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IEEE/CIC International Conference on Communications in China (ICCC)

Low-Complexity BP-ORBOSD Algorithm for Short 5G LDPC Codes

Qianfan Wang, Yiwen Wang, Jiayi Yang, Linqi Song, Xiao Ma

Published Aug 10, 2025• 1 citation
Publisher

Abstract

Belief propagation (BP) combined with ordered statistics decoding (OSD) achieves near-optimal frame error rate (FER) for short LDPC codes, but the extensive re-encoding overhead of OSD limits its practicality. To address this, we propose the BPORBOSD, a low-complexity and high-performance decoder that replaces conventional OSD with the ordered reliability bits OSD (ORBOSD), where the test error patterns are produced by the ORB technique. Moreover, in contrast to conventional BP-OSD, which directly adopts the soft information from standard BP into OSD after BP fails, we employ a modified BP scheme with a normalization factor α to produce soft reliability metrics better suited for ORBOSD. We derive the decoder’s complexity and demonstrate that, in the high-SNR regime, the average decoding complexity of BPORBOSD approaches that of standard BP. Simulation results confirm that BP-ORBOSD achieves FERs close to those of conventional BPOSD and the finite-length bound while significantly reducing the average number of re-encodings.

DOI
10.1109/icccworkshops67136.2025.11148135

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Belief propagation (BP) combined with ordered statistics decoding (OSD) achieves near-optimal frame error rate (FER) for short LDPC codes, but the extensive re-encoding overhead of OSD limits its practicality. To address this, we propose the BPORBOSD, a low-complexity and high-performance decoder that replaces conventional OSD with the ordered reliability bits OSD (ORBOSD), where the test error patterns are produced by the ORB technique. Moreover, in contrast to conventional BP-OSD, which directly adopts the soft information from standard BP into OSD after BP fails, we employ a modified BP scheme with a normalization factor α to produce soft reliability metrics better suited for ORBOSD. We derive the decoder’s complexity and demonstrate that, in the high-SNR regime, the average decoding complexity of BPORBOSD approaches that of standard BP. Simulation results confirm that BP-ORBOSD achieves FERs close to those of conventional BPOSD and the finite-length bound while significantly reducing the average number of re-encodings.
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.
Low-density parity-check (LDPC) codes have been widely used in practice due to their excellent error correction capabilities. However, the error correction performance of traditional decoding algorithms for LDPC codes is limited under short block lengths. To address this problem, this paper proposes an effective scheme that contains two stages for decoding short LDPC codes. In the first stage, the traditional belief propagation (BP) iterative algorithm is used to decode an LDPC code. The decoding process terminates if a codeword is obtained in this stage. Otherwise, the second stage decoding is invoked, in which the ordered reliability bits guessing random additive noise decoding (ORBGRAND) algorithm is applied. The accumulated log-likelihood ratios in the first stage are used to order the test error patterns in the ORBGRAND algorithm. Simulation results indicate that the proposed BP-ORBGRAND scheme can outperform the traditional BP iterative algorithm with relatively low additional complexity. Compared with the decoding scheme that concatenates the BP algorithm and the order statistics decoding (OSD) algorithm, the proposed decoding scheme has similar performance and the operations involved can be efficiently implemented in the hardware platform. All these indicate that the proposed scheme is desirable for practical purposes.
This paper proposes a concatenated multi-belief ordered likelihood decoding (MB-OLD) algorithm for rate-compatible (RC) short low-density parity check (LDPC) codes, where the output log-likelihood ratios (LLRs) of belief propagation (BP) are sent to a well-designed bit-flipping decoder, which we called ordered likelihood decoder (OLD). In contrast to conventional ordered statistic decoder (OSD), the test error patterns (TEPs) sequence of OLD is generated from most likely to least likely, where the ordered reliability sequence associated with the most reliable basis (MRB) is approximated as multiple lines, and a stopping criterion (SC) is taken to reduce the decoding complexity. Furthermore, we analyze the LLR behavior of BP decoder in short block-length regimes, and propose an optimal iteration number. Based on these analyses, the output LLRs of BP within the optimal number of iterations are well combined and sent to OLD. Simulation results show that the proposed MB-OLD has the superior decoding performances in terms of error-rate and decoding complexity than its counterparts.
To enhance the performance of short low-density parity-check (LDPC) codes, we introduce an innovative hybrid decoder that seamlessly integrates belief propagation (BP) with ordered statistics decoding (OSD). This hybrid approach initially employs BP to decode received vectors until successful or upon reaching specified conditions, either a maximum iteration limit or a trapping iteration threshold, indicating the stagnation of BP’s hard output. Upon these conditions, the decoder transitions to a pre-configured error pattern (PEP) OSD. The PEPOSD phase then pursues a valid result, flexibly utilizing either the received vectors or the soft values of BP as input, contingent upon the signal-to-noise ratio (SNR). Given the minimal error overlap between BP and OSD, simulations reveal that this hybrid decoder achieves a notable gain of 1.5dB over BP and 0.3-0.6dB over PEPOSD, while maintaining comparable complexity to BP alone.
In this work, we use restricted likelihood information of belief propagation (BP) algorithm to improve the accuracy of sorting in order statistic decoding (OSD) for low-density parity-check (LDPC) codes. The reliability information delivered from the last BP iteration to OSD algorithm is inaccurate because that the propagation information may be enlarged for the existence of girths, thence limitation on iterative information can been applied to improve the OSD decoding performance. Simulation results show that the proposed method is effective.
Belief propagation (BP) combined with ordered statistics decoding (OSD) can achieve near-optimal logical error rates for surface codes. However, OSD requires high-latency and unstable-complexity Gaussian elimination (GE), limiting its practicality. In this paper, we propose BP-LCGCD, a GE-free and high-performance decoder that replaces the GE-based OSD with the GE-free LC-GCD. Moreover, in contrast to the original BP-OSD, which adopts a single fixed normalization factor α, we further propose a list-parameterized variant, BP-LCGCD+ α, which performs multiple BP decodings with different α to generate diverse posterior LLRs. We present complexity analysis, demonstrating that at low physical error rates, the average decoding complexity of the proposed algorithm approaches that of standard BP. Simulation results demonstrate that BP-LCGCD achieves logical error rates close to BP-OSD, while BP-LCGCD+α nearly matches the performance of the BP-OSD. They also show that both proposed decoders significantly outperform standard BP and minimum-weight perfect matching (MWPM) in terms of logical error rate and threshold.