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International Workshop on Signal Design and its Applications in Communications

Reduced complexity-and-latency variable-to-check residual belief propagation decoding algorithms for LDPC codes

Jung Hyun Kim, Hong‐Yeop Song

Published Oct 1, 2009• 1 citation
Publisher

Abstract

This paper proposes some new improved versions of node-wise VCRBP algorithm, called forced-convergence node-wise VCRBP and sign-based node-wise VCRBP, both of which significantly reduce the decoding complexity and latency, with only negligible deterioration in error correcting performance.
DOI
10.1109/iwsda.2009.5346442

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We propose Variable-to-Check Residual Belief Propagation (VCRBP) for LDPC decoding for faster convergence, better error correcting performance and lower complexity. It is similar to Residual Belief Propagation (RBP) that was recently applied to LDPC decoding by Vila Casado et al. because it is also a dynamic scheduling belief propagation using residuals, but it is different because its residuals are computed from variable-to-check message. Simulation shows that it out-performs with only maximum 8 iterations by about 0.3 dB compared with RBP at an FER of 10-4. Also, we propose node-wise VCRBP (N-VCRBP) for reducing complexity of VCRBP. N-VCRBP also exhibits the performance very close to VCRBP but with significantly lower decoding complexity.
A new strategy of belief propagation (BP) decoder for LDPC codes is presented by sequentially concatenating the scheduling algorithms of flooding and node-wise residual belief propagation (NW RBP) without increasing the complexity of hardware implementation. Compared to NW RBP, the concatenated BP decoder significantly decreases the decoding latency caused by computing and sorting the residual of each message in the factor graph of an LDPC code. As the signal-to-noise ratio (SNR) increases, the decoding performance of the concatenated BP decoder outperforms that of purely applying flooding or NW RBP, and the average number of decoding iterations required for the concatenated decoder decreases and tends to be approximately the same as the other two.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
Belief-propagation (BP) algorithm and its variants are well-established methods for iterative decoding of LDPC codes. Among them, residual belief-propagation (RBP), which is the most primitive and representative informed dynamic scheduling (IDS) strategy, can significantly accelerate the convergence speed. However, RBP decoding suffers from a poor convergence error-rate performance due to its greedy property, which is one of the challenging issues in the design of IDS strategies. To tackle this problem, a novel IDS scheme, namely residual-decaying-based residual belief-propagation (RD-RBP) algorithm, is presented in this paper. In RD-RBP, a decaying mechanism is introduced to manipulate the residuals of those check-to-variable messages, preventing the decoding resources from being unreasonably occupied by a small group of edges in the Tanner graph. The greediness is therefore alleviated and better performance of convergence error-rate is achieved. Besides, a two-stage scheduling scheme combining prior-art variable-node and variable-to-check-edge RBP (V-VCRBP) with RD-RBP, named V-VC-RD-RBP, is proposed for achieving both fast convergence speed and a low convergence error-rate. The simulation results validate the advantages of the proposed schemes.
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.