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IET Communications

Informed shuffled belief‐propagation decoding for low‐density parity‐check codes

Yi Gong, Xingcheng Liu, Guojun Han, Bin Wu

Published Nov 18, 2015• 0 citations
Publisher

Abstract

Shuffled belief propagation (SBP), as a sequential belief propagation (BP) algorithm, speeds up the convergence of BP decoding, and maintains the least complexity of flooding BP. However, its performance is remarkably inferior to informed dynamic scheduling (IDS) BP algorithms. The authors design an informed dynamic location method, based on the residuals of variable node log‐likelihood ratio values, to reorder variable nodes of SBP to be updated. The location method significantly accelerates the convergence of SBP algorithm from two aspects: the unstable variable node with the largest residual to be updated first, and selecting the largest residual locally. Simulation results show that the proposed algorithm performs nearly the same as the best performance of IDS BP algorithms, and behaves prominently at high signal‐to‐noise ratios.

DOI
10.1049/iet-com.2014.1169

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Shuffled belief propagation (SBP), as a sequential belief propagation (BP) algorithm, speeds up the convergence of BP decoding, and maintains the least complexity of flooding BP. However, its performance is remarkably inferior to informed dynamic scheduling (IDS) BP algorithms. The authors design an informed dynamic location method, based on the residuals of variable node log‐likelihood ratio values, to reorder variable nodes of SBP to be updated. The location method significantly accelerates the convergence of SBP algorithm from two aspects: the unstable variable node with the largest residual to be updated first, and selecting the largest residual locally. Simulation results show that the proposed algorithm performs nearly the same as the best performance of IDS BP algorithms, and behaves prominently at high signal‐to‐noise ratios.
The simultaneous flooding scheduling is popular for Low-Density Parity-Check (LDPC) Belief Propagation (BP) decoding. Non-simultaneous sequential scheduling is superior to the flooding scheduling, and asynchronous dynamic scheduling has better FER performance than the sequential scheduling. However, all strategies encounter the trouble of locating the error variable node. This paper proposes an informed dynamic scheduling strategy, which utilizes the instability of the variable node and the residual of the variable-to-check message to locate the message to be updated first. The informed dynamic scheduling overcomes the trapping sets effectively. This paper also designs an informed dynamic scheduling strategy with adaptivity to pass more messages in parallel, which effectively postpones the influence of cycles in the Tanner graph. In some sense, the strategy lengthens cycles. Simulation results show that the two informed dynamic scheduling strategies outperform other algorithms.
The simultaneous flooding scheduling is popular for Low-Density Parity-Check (LDPC) Belief Propagation (BP) decoding. Non-simultaneous sequential scheduling is superior to the flooding scheduling, and asynchronous dynamic scheduling has better FER performance than the sequential scheduling. However, all strategies encounter the trouble of locating the error variable node. This paper proposes an informed dynamic scheduling strategy, which utilizes the instability of the variable node and the residual of the variable-to-check message to locate the message to be updated first. The informed dynamic scheduling overcomes the trapping sets effectively. This paper also designs an informed dynamic scheduling strategy with adaptivity to pass more messages in parallel, which effectively postpones the influence of cycles in the Tanner graph. In some sense, the strategy lengthens cycles. Simulation results show that the two informed dynamic scheduling strategies outperform other algorithms.
Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation (BP), or message-passing, algorithm over the factor graph of the code. The traditional message-passing scheduling, called flooding, consists of updating all the variable nodes in the graph, using the same pre-update information, followed by updating all the check nodes of the graph, again, using the same pre-update information. Recently, several studies show that sequential scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. Sequential scheduling introduces the problem of finding the best sequence of message updates. We propose Informed Dynamic Scheduling (IDS) strategies that select the message-passing schedule according to the observed rate of change of the messages. In general, IDS strategies require computation to select the message to update but converge in fewer message updates because they focus on the part of the graph that has not converged. Moreover, IDS yields a lower error-rate performance than either flooding or sequential scheduling because IDS strategies overcome traditional trapping-set errors. This paper presents IDS strategies that address several issues including performance for short-blocklength codes, complexity, and implementability.
A novel informed fixed scheduling (IFS) scheme for shuffled belief-propagation (BP) decoding of binary low-density parity-check (LDPC) code is introduced to improve the BP decoding convergence. The IFS finds an appropriate order of variable nodes in accordance with the number of updated neighbors in the code graph, ensuring that the maximum number of latest message updates is utilized within a single iteration. This allows the utilization of most reliable message updates in a timely manner, leading to faster error-rate convergence. Simulation results show that the proposed IFS scheme improves the convergence speed of BP decoder by up to 20% for regular LDPC codes and 45% for irregular LDPC codes, without affecting the error-rate performance, at medium-to-high signal-to-noise ratio over binary-input additive white Gaussian noise channel.
A new decoding strategy of belief propagation (BP) for low‐density parity‐check codes is presented by serially concatenating the traditional simultaneous decoding (also known as flooding) and the informed dynamic decoding (IDD) (e.g. node‐wise residual belief propagation (NW RBP) or informed variable‐to‐check (IVC) RBP). The frame error rates (FER) and bit error rates (BER) of the concatenated BP decoder outperform that of the non‐concatenated single decoder. In addition, as the signal‐to‐noise ratio (SNR) increases, the average number of decoding iterations required for the concatenated BP decoder decreases, and tends to merge with that of the first sub‐decoder in the high SNR region. Moreover, since the IDD strategies concerned in this paper require extra effort for the residual computation, and the sequential updating of IDD is much more time consuming than the simultaneous updating of flooding. Therefore, compared with using a single IDD, serially concatenating flooding and IDD reduces both the approximate decoding complexity and the decoding latency because the concatenated decoder is still dominated by the sub‐decoder flooding.
This paper proposes an improved variable-to-check residual belief propagation algorithm, called Lazy-RBP, in which a new informed dynamic schedule (IDS) combined with the lazy schedule (LS) is adopted. Firstly, Lazy-RBP exploits the probabilistic girth-based approach, one of the LS strategies, to decide the set of updated variable nodes in each iteration. Then among this set, a new IDS scheme is introduced, where both the unreliable variable nodes and the residual of the variable-to-check messages are utilized to locate the message to be propagated first. Simulation results show that the Lazy-RBP algorithm can not only improve the error performance but accelerate the convergence compared with the VC-RBP algorithm.