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arXiv:2305.05286 · IEEE Transactions on Communications

Check-Belief Propagation Decoding of LDPC Codes

Wu Guan, Liping Liang

Published Aug 24, 2023• 16 citations
arXivHTMLPDF

Abstract

Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.

DOI
10.1109/tcomm.2023.3308155

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Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.
Reliability-based belief propagation (RBP) decoding algorithms are used to decode low-density parity-check (LDPC) codes. However, due to the reliability of comparing and sorting in traditional algorithms, conventional RBP decoders significantly lose in resource consumption. This letter presents an enhanced reliability list-based check-belief propagation (RL-CBP) algorithm. The RL-CBP algorithm reduces computational complexity by scheduling a concise list of check-beliefs. Moreover, the list is applied for comparisons and selections of check-beliefs. The selected check-belief transforms the decoding message between edges; all check-beliefs are iteratively enlarged according to the reliabilities, and high-performance decoding will be achieved. The simulation results and analyses show that the proposed method achieves a reliability-list gain compared with the check-belief propagation (CBP) algorithm but consumes much fewer calculations than the traditional RBP algorithm.
This paper proposes a two-stage iterative decoding scheme named matrix transform belief propagation scheme (MT-BP) based on conventional belief propagation (BP) algorithm for lowdensity parity-check (LDPC) codes.By introducing information measurement, location vectors and parity check matrix transform, the proposed method can establish additional parity check equations and take more information bits of variable nodes into consideration compared with conventional BP algorithm.The simulations are performed on random regular LDPC codes and algebraic quasi-cyclic codes (QC-LDPC), the experimental results show MT-BP method can efficiently reduce the bit error rate (BER).
We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.
For the scenarios with high throughput requirements, the belief propagation (BP) decoding is one of the most promising decoding strategies for polar codes. By pruning the redundant variable nodes (VNs) and check nodes (CNs) in the original factor graph, the graph is condensed to a sparse bipartite graph which is similar to the graph for low-density parity-check (LDPC) codes. In this paper, we introduce the bit-flipping scheme into the LDPC-like BP (L-BP) decoding and propose two methods to identify the error-prone VNs. By additional decoding attempts, the L-BP flip (L-BPF) decoding improves the error-rate performance with a similar average complexity for high Eb=N0values. The simulation results show that the L-BPF decoding achieves 0:25 dB gain compared with the L-BP decoding.
Two methods are proposed to reduce the complexity of the belief propagation (BP) decoding for low-density parity-check (LDPC) codes, with the focus on the layered decoding for quasi-cyclic LDPC (QC-LDPC) codes. The two methods can be separately incorporated into the layered decoding procedures and combined seamlessly to provide the two-fold complexity reduction. In the first method, the message updates regarding a subset of variable nodes are omitted. To construct the subset, the most reliable bit-level channels, derived fromM-ary input channels, are identified. Then, we select the variable nodes with initial log-likelihood ratios (LLRs) exceeding a threshold among the ones assigned to the most reliable bit-level channels to form the subset. The threshold is designed and adjusted based on characteristics of the most reliable bit-level channels. Our numerical results demonstrate that the first method significantly reduces the complexity with negligibly impacting the error-correcting performance. In the second method, each layer of base graphs of QC-LDPC codes uses either sum-product algorithm (SPA) or min-sum algorithm (MSA) to update LLRs. A degree-based algorithm is presented to determine the layers employing either SPA or MSA. We compare with two intuitive methods: 1) applying SPA to randomly selected layers and MSA to the remaining layers, and 2) applying SPA to the core layers of 5G NR LDPC codes and MSA to the remaining layers. According to the numerical results, the degree-based algorithm maximally reduces the complexity while maintaining the same performance. To evaluate the joint method, the first method is applied on top of the second method. Further complexity reduction is achieved without degrading the performance of the second method.
In this paper, a modification to belief propagation (BP) decoding algorithm is proposed, which is based on extracting the prior messages of each variable node to help the BP decoding, and is particularly effective for low-density parity-check (LDPC) codes with short cycles, where the existence of cycles makes the original BP algorithm perform suboptimal.The proposed algorithm, referred to as "employing the positive effects of the feedback messages (EPEFM)", extracts the positive effects of the feedback messages and then makes use of them as prior messages to assist the decoding of the BP algorithm.Simulation results confirm the effectiveness of our proposed algorithm, which improves the performance in high signal-to-noise-ratio (SNR) region without loss in low SNR region.