decoding for Short LDPC Codes

Weiyang Zhang, Chentao Yue, Yonghui Li +1 more

In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and ordered statistics decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order- (m -1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.

arXiv:2306.00443•International Conference on Communications•Jun 9, 2024•8 citations

Combination of Belief Propagation and Beam Search Algorithms for the Decoding of LDPC Codes

Feng Guang-zeng

For short low-density parity-check codes,due to the message dependency,there exists a performance gap between the belief propagation (BP) and the maximum likelihood decoding (MLD) algorithms.Aiming at bridging the gap at the cost of some complexity,we put forward a beam search (BS) postprocessing scheme,based on the fact that LDPC codes commonly have sparsely distributed codewords and only a small portion of the codeword bits are erroneous in a BP decoding failure.In the implementation of BS to search for the error pattern,when evaluating the intermediate individuals given a limited beam width,we take advantage of the information about the decoding syndrome and the reliability metric of each bit fully.Simulation results show that the proposed method achieves a good tradeoff between performance and complexity.

Journal of Nanjing University of Posts and Telecommunications•Jan 1, 2008•0 citations

A Hybrid Decoding Scheme for Short Non-Binary LDPC Codes

Marco Baldi, Franco Chiaraluce, Nicola Maturo +2 more

In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (LDPC) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative LDPC decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) ≈ 10-5. Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER ≈ 10-5with respect to BP decoding and MRB decoding used alone.

IEEE Communications Letters•Nov 4, 2014•27 citations

Reliability-based syndrome decoding of LDPC codes

Guangwen Li, Guangzeng Feng

Aiming at bridge gap between maximum likelihood decoding (MLD) and belief propagation (BP) decoding for short or medium LDPC codes, we present one modified ordered statistics decoding (OSD) reprocessing method, which is serially concatenated with standard BP. Meanwhile, two novel points in implementation are addressed. For one thing, the new definition of bit reliability proposed enhances error-correcting performance via centralizing more decoding errors of standard BP within the scope of order-p OSD where p ≤ 2. For another, one way of reducing computational complexity is put forward in selecting optimal error pattern among all candidates. Simulation results demonstrate our approach could achieve good tradeoff between reprocessing performance and computational complexity. Techniques on further improvement are also discussed briefly. Reliability-based syndrome decoding of LDPC codes 1 I.

•Jan 1, 2007•0 citations

A hybrid low complexity decoding of LDPC codes

Hua Wang, Guangrong Fan, Jingming Kuang

An efficient early stopping criterion based on the evolution of the number of reliable variable nodes (NRVN) is proposed for low density parity check (LDPC) codes in this paper. This criterion can significantly reduce the average number of iterations (ANI) at low to middle signal to noise ratios (SNRs) with minimal performance degradation. Furthermore, a hybrid decoding method is presented to reduce the decoding complexity of LDPC codes by combining the proposed stopping criterion and forced convergence (FC) decoding algorithm. Compared with the classic belief propagation (BP) decoding, significant computation complexity reduction can be achieved with small computation overhead.

IET International Conference on Wireless, Mobile and Multimedia Networks (ICWMMN)•Jan 1, 2010•1 citation
In this work, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between BP decoding which remains suboptimum, and maximum likelihood decoding (MLD) which is too complex to be implemented for the codes considered. A stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is also proposed for this combined decoding approach. Simulations results for several Gallager LDPC codes and different set cyclic (DSC) codes of hundreds of information bits are given and elaborated.
In this paper, reliability based decoding is combined with belief propagation (BP) decoding for low-density parity check (LDPC) codes. At each iteration, the soft output values delivered by the BP algorithm are used as reliability values to perform reduced complexity soft decision decoding of the code considered. This approach allows to bridge the error performance gap between belief propagation decoding which remains suboptimum, and maximum likelihood decoding which is too complex to be implemented for the codes considered. Trade-offs between decoding complexity and error performance are also investigated. In particular, a stopping criterion which reduces the average number of iterations at the expense of very little performance degradation is proposed for this combined decoding approach. Simulation results for several Gallager (1963, 1968) LDPC codes and different set cyclic codes of hundreds of information bits are given and elaborated.
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and ordered statistics decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order- (m -1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.
For short low-density parity-check codes,due to the message dependency,there exists a performance gap between the belief propagation (BP) and the maximum likelihood decoding (MLD) algorithms.Aiming at bridging the gap at the cost of some complexity,we put forward a beam search (BS) postprocessing scheme,based on the fact that LDPC codes commonly have sparsely distributed codewords and only a small portion of the codeword bits are erroneous in a BP decoding failure.In the implementation of BS to search for the error pattern,when evaluating the intermediate individuals given a limited beam width,we take advantage of the information about the decoding syndrome and the reliability metric of each bit fully.Simulation results show that the proposed method achieves a good tradeoff between performance and complexity.
In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (LDPC) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative LDPC decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) ≈ 10-5. Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER ≈ 10-5with respect to BP decoding and MRB decoding used alone.
Aiming at bridge gap between maximum likelihood decoding (MLD) and belief propagation (BP) decoding for short or medium LDPC codes, we present one modified ordered statistics decoding (OSD) reprocessing method, which is serially concatenated with standard BP. Meanwhile, two novel points in implementation are addressed. For one thing, the new definition of bit reliability proposed enhances error-correcting performance via centralizing more decoding errors of standard BP within the scope of order-p OSD where p ≤ 2. For another, one way of reducing computational complexity is put forward in selecting optimal error pattern among all candidates. Simulation results demonstrate our approach could achieve good tradeoff between reprocessing performance and computational complexity. Techniques on further improvement are also discussed briefly. Reliability-based syndrome decoding of LDPC codes 1 I.
An efficient early stopping criterion based on the evolution of the number of reliable variable nodes (NRVN) is proposed for low density parity check (LDPC) codes in this paper. This criterion can significantly reduce the average number of iterations (ANI) at low to middle signal to noise ratios (SNRs) with minimal performance degradation. Furthermore, a hybrid decoding method is presented to reduce the decoding complexity of LDPC codes by combining the proposed stopping criterion and forced convergence (FC) decoding algorithm. Compared with the classic belief propagation (BP) decoding, significant computation complexity reduction can be achieved with small computation overhead.