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Informed dynamic scheduling for majority-logic decoding of non-binary LDPC codes

Nanfan Qiu, Wen Chen, Yichao Lu, Yang Yu

Published Dec 1, 2013• 4 citations
Publisher

Abstract

Recent studies show that dynamic scheduling using the latest available information is superior to the flooding scheduling. While the existing works on informed dynamic scheduling focus on belief propagation (BP) based algorithm for binary LDPC codes, in this paper we devise a novel method which is appropriate for majority-logic decoding of non-binary LDPC codes. We firstly clarify that previous methods are not suitable for majority-logic decoding of non-binary LDPC codes. Then we give a practical scheduling strategy which utilizes the stability of check nodes to select the messages for propagation. Furthermore, we discuss the computational complexity of this proposed scheme in detail. Simulation results verify that our approach can achieve better performance compared with layered and flooding schemes.

DOI
10.1109/glocom.2013.6831347

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Recent studies show that dynamic scheduling using the latest available information is superior to the flooding scheduling. While the existing works on informed dynamic scheduling focus on belief propagation (BP) based algorithm for binary LDPC codes, in this paper we devise a novel method which is appropriate for majority-logic decoding of non-binary LDPC codes. We firstly clarify that previous methods are not suitable for majority-logic decoding of non-binary LDPC codes. Then we give a practical scheduling strategy which utilizes the stability of check nodes to select the messages for propagation. Furthermore, we discuss the computational complexity of this proposed scheme in detail. Simulation results verify that our approach can achieve better performance compared with layered and flooding schemes.
Recent studies show that dynamic scheduling using the latest available information is superior to the flooding scheduling. While the existing works on informed dynamic scheduling focus on belief propagation (BP) based algorithm for binary LDPC codes, in this paper we devise novel methods which are appropriate for majority-logic decoding of non-binary LDPC codes. Firstly we propose a low complexity extrinsic message based decoding algorithm for non-binary LDPC codes. The novelty of this decoding algorithm lies in that we compute extrinsic messages and iteratively update the messages in every iteration. Then we propose a dynamic scheduling schemes specifically designed for majority-logic decoding of non-binary LDPC codes. The proposed scheduling method, named informed dynamic scheduling, can achieve better performance compared with the layered and the flooding schemes.
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.
Recently low-density parity check (LDPC) codes have been applied in more areas, and the research of non-binary LDPC codes has become more significant. In this paper, we establish a dynamic scheduling strategy to reduce complexity of non-binary LDPC codes decoding, and choose extended min-sum algorithm as the model. The dynamic scheduling strategy is based on the idea of nodes reliability. When decoding, we select a part of check nodes to update messages in real time according to the reliability rules, and only the variable nodes getting new messages can participate in the message propagation. Compared with usual standard flooding scheduling, this dynamic scheduling strategy can reduce decoding complexity effectively. We also optimize the message of variable nodes according to reliability, which ensure that the error correction performance of decoding algorithm is not affected. Our simulations over a BPSK-AWGN channel show that this dynamic scheduling strategy can reduce complexity in non-binary LDPC codes belief propagation decoding without affecting error correction performance.
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.
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 utterly complex, suboptimal decoders have to be employed. One of the most popular decoding algorithms of LDPC codes is belief propagation (BP) decoding. In this paper, we present a novel scheduling for belief propagation decoding of LDPC codes. The new approach combines probabilistic scheduling with the known shuffled and check-shuffled serial scheduling algorithms. The resulting probabilistic shuffled and probabilistic check-shuffled decoders show a superior performance in terms of residual bit error rate. The drawback is that the convergence speed is slightly decreased. However, the convergence is still faster than for the standard and probabilistic flooding algorithms. Furthermore, we have adapted the probabilistic flooding schedule and the proposed probabilistic shuffled schedule to the non-binary case. We show that the aforementioned effects on the binary decoder can similarly be observed when applying the different schedules to the decoding of LDPC codes over higher order Galois fields.