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

Stopping-Set Assisted Reinforced Belief Propagation for Decoding Short LDPC Codes

Asif Ali Zamzami, Kuan-Chuan Chao, Shih‐Chun Lin

Published Dec 21, 2021• 5 citations
Publisher

Abstract

The low-density parity-check (LDPC) code is chosen to be a channel coding scheme for ultra-reliable and low-latency communications (URLLC) in 5G. However, short LDPC compromises the belief propagation (BP) decoder because of the stopping set (SS) in the decoding graph. We propose to perform different node operations according to the SS. A dynamic SS selection according to the received sequence is further applied. In the length 308 5G LDPC, our decoders outperform prior work, improving BP and collaborative BP at block error probability (BLER) of$3 \times 10^{-5}$by around 0.176 and 0.092 dB respectively, with almost the same number of iterations.

DOI
10.1109/lcomm.2021.3137222

Related papers

Trapping-Set-Assisted Decoding for Short-Length Low-Density Parity-Check Codes

Asif Ali Zamzami, Zhu-En Yu, Yuh-Tser Wu +1 more

To guarantee that every device in industrial Internet of Things (IoT) is reliable for fast data exchange, ultrareliable and low-latency communication (URLLC) technology from 5G is crucial. To reduce latency, typically, only up to 1000 code blocklength is allowed. Indeed, a block error rate (BLER) of less than$10^{-5}$and latency of less than 1 ms are achievable in 5G URLLC. The short code blocklength feature is also required in satellite IoT. Though low-density parity-check (LDPC) decoding via belief propagation (BP) shows promise for achieving low BLER with long blocklength, its BLER is high in short LDPC codes due to error-prone patterns, with the trapping set (TS) being one of the most significant patterns. To alleviate the damage of TS, which can be identified offline, we propose two decoding algorithms named dynamic TS-assisted reinforced BP (DTS-RBP) and TS-assisted relaxation for neural-network BP (TSR-NNBP), respectively. Compared with previous works, only proposed TS assisted decoders can meet URLLC requirements under 308 code blocklength at a 3 dB signal-to-noise ratio (SNR). Moreover, under 128 code blocklength for satellite IoT, our DTS-RBP decoder provides the best memory-performance tradeoff with approximately the same number of iterations as BP.

IEEE Internet of Things Journal•Apr 24, 2025•2 citations

Improving Short-Block LDPC Decoding Using Perturbation-Based Rescue with Maximum Likelihood Based Candidate Validation

Haider Abdulkarim, Hussein Khaleel, Marwa K. Farhan

Abstract Meeting the latency and reliability requirements of 5G Ultra-Reliable Low-Latency Communications (URLLC) is enabled through the adoption of short-block Low-Density Parity-Check (LDPC) codes. Traditional decoding of short-block LDPC using Belief Propagation (BP) may fail due to trapping sets, resulting in degraded decoding performance. This paper proposes a three-stage decoding algorithm that combines low-iteration BP decoding, a perturbation-based rescue process, and Maximum Likelihood (ML) based candidate validation to improve decoding reliability. When the low-iteration BP decoding stage fails to converge, the rescue stage perturbs the least reliable bits to generate multiple decoding candidates, which are subsequently evaluated using an ML-based metric to select the most likely candidate and reduce miscorrections. The proposed algorithm was evaluated through MATLAB simulations with a short-block LDPC configuration for 5G URLLC systems. QAM modulation was used and two channel models were considered, Additive White Gaussian Noise and flat Rayleigh fading. The performance was investigated for different numbers of perturbed bits and different coding rates. The results show improved decoding performance compared to standard LDPC, achieving coding gains exceeding 1 dB at low bit error rates while reducing decoding failures caused by trapping sets.

•Oct 12, 2026•0 citations

Performance improvement of short-length regular low-density parity-check codes with low-complexity post-processing

Raghunadh K. Bhattar, K.R. Ramakrishnan, K. S. Dasgupta

It is well known that extremely long low-density parity-check (LDPC) codes perform exceptionally well for error correction applications, short-length codes are preferable in practical applications. However, short-length LDPC codes suffer from performance degradation owing to graph-based impairments such as short cycles, trapping sets and stopping sets and so on in the bipartite graph of the LDPC matrix. In particular, performance degradation at moderate to high Eb/N0 is caused by the oscillations in bit node a posteriori probabilities induced by short cycles and trapping sets in bipartite graphs. In this study, a computationally efficient algorithm is proposed to improve the performance of short-length LDPC codes at moderate to high Eb/N0. This algorithm makes use of the information generated by the belief propagation (BP) algorithm in previous iterations before a decoding failure occurs. Using this information, a reliability-based estimation is performed on each bit node to supplement the BP algorithm. The proposed algorithm gives an appreciable coding gain as compared with BP decoding for LDPC codes of a code rate equal to or less than 1/2 rate coding. The coding gains are modest to significant in the case of optimised (for bipartite graph conditioning) regular LDPC codes, whereas the coding gains are huge in the case of unoptimised codes. Hence, this algorithm is useful for relaxing some stringent constraints on the graphical structure of the LDPC code and for developing hardware-friendly designs.

