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IEEE Globecom Workshops (GC Wkshps)

The Hybrid Decoder of Belief Propagation and Ordered Statistics Decoding for LDPC Codes

Xuanyu Li, Kai Niu, Yuxin Han

Published Dec 8, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/gcwkshp64532.2024.11101127

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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.
For high rate LDPC codes with light column weight and few redundant checks in their parity check matrix, the belief propagation (BP) decodings yield good error performance at the cost of high complexity. Aiming at seeking a effective decoder with good performance versus complexity tradeoff for this kind of LDPC codes, we present a new decoding framework which cascades a bit flipping (BF) variant with the ordered statistic decoding (OSD). During the iterative decoding of BF variant, the flipping value for each codeword bit is summed. The summation for each bit will be utilized as the reliability input for the OSD postprocessing, if no valid codeword is found after the maximum number of iterations for the BF variant is reached. With respect to the BP, simulation results show that the proposed BF-OSD achieves comparable performance with much less complexity.
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.
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.
A hybrid belief propagation (BP) decoding algorithm for low-density parity-check code is proposed to accelerate the convergence of decoding and reduce the number of decoding iterations. The hybrid scheme is presented by integrating the BP algorithm with the bit-flipping function which is used as adaptive weighted factor in the BP iteration decoding. The adaptive weighting factor is based on the average weighted reliability measure of the hard output of decoder. The proposed hybrid adaptive weighted iteration scheme can efficiently increase the convergence speed of the belief propagation decoding and therefore improve the error performance. Simulation results show that the proposed algorithm can significantly reduce the decoding complexity and achieve better error performances as compared with the sum-product algorithm.
This article deals with Ordered Statistics Decoding (OSD) applied to the soft outputs of the Belief Propagation (BP) algorithm. We first model the weighted sum of the a posteriori LLRs across BP decoding iterations into a neuron. The neuron is then trained with the focal loss to compute for each BP decoding failure a set of accumulated Log Likelihood Ratios (LLRs) suited for OSD post-processing. Then, we propose a recursive selection procedure of LLRs sets, for multiple OSD post-processing. This selection is carried out from the sets of a posteriori LLRs calculated at each BP iteration, and from the accumulated LLRs optimized for the OSD, based on their joint probabilities of failure with OSD post-processing. An OSD is then applied to each set of LLRs belonging to the selection. In addition, we propose to reduce the OSD post-processing decoding complexity without significantly degrading its performance. Our results show that this new decoding method provides an effective way to bridge the gap to maximum likelihood decoding for short and long Low Density Parity Check (LDPC) codes.