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arXiv:1805.02902 · IEEE Communications Letters

Reliability-Based Windowed Decoding for Spatially Coupled LDPC Codes

Peng Kang, Yixuan Xie, Lei Yang, Jinhong Yuan

Published May 11, 2018• 21 citations
arXivHTMLPDF

Abstract

In this letter, we propose a reliability-based windowed decoding scheme for spatially coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial message reservation method is proposed where only the reliable messages generated in the previous decoding window are reserved for the next decoding window. We also propose a partial syndrome check stopping rule for each decoding window, in which only the complete variable nodes are checked. Simulation results show that our proposed scheme significantly improves the error-floor performance compared to the sliding windowed decoder with the conventional weighted bit-flipping algorithm.

DOI
10.1109/lcomm.2018.2835466

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In this letter, we propose a reliability-based windowed decoding scheme for spatially coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial message reservation method is proposed where only the reliable messages generated in the previous decoding window are reserved for the next decoding window. We also propose a partial syndrome check stopping rule for each decoding window, in which only the complete variable nodes are checked. Simulation results show that our proposed scheme significantly improves the error-floor performance compared to the sliding windowed decoder with the conventional weighted bit-flipping algorithm.
In this paper, a bi-directional sliding window decoder is proposed for spatially coupled low-density parity-check (SC-LDPC) codes, which improves the decoding complexity and performance compared to the conventional sliding window decoding (SWD) by sharing messages at the overlapped part of forward and backward decoding windows. Moreover, by using proper scaling factors that determine the weight of each message at the overlapped part of two sliding windows, good local decoding effects can be efficiently spread out to both ends of SC-LDPC code during decoding process. Such effective message updates of the proposed bi-directional overlapped sliding window decoding (BO-SWD) improve error floor performance compared to the conventional SWD. The validity of BO-SWD is verified by simulation with various SC-LDPC ensembles.
In this paper, we investigate the problem of decoder error propagation for spatially coupled low-density parity-check (SC-LDPC) codes with sliding window decoding (SWD). This problem typically manifests itself at signal-to-noise ratios (SNRs) close to capacity under low-latency operating conditions. In this case, infrequent but severe decoder error propagation can sometimes occur. To help understand the error propagation problem in SWD of SC-LDPC codes, a multi-state Markov model is developed to describe decoder behavior and to analyze the error performance of spatially coupled LDPC codes under these conditions. We then present two approaches -check node (CN) doping and variable node (VN) doping -to combating decoder error propagation and improving decoder performance. Next we describe how the performance can be further improved by employing an adaptive approach that depends on the availability of a noiseless binary feedback channel. To illustrate the effectiveness of the doping techniques, we analyze the error performance of CN doping and VN doping using the multi-state decoder model. We then present computer simulation results showing that CN and VN doping significantly improve the performance in the operating range of interest at a cost of a small rate loss and that adaptive doping further improves the performance. We also show that the rate loss is always less than that resulting from encoder termination and can be further reduced by doping only a fraction of the VNs at each doping position in the code graph with only a minor impact on performance. Finally, we show how the encoding problem for VN doping can be greatly simplified by doping only systematic bits, with little or no performance loss.
In this paper, an efficient encoding scheme for spatially coupled low-density parity-check (SC-LDPC) codes is proposed. In order to lower the error floor, we optimize the degree distribution of SC-LDPC codes and propose a split variable nodes algorithm constructing sub-matrices with large girth of SC-LDPC codes. The corresponding sliding window decoding is studied as well to fasten the decoding convergence. Simulation results show that on the AWGN channel, SC-LDPC codes can obtain better error performance, lower decoding complexity and faster decoding convergence as compared with the LDPC block codes (LDPC-BC).
In this paper, we address a number of weaknesses of the windowed decoding of spatially coupled low-density parity-check (SC LDPC) codes and propose three modifications that simultaneously improve its performance, complexity, and latency. An effective termination method of the windowed decoding and the reuse of edge messages of previous target symbols provide a good performance-latency tradeoff when compared with the conventional windowed decoder. Also, we propose a scheme that lowers the error floor, in which the amplified edge messages of the previous window are used in the present window. The proposed windowed decoding, consisting of the three schemes, provides a significant performance gain with smaller latency. The validity of the new windowed decoding is verified by the evaluation with codes from different SC LDPC ensembles.
Spatially coupled low-density parity-check (SC-LDPC) codes can achieve capacity approaching performance with a small message recovery latency due to the sliding window decoding (SWD). Using a partial Tanner graph, the SWD performs iterative message passing until the average error probability Peof the target symbols falls below a threshold or the maximum iteration number is reached. However, Pedoes not decrease monotonically as iteration progresses. This implies the symbol likelihoods that were yielded when the decoding terminates may not be optimal for making decisions. Therefore, this paper proposes an improved SWD (ISWD) for SC-LDPC codes. The proposal monitors the achievable minimum of Peand stores its associated likelihoods, so that when the decoding terminates the target symbols will be estimated based on the stored likelihoods. Our research shows the ISWD is able to enhance the decoding performance, especially in the waterfall region. It exhibits an asymptotic convergence to the SWD performance. A complexity reducing variant of the ISWD is also proposed to facilitate the decoding but at the cost of error-correction performance.
Windowed decoding (WD) based on the belief propagation (BP) algorithm, which slides along a code chain with fixed computational resources, is an efficient decoding scheme for spatially-coupled low-density parity-check (SC-LDPC) codes, particularly for long-length codes. However, due to the lack of decoding waves, WD suffers from a performance degradation compared to full BP decoding. In this paper, we propose a novel decoding schedule for WD, termed dual-WD, which enhances the decoding waves by dynamically merging and splitting two decoding windows that slide in opposite directions. Moreover, a sliding-step selection method based on partial syndrome checks is introduced to reduce decoding complexity. Simulation results demonstrate that the proposed dual-WD outperforms the conventional WD schemes under identical computational complexity constraints, thereby narrowing the performance gap between WD and full BP decoding.