IET Communications•Oct 16, 2012•1 citation

Row-Boosted Ensemble Belief Propagation for Short LDPC Codes

Paul Bezner, Felix Krieg, Stephan ten Brink

Belief-propagation (BP) decoding of short and moderate-length low-density parity-check (LDPC) codes is limited by finite-length graph effects: a single decoder trajectory can become trapped or oscillatory even when an alternative trajectory would decode the received word. Existing ensemble-BP decoders create the required diversity through multiple parity-check matrices, automorphisms, modified schedules, subcodes, or altered update rules. We introduce row-boosted ensemble (RBE) decoding as a minimal decoder-side diversity mechanism: all ensemble members share the same parity-check matrix and the same BP kernel, and differ only in a small set of parity-check rows whose outgoing messages are boosted. On the 5G~NR BG1 \((144,96)\) code, RBE with \(32\) members lowers the frame-error rate of BP with \(20\) iterations (BP-20) from \(1.6\times10^{-2}\) to \(1.6\times10^{-3}\) at \(E_\mathrm{b}/N_0=4.0\,\mathrm{dB}\), outperforming saturated-min-sum and affine subcode ensembles of equal size. Increasing the ensemble size yields additional gains, indicating that RBE provides a scalable performance-complexity tradeoff. The gains transfer across 5G~NR block lengths and rates, to non-5G short LDPC codes, and across flooding and layered schedules.

arXiv:2608.09560•Aug 10, 2026•0 citations

CRC-Aided Adaptive Belief Propagation Decoding of NR LDPC Codes

Xianwen Zhang, Ming Jiang, Mingyang Zhu +2 more

In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.

IEEE Vehicular Technology Conference•Jun 1, 2022•3 citations

A Weighted Belief Propagation Decoding Algorithm of LDPC Codes for Fast Convergence and Early Stopping

Tso-Cho Chen

A weighted belief propagation decoding algorithm for low-density parity-check decoding is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. We propose an early stopping criterion which is based on the average weighted reliability measure of the hard output of decoder to detect undecodable blocks in an early stage of the decoding process. In addition, an adaptive weighted iteration scheme is proposed to increase the convergence speed of belief propagation (BP) decoding and therefore improve the error performance. The evolution of the adaptive weighting factor with the number of decoding iterations is based on the relative entropy between two consecutive ”a posteriori” probabilities distribution at decoder output. Simulation results show that the proposed algorithm can achieve about 0.2-0.4 dB coding gain improvement on average while reducing up to about 50%-85% iterations for decoding at low to medium E(subscript b)/ N(subscript 0) , compared with the conventional BP based algorithms.

