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IEEE Information Theory Workshop (ITW)

Adaptive Doping of Spatially Coupled LDPC Codes

Min Zhu, David G. M. Mitchell, Michael Lentmaier, Daniel J. Costello

Published Apr 11, 2021• 8 citations
Publisher

Abstract

In this paper, we study the problem of error propagation in sliding window decoding (SWD) of spatially coupled LDPC (SC-LDPC) codes. A general decoder model that accounts for error propagation is proposed and analyzed, and the decoded block error rate (BLER) is calculated using the model. In order to improve the BLER performance under decoder error propagation conditions, adaptive variable node (VN) doping is proposed, assuming a noiseless binary feedback channel is available. Example calculations using the proposed model, as well as numerical simulation results, are used to show that adaptive VN doping improves the BLER performance compared to the periodic VN doping and to the undoped case.

DOI
10.1109/itw46852.2021.9457651

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In this paper, we study the problem of error propagation in sliding window decoding (SWD) of spatially coupled LDPC (SC-LDPC) codes. A general decoder model that accounts for error propagation is proposed and analyzed, and the decoded block error rate (BLER) is calculated using the model. In order to improve the BLER performance under decoder error propagation conditions, adaptive variable node (VN) doping is proposed, assuming a noiseless binary feedback channel is available. Example calculations using the proposed model, as well as numerical simulation results, are used to show that adaptive VN doping improves the BLER performance compared to the periodic VN doping and to the undoped case.
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.
Due to their capacity achieving performance with sliding window decoding (SWD), spatially coupled LDPC (SC-LDPC) codes are emerging as candidates for next generation channel coding applications. In this paper we present a general model of SWD of SC-LDPC codes and develop an analysis that allows us to estimate error probability performance under decoder error propagation conditions that can occur when low latency operation is desired. We also show how the model parameters can be estimated and indicate how the model can be used to predict the performance of code doping techniques used to mitigate the effects of decoder error propagation.
Spatially Coupled Low-Density Parity-Check (SCLDPC) codes are characterized by very long codeword lengths. For this reason, they are usually decoded with sliding window algorithms, which allow piecewise processing and decoding of the codeword symbols. In order to mitigate error propagation, it is possible to adapt strategies, such as non-uniform window sizes and node doping. In this paper, we propose a novel adaptive decoding schedule, which can be integrated with the aforementioned strategies. Numerical results confirm that the proposed approach can successfully detect error propagation events with more accuracy than conventional log-likelihood ratio-based approaches. Simulation results show that the error rate performance of time-invariant SC-LDPC codes significantly improves when the proposed strategies are adopted.
We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.
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 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.