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International Symposium on Wireless Communication Systems

Weighted Residual Layered Belief Propagation for LDPC Decoding

Hassan Touati, Rodrigo C. de Lamare

Published Jul 14, 2024• 1 citation
Publisher

Abstract

In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief propagation (WR-LBP) decoding algorithm, which exploits the residual within a structured layer framework to speed the number of required decoding iterations. The proposed WR-LBP algorithm is assessed against important LDPC decoding algorithms, in terms of the number of iterations required for convergence and the bit error rates.

DOI
10.1109/iswcs61526.2024.10639097

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In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief propagation (WR-LBP) decoding algorithm, which exploits the residual within a structured layer framework to speed the number of required decoding iterations. The proposed WR-LBP algorithm is assessed against important LDPC decoding algorithms, in terms of the number of iterations required for convergence and the bit error rates.
In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief propagation (WR-LBP) decoding algorithm, which exploits the residual within a structured layer framework to speed the number of required decoding iterations. The proposed WR-LBP algorithm is assessed against important LDPC decoding algorithms, in terms of the number of iterations required for convergence and the bit error rates.
An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
Low-density parity-check (LDPC) codes have been chosen for the fifth-generation (5G) new radio (NR) enhanced Mobile Broad Band (eMBB) data channel. Since NR LDPC codes puncture the first two block columns of the parity-check matrix, the decoding complexity is reduced, but it slows down the convergence rate. In this letter, we propose a fixed schedule that decodes the layers with the least-punctured edges and those with the highest-degree (LPHD), which has much faster convergence speed than conventional schemes. The fixed scheduling schemes cannot take full advantage of the dynamic changes of decoding messages. As a result, the residual-based layered belief propagation (RB-LBP) is proposed to rearrange the layers dynamically among different iterations. Compared with some informed dynamic scheduling (IDS) strategies, RB-LBP reduces the decoding complexity with slight performance loss.
Layered belief-propagation (LBP) with dynamic schedule for low-density parity-check (LDPC) codes using variable nodes residual is presented. The proposed schedule outperforms the conventional LBP with predetermined schedule both in terms of convergence speed and error performance. As compared with node-wised residual belief-propagation (NRBP), it has much lower extra complexity. For LDPC code constructed by PEG, simulation results show that the new schedule offers better error performance and requires much lower extra complexity.
Reliability-Based-Layered Belief Propagation (RBL-BP) decoding algorithm for LDPC codes is proposed in this paper. Being an informed dynamic schedule (IDS), it measures convergence and selects iterations by the absolute value of logarithmic likelihood ratio information obtained from channel (ABS-LLR-CH). Each variable node can select its own iterations by estimating its own convergence, and finish iterative decoding. Simulation results show that the proposed RBL-BP algorithm has better performance than those of flooding schedule, layered belief propagation (LBP) and variable-to-check residual belief propagation (VC-RBP). For the convergence property of IDS, the proposed algorithm has faster speed than those of flooding schedule and LBP with a little increase in complexity while it has almost no speed decrease with much lower computational complexity than VC-RBP.
Beside the well known iterative Belief Propagation algorithm several alternative decoding schemes for Low-Density Parity-Check (LDPC) codes providing better performance in terms of residual error rate, convergence speed or computational complexity have been developed in the last years. Recently, Informed Dynamic Scheduling has been proposed in [1] providing different decoding strategies that dynamically decide which messages are passed throughout the decoding process. It was shown that the overall convergence can be sped up considerably and also more errors can be corrected compared to other (non-dynamic) decoding strategies. However, these improvements are somehow overshadowed by a significant amount of additional computational complexity that is needed for the selection of the messages to be updated in each decoding step. We propose two novel dynamic decoding strategies that allow for a flexible adaptation of the decoder's dynamics and reduce the additional complexity remarkably while maintaining, and in some cases even exceeding, the convergence speed and error rate performance of currently known dynamic schedules.