•Jul 1, 2012•0 citations
The low-density parity-check (LDPC) code is chosen to be a channel coding scheme for ultra-reliable and low-latency communications (URLLC) in 5G. However, short LDPC compromises the belief propagation (BP) decoder because of the stopping set (SS) in the decoding graph. We propose to perform different node operations according to the SS. A dynamic SS selection according to the received sequence is further applied. In the length 308 5G LDPC, our decoders outperform prior work, improving BP and collaborative BP at block error probability (BLER) of3×10−53 \times 10^{-5}3×10−5by around 0.176 and 0.092 dB respectively, with almost the same number of iterations.
To guarantee that every device in industrial Internet of Things (IoT) is reliable for fast data exchange, ultrareliable and low-latency communication (URLLC) technology from 5G is crucial. To reduce latency, typically, only up to 1000 code blocklength is allowed. Indeed, a block error rate (BLER) of less than10−510^{-5}10−5and latency of less than 1 ms are achievable in 5G URLLC. The short code blocklength feature is also required in satellite IoT. Though low-density parity-check (LDPC) decoding via belief propagation (BP) shows promise for achieving low BLER with long blocklength, its BLER is high in short LDPC codes due to error-prone patterns, with the trapping set (TS) being one of the most significant patterns. To alleviate the damage of TS, which can be identified offline, we propose two decoding algorithms named dynamic TS-assisted reinforced BP (DTS-RBP) and TS-assisted relaxation for neural-network BP (TSR-NNBP), respectively. Compared with previous works, only proposed TS assisted decoders can meet URLLC requirements under 308 code blocklength at a 3 dB signal-to-noise ratio (SNR). Moreover, under 128 code blocklength for satellite IoT, our DTS-RBP decoder provides the best memory-performance tradeoff with approximately the same number of iterations as BP.
Abstract Meeting the latency and reliability requirements of 5G Ultra-Reliable Low-Latency Communications (URLLC) is enabled through the adoption of short-block Low-Density Parity-Check (LDPC) codes. Traditional decoding of short-block LDPC using Belief Propagation (BP) may fail due to trapping sets, resulting in degraded decoding performance. This paper proposes a three-stage decoding algorithm that combines low-iteration BP decoding, a perturbation-based rescue process, and Maximum Likelihood (ML) based candidate validation to improve decoding reliability. When the low-iteration BP decoding stage fails to converge, the rescue stage perturbs the least reliable bits to generate multiple decoding candidates, which are subsequently evaluated using an ML-based metric to select the most likely candidate and reduce miscorrections. The proposed algorithm was evaluated through MATLAB simulations with a short-block LDPC configuration for 5G URLLC systems. QAM modulation was used and two channel models were considered, Additive White Gaussian Noise and flat Rayleigh fading. The performance was investigated for different numbers of perturbed bits and different coding rates. The results show improved decoding performance compared to standard LDPC, achieving coding gains exceeding 1 dB at low bit error rates while reducing decoding failures caused by trapping sets.
It is well known that extremely long low-density parity-check (LDPC) codes perform exceptionally well for error correction applications, short-length codes are preferable in practical applications. However, short-length LDPC codes suffer from performance degradation owing to graph-based impairments such as short cycles, trapping sets and stopping sets and so on in the bipartite graph of the LDPC matrix. In particular, performance degradation at moderate to high Eb/N0 is caused by the oscillations in bit node a posteriori probabilities induced by short cycles and trapping sets in bipartite graphs. In this study, a computationally efficient algorithm is proposed to improve the performance of short-length LDPC codes at moderate to high Eb/N0. This algorithm makes use of the information generated by the belief propagation (BP) algorithm in previous iterations before a decoding failure occurs. Using this information, a reliability-based estimation is performed on each bit node to supplement the BP algorithm. The proposed algorithm gives an appreciable coding gain as compared with BP decoding for LDPC codes of a code rate equal to or less than 1/2 rate coding. The coding gains are modest to significant in the case of optimised (for bipartite graph conditioning) regular LDPC codes, whereas the coding gains are huge in the case of unoptimised codes. Hence, this algorithm is useful for relaxing some stringent constraints on the graphical structure of the LDPC code and for developing hardware-friendly designs.
Belief-propagation (BP) decoding of short and moderate-length low-density parity-check (LDPC) codes is limited by finite-length graph effects: a single decoder trajectory can become trapped or oscillatory even when an alternative trajectory would decode the received word. Existing ensemble-BP decoders create the required diversity through multiple parity-check matrices, automorphisms, modified schedules, subcodes, or altered update rules. We introduce row-boosted ensemble (RBE) decoding as a minimal decoder-side diversity mechanism: all ensemble members share the same parity-check matrix and the same BP kernel, and differ only in a small set of parity-check rows whose outgoing messages are boosted. On the 5G~NR BG1 (144,96)(144,96)(144,96) code, RBE with 323232 members lowers the frame-error rate of BP with 202020 iterations (BP-20) from 1.6×10−21.6\times10^{-2}1.6×10−2 to 1.6×10−31.6\times10^{-3}1.6×10−3 at Eb/N0=4.0 dBE_\mathrm{b}/N_0=4.0\,\mathrm{dB}Eb​/N0​=4.0dB, outperforming saturated-min-sum and affine subcode ensembles of equal size. Increasing the ensemble size yields additional gains, indicating that RBE provides a scalable performance-complexity tradeoff. The gains transfer across 5G~NR block lengths and rates, to non-5G short LDPC codes, and across flooding and layered schedules.
In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.
A weighted belief propagation decoding algorithm for low-density parity-check decoding is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. We propose an early stopping criterion which is based on the average weighted reliability measure of the hard output of decoder to detect undecodable blocks in an early stage of the decoding process. In addition, an adaptive weighted iteration scheme is proposed to increase the convergence speed of belief propagation (BP) decoding and therefore improve the error performance. The evolution of the adaptive weighting factor with the number of decoding iterations is based on the relative entropy between two consecutive ”a posteriori” probabilities distribution at decoder output. Simulation results show that the proposed algorithm can achieve about 0.2-0.4 dB coding gain improvement on average while reducing up to about 50%-85% iterations for decoding at low to medium E(subscript b)/ N(subscript 0) , compared with the conventional BP based algorithms.