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IEEE Transactions on Broadcasting

Sliding Window Decoding for QC-SC-LDPC Codes Under the Constraint of Implementation Complexity

Zhitong He, Kewu Peng, Jian Song, Yushu Zhang

Published Jan 24, 2022• 10 citations
Publisher

Abstract

Sliding window decoding has been employed as the decoding scheme of quasi-cyclic spatially-coupled low-density parity-check (QC-SC-LDPC) codes, with the decoding latency and complexity independent of the coupling length but proportional to the window size. The window size was empirically chosen at least three times the constraint length in previous works, which results in the preference of QC-SC-LDPC codes with small constraint length, to reduce the decoding latency and complexity in practical systems. However, the code design freedom and the decoder throughput are limited for these QC-SC-LDPC codes. In this paper, the optimal window size under the constraint of practical decoding complexity is analyzed employing multi-edge-type density evolution (MET-DE). It can be verified from the MET-DE analytical result that the optimal window size could achieve less than twice the constraint length for several edge spreading patterns, which largely loose this restriction in practical code design. Furthermore, it could be observed that besides the constraint length, the specific structure of the edge spreading pattern could affect the optimal window size as well, and thus the MET-DE analytical method for the optimal window size could effectively guide the design of QC-SC-LDPC codes in practical systems. Then an improved sliding window decoding scheme is proposed, including the optimal choice of window size and a parity-check based early termination scheme. Finally, the performance and robustness of the proposed sliding window decoding scheme for QC-SC-LDPC codes are demonstrated via simulation, with the decoding complexity at most twice as that of the conventional LDPC coded schemes.

DOI
10.1109/tbc.2022.3143367

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Sliding window decoding has been employed as the decoding scheme of quasi-cyclic spatially-coupled low-density parity-check (QC-SC-LDPC) codes, with the decoding latency and complexity independent of the coupling length but proportional to the window size. The window size was empirically chosen at least three times the constraint length in previous works, which results in the preference of QC-SC-LDPC codes with small constraint length, to reduce the decoding latency and complexity in practical systems. However, the code design freedom and the decoder throughput are limited for these QC-SC-LDPC codes. In this paper, the optimal window size under the constraint of practical decoding complexity is analyzed employing multi-edge-type density evolution (MET-DE). It can be verified from the MET-DE analytical result that the optimal window size could achieve less than twice the constraint length for several edge spreading patterns, which largely loose this restriction in practical code design. Furthermore, it could be observed that besides the constraint length, the specific structure of the edge spreading pattern could affect the optimal window size as well, and thus the MET-DE analytical method for the optimal window size could effectively guide the design of QC-SC-LDPC codes in practical systems. Then an improved sliding window decoding scheme is proposed, including the optimal choice of window size and a parity-check based early termination scheme. Finally, the performance and robustness of the proposed sliding window decoding scheme for QC-SC-LDPC codes are demonstrated via simulation, with the decoding complexity at most twice as that of the conventional LDPC coded schemes.
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW) decoding. An SC-LDPC code constructed from a protograph can be generated by first coupling a chain of block protographs and then lifting the coupled protograph using permutation matrices. This paper introduces a systematic design of SC-LDPC codes to eliminate 4-cycles in the coupled photograph. Using a quasi-cyclic (QC) lifting, we obtain QC-SC-LDPC codes of girth at least eight. Coupling a chain of block protographs implies spreading edges from one protograph to the others. Our protograph-based design can be viewed as guiding the edge spreading and also the graph-lifting process. Simulation results show the design leads to improved decoding performance, particularly in the error floor, compared to random designs.
Spatially coupled (SC) low-density parity-check (LDPC) codes can achieve capacity approaching performance with low message recovery latency when using sliding window (SW) decoding. An SC-LDPC code constructed from a protograph can be generated by first coupling a chain of block protographs and then lifting the coupled protograph using permutation matrices. In this paper, we introduce a systematic design to eliminate 4-cycles in a coupled protograph. Further using a quasi-cyclic (QC) lifting, we introduce a procedure for constructing QC-SC-LDPC codes of girth at least eight. This can be interpreted as a multi-stage graph lifting process that yields a greater flexibility in designing QC-SC-LDPC codes with a large girth than previous approaches. Simulation results show the design leads to improved decoding performance, particularly in the error floor, compared to random constructions. Finally, we determine the minimum coupling width required to eliminate 4-cycles in a coupled protograph.
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.
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 (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.