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

arXiv:2403.19266 · IEEE Transactions on Green Communications and Networking

On the Performance of Low-Complexity Decoders of LDPC Codes

Qingqing Peng, Dawei Yin, Dongxu Chang, Yuan Li, Huazi Zhang, Guiying Yan, Guanghui Wang

Published Jan 1, 2026• 1 citation
arXivHTMLPDF

Abstract

Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of the fundamental limits in the above-mentioned scenarios. This study aims to explore the performance of LDPC codes under belief propagation (BP) decoding with complexity constraints. In other words, for a small number of iterations, we present a closed-form lower bound on the bit error rate (BER) of LDPC codes as a function of complexity. Specifically, for the regular LDPC code ensembles, the dominant term in the order of the lower bound we provide matches that of the upper bound given by Lentmaier. Furthermore, for irregular LDPC code ensembles, in addition to adopting the approach used for regular codes, we also propose a method to iteratively obtain the lower bound on the average BER.

DOI
10.1109/tgcn.2026.3718068

Related papers

Performance Study of a Class of Irregular LDPC Codes through Low Complexity Bounds on Their Belief-Propagation Decoding Thresholds

F. Vatta, Alessandro Soranzo, Massimiliano Comisso +2 more

This paper investigates about the usefulness of some recently published low complexity upper bounds on belief-propagation decoding thresholds for irregular low-density parity-check (LDPC) codes to analyze their performance on memoryless binary input - additive white Gaussian noise (BI-AWGN) channels, with sum-product decoding. Irregular LDPC codes are known to perform better than regular ones, and to exhibit, like them, the so called “threshold phenomenon”, being the threshold defined as the maximum noise level such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We use a simplified analysis of the belief-propagation decoding algorithm, i.e., consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes on BI-AWGN channels.

AEIT International Annual Conference•Sep 1, 2019•11 citations

Estimating BP Decoding Performance of Moderate-Length Irregular LDPC Codes with Sphere Bounds

Kyuhyuk Chung

This paper estimates belief-propagation (BP) decoding performance of moderate-length irregular low-density parity-check (LDPC) codes with sphere bounds. We note that for moderate-length(10³≤ N ≤ 4×10³) irregular LDPC codes, BP decoding performance, which is much worse than maximum likelihood (ML) decoding performance, is well matched with one of loose upper bounds, i.e., sphere bounds. We introduce the sphere bounding technique for particular codes, not average bounds. The sphere bounding estimation technique is validated by simulation results. It is also shown that sphere bounds and BP decoding performance of irregular LDPC codes are very close at bit-error-rates (BERs) P b of practical importance(10?≤ P b ≤10 -4 ).

한국통신학회논문지•Jul 1, 2010•0 citations

Performance Analysis of Different Flexible Decoding Algorithms for NR-LDPC Codes

Layla Mahdi Salih, Thuraya Mahmood Qaradaghi, Jalal J. Hamad Ameen

Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.

Tikrit Journal of Engineering Sciences•Dec 11, 2022•3 citations

LDPC Codes Over the BEC: Bounds and Decoding Algorithms

Irina E. Bocharova, Boris D. Kudryashov, Vitaly Skachek +2 more

The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson-Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique.

IEEE Transactions on Communications•Nov 6, 2018•5 citations

Irregular Generalized LDPC codes in Practical Communication Scenarios

Irina E. Bocharova, Boris D. Kudryashov, Sander Mikelsaar

High-rate irregular Generalized LDPC (GLDPC) codes with low-complexity constituent codes are studied. The main area of focus is the optimization of the underlying irregular binary LDPC codes and their matching with constituent codes. Finite length random coding bound on the maximum-likelihood decoding error probability of a random ensemble of irregular GLDPC codes is derived and compared with a similar bound for non-binary (NB) LDPC codes over small alphabets.A new algorithm for assigning columns of the parity-check matrix of a constituent code to nonzero elements of a base matrix of the quasi-cyclic (QC)-GLDPC code is presented. Examples of the constructed QC-GLDPC codes are given. The simulation results for frame error rate (FER) performance of the belief-propagation (BP) decoding for the QC-GLDPC codes are presented and compared with the same performance of NB QC-LDPC codes over small alphabets and binary LDPC codes in the WiFi and 5G standards.Both GLDPC codes and NB LDPC codes with sufficiently low decoding complexity are shown to outperform their binary LDPC counterparts, while GLDPC codes appear to be more advantageous in terms of decoding complexity.

