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International Conference on Digital Signal and Computer Communications (DSCC)

The optimized sliding window layered decoding algorithm for SC LDPC codes

Jiayi Sun, Xiurong Ma, Yunlong Shan

Published Jul 7, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3071273

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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.
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.
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 (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.
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).
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.