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Effective bi-directional overlapped sliding window decoding of SC-LDPC codes

Jiho Kim, Hyeong‐Gun Joo, Dong‐Joon Shin

Published Nov 16, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1016/j.icte.2023.11.006

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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.
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.
Spatially coupled low-density parity-check (SCLDPC) codes provide excellent performance and low latency under sliding window decoding (SWD). To achieve a low-power and low-complexity SC-LDPC decoder, we propose a variant of SWD called size-λ\lambdaλmonotonic double-ended queue SWD (λ\lambdaλMDQSWD), whereλ\lambdaλrefers to the storage complexity of the update at a check node (CN). Ourλ\lambdaλMDQ-SWD employs the shuffled schedule in SWD and uses the MDQ structure to implement the CN update. Moreover, it considers using only the minimum magnitude from target symbols for the CN update to avoid redundant computations. Simulation results show that, although underλ=2\lambda=2λ=2, the proposed algorithm achieves comparable error correction performance to the state-of-the-art algorithms. Moreover, a detailed hardware implementation for the CN update is designed. Analysis using the 90 nm CMOS technology library shows that, compared to the state-of-the-art algorithms, theλ\lambdaλMDQ-SWD withλ=2\lambda=2λ=2reduces the area and increases the clock frequency of CN update by 63.7 % and 107.6 %, respectively.
This study investigates the Layered Sliding Window Decoding (LSWD) algorithm for Spatially Coupled Low-Density Parity-Check (SC LDPC) codes and proposes an enhanced decoding approach, the Improved Sliding Window Layered Decoding (ILSWD). While the LSWD algorithm reduces decoding latency and iteration counts compared to traditional Sliding Window Decoding (SWD), it does not significantly improve decoding performance. To address this, the ILSWD algorithm incorporates dynamic sliding window techniques, reorganizes decoding layers, and intro-duces suppression factors when errors enter the extended sliding window. Simulation results for 5G SC LDPC codes with single-sided coupling demonstrate that ILSWD achieves a 0.25 dB gain over LSWD at a specific bit error rate, alongside a notable improvement in decoding iteration rate. These findings highlight that ILSWD overcome the limitations of LSWD, offering a more efficient decoding solution with enhanced performance for SC LDPC codes in 5G applications.
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.
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.
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.