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IET Communications

Serially concatenated belief propagation decoder for low‐density parity‐check codes

Hua Ren Zhou, Erbao Li, Jing Lei

Published Jul 17, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1049/iet-com.2016.1318

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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.
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.
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.
Abstract Among numerous dynamic scheduling strategies for low‐density parity‐check codes, many of them are of high complexity due to repetitive computation and ordering of belief residuals. To address these challenges, two novel approaches are proposed: the derived informed variable‐to‐check residual belief propagation and the derived variable‐node and variable‐to‐check‐edge residual belief propagation for low‐density parity‐check codes. Simulation results show that the derived dynamic scheduling exhibits a substantial gain of approximately 0.15 dB in signal‐to‐noise ratio over the non‐derived one with considerably lower decoding complexity when targeting a bit‐error rate of 10 −4 .
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.
Compared to classic channel coding,Low-density parity-check(LDPC) codes have proved to be very powerful channel coding schemes with a broad range of applications.However,as maximum-likelihood decoding is too complex to implement,suboptimal decoders have to be employed.One of the most popular decoding algorithms of LDPC codes is belief propagation(BP) decoding.Informed Dynamic Scheduling(IDS) can provide a better BER performance,but hard to implement due to high computational complexity increased.In order to improve the convergence,a simple low-complexity sequential check-node-based scheduling strategy is proposed.A new check-node-based reliability measure is defined,which represents the degree of reliability approximately.The reliability measure is used for ordering while the actual message updates still use the exact BP equations.During an iteration,the schedule strategy finds an update sequence,which is arranged by the new defined reliability measure in ascending order.Complexity is compared among those algorithms.Mechanism why the new strategy works effective is presented.Simulation shows that the new approach significantly improves the BER performance using short-length block LDPC codes and reduces iterations.
Four reliability-based high-efficient dynamic schedules (RHDS) for belief propagation (BP) decoding of low-density parity-check codes are proposed. The RHDS only processes one variable (or check) node, which has the maximum relative residual among all the variable (or check) nodes in each decoding iteration, thus keeping less greediness and decreasing complexity in comparison with egde-wise variable-to-check residual belief propagation (VC-RBP) algorithm. Simulation results show that RHDS's convergence rate is higher than VC-RBP while still keeping very low computational complexity.