IEEE Information Theory Workshop (ITW)•Nov 1, 2022•1 citation

Finite-length analysis of irregular expurgated LDPC codes under finite number of iterations

Ryuhei Mori, Toshiyuki Tanaka, Kenta Kasai +1 more

Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of iterations converges to a limit, which is calculated via density evolution, as the blocklength n tends to infinity. The difference between the bit error probability with blocklength n and the large-blocklength limit behaves asymptotically like ¿/n, where the coefficient ¿ depends on the ensemble, the number of iterations and the erasure probability of the BEC. In, ¿ is calculated for regular ensembles. In this paper, ¿ for irregular expurgated ensembles is derived. It is demonstrated that convergence of numerical estimates of ¿ to the analytic result is significantly fast for irregular unexpurgated ensembles.

arXiv:0901.2204•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2009•2 citations
Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of the fundamental limits in the above-mentioned scenarios. This study aims to explore the performance of LDPC codes under belief propagation (BP) decoding with complexity constraints. In other words, for a small number of iterations, we present a closed-form lower bound on the bit error rate (BER) of LDPC codes as a function of complexity. Specifically, for the regular LDPC code ensembles, the dominant term in the order of the lower bound we provide matches that of the upper bound given by Lentmaier. Furthermore, for irregular LDPC code ensembles, in addition to adopting the approach used for regular codes, we also propose a method to iteratively obtain the lower bound on the average BER.
This paper investigates about the usefulness of some recently published low complexity upper bounds on belief-propagation decoding thresholds for irregular low-density parity-check (LDPC) codes to analyze their performance on memoryless binary input - additive white Gaussian noise (BI-AWGN) channels, with sum-product decoding. Irregular LDPC codes are known to perform better than regular ones, and to exhibit, like them, the so called “threshold phenomenon”, being the threshold defined as the maximum noise level such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We use a simplified analysis of the belief-propagation decoding algorithm, i.e., consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes on BI-AWGN channels.
This paper estimates belief-propagation (BP) decoding performance of moderate-length irregular low-density parity-check (LDPC) codes with sphere bounds. We note that for moderate-length(10³≤ N ≤ 4×10³) irregular LDPC codes, BP decoding performance, which is much worse than maximum likelihood (ML) decoding performance, is well matched with one of loose upper bounds, i.e., sphere bounds. We introduce the sphere bounding technique for particular codes, not average bounds. The sphere bounding estimation technique is validated by simulation results. It is also shown that sphere bounds and BP decoding performance of irregular LDPC codes are very close at bit-error-rates (BERs) P b of practical importance(10?≤ P b ≤10 -4 ).
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. A tightened union-type upper bound on the ML decoding error probability based on the precise coefficients of the average weight spectrum is presented. For LDPC codes from the Gallager ensemble and the Richardson-Urbanke ensemble, new upper bounds on the ML decoding performance based on computing the rank of submatrices of the code parity-check matrix are derived. A new lower bound on the ML decoding threshold followed from the latter error probability bound is obtained. An improved lower bound on the error probability for codes with a known estimate on the minimum distance is presented as well. A new low-complexity near-ML decoding algorithm for quasi-cyclic LDPC codes is proposed and simulated. Its performance is compared to the simulated belief propagation and ML decoding performance and simulated performance of the best known improved iterative decoding techniques, as well as, with the derived upper bounds on the ML decoding performance and with decoding thresholds obtained by the density evolution technique.
High-rate irregular Generalized LDPC (GLDPC) codes with low-complexity constituent codes are studied. The main area of focus is the optimization of the underlying irregular binary LDPC codes and their matching with constituent codes. Finite length random coding bound on the maximum-likelihood decoding error probability of a random ensemble of irregular GLDPC codes is derived and compared with a similar bound for non-binary (NB) LDPC codes over small alphabets.A new algorithm for assigning columns of the parity-check matrix of a constituent code to nonzero elements of a base matrix of the quasi-cyclic (QC)-GLDPC code is presented. Examples of the constructed QC-GLDPC codes are given. The simulation results for frame error rate (FER) performance of the belief-propagation (BP) decoding for the QC-GLDPC codes are presented and compared with the same performance of NB QC-LDPC codes over small alphabets and binary LDPC codes in the WiFi and 5G standards.Both GLDPC codes and NB LDPC codes with sufficiently low decoding complexity are shown to outperform their binary LDPC counterparts, while GLDPC codes appear to be more advantageous in terms of decoding complexity.
Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of iterations converges to a limit, which is calculated via density evolution, as the blocklength n tends to infinity. The difference between the bit error probability with blocklength n and the large-blocklength limit behaves asymptotically like ¿/n, where the coefficient ¿ depends on the ensemble, the number of iterations and the erasure probability of the BEC. In, ¿ is calculated for regular ensembles. In this paper, ¿ for irregular expurgated ensembles is derived. It is demonstrated that convergence of numerical estimates of ¿ to the analytic result is significantly fast for irregular unexpurgated ensembles.