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International Conference on Cloud Computing and Big Data Analytics (ICCCBDA)

Layered Bit-Flipping Algorithms for Decoding LDPC Codes

Fangxia Luo, Xuan He, Jiongyue Xing, Xiaohu Tang

Published Apr 22, 2022• 3 citations
Publisher

Abstract

At present, various communication and storage systems have put forward high requirements on both the complexity and performance of low-density parity-check (LDPC) decoders. Bit flipping decoders are a good candidate for these applications. This letter proposes to utilize the column layered scheduling to speed up the convergence and improve the error correcting performance of existing bit flipping algorithms. As the information storage bit flipping (ISBF) algorithm generally performs the best, we investigate the layered ISBF (LISBF) algorithm in detail, including developing two efficient techniques for optimizing the computation of flipping thresholds: forward-backward computation and two-max computation. Simulation results on a (3, 6) LDPC code show that, compared to the ISBF algorithm, the LISBF algorithm can reduce the frame error rate by up to an order and reduce the average number of iterations by around 40%.

DOI
10.1109/icccbda55098.2022.9778904

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At present, various communication and storage systems have put forward high requirements on both the complexity and performance of low-density parity-check (LDPC) decoders. Bit flipping decoders are a good candidate for these applications. This letter proposes to utilize the column layered scheduling to speed up the convergence and improve the error correcting performance of existing bit flipping algorithms. As the information storage bit flipping (ISBF) algorithm generally performs the best, we investigate the layered ISBF (LISBF) algorithm in detail, including developing two efficient techniques for optimizing the computation of flipping thresholds: forward-backward computation and two-max computation. Simulation results on a (3, 6) LDPC code show that, compared to the ISBF algorithm, the LISBF algorithm can reduce the frame error rate by up to an order and reduce the average number of iterations by around 40%.
The performance and complexity of low-density parity-check (LDPC) decoders have strict requirements since they are widely demanded in both communication and storage systems. Information storage bit flipping (ISBF) decoder and layered ISBF (LISBF) decoder demonstrate excellent decoding performance and throughput in which the global maximumfinding operation can be calculated in parallel to other decoding operations. However, their error-correction performance is not satisfactory. In this paper, we consider a variety of optimizations based on LISBF and propose a new algorithm named multiple flipping strategy LISBF (MLISBF). First, a high probability is adopted to flip those bits with high energy values. Second, strict flipping with a lower threshold is triggered when the syndrome weight is negligible. Then, we introduce perturbation flipping at specific iterations to help the decoder overcome trapping sets. We designed an efficient hardware implementation which realizes the layered calculation for BF decoders and reduces hardware resources for the MLISBF algorithm.
Tabu-list random-penalty gradient descent bit-flipping (TRGDBF) decoder is the state-of-the-art hard-decision low-density parity-check (LDPC) decoder in terms of error-correction performance on binary symmetric channel (BSC). However, the TRGDBF decoder suffers from a long critical path caused by the global maximum-finding operation, limiting the achievable throughput. This brief proposes an information storage bit-flipping (ISBF) decoder to solve this problem. Different from the existing bit-flipping (BF) decoders which adopt serial decoding manner, in the ISBF decoder, by storing the previous decoding information, the global maximum-finding operation can be executed in parallel to other decoding operations, significantly shortening the critical path. Moreover, a nonuniform flipping rule is incorporated to achieve a better decoding performance. We also present an efficient architecture to implement the ISBF decoder. The design example demonstrates that compared to other hard-decision BF decoders, the ISBF decoder could provide both the best decoding performance and throughput on BSC.
The bit-flipping (BF) algorithm for decoding of low-density parity-check (LDPC) codes requires less complex hardware than other decoding algorithms, but its error correcting performance needs to be improved. In this letter, a threshold adaptation scheme is applied to BF algorithm based decoding of LDPC codes. Our experiments show that the optimal threshold value for BF depends on the error conditions, and threshold adjustment during decoding helps to prevent meaningless no-flipping iterations. Based on these statistical observations, the adaptive threshold technique is proposed to pursue both the maximum error correcting capability and the fastest decoding convergence.
The Gradient descent bit flipping (GDBF) algorithm is a representative approach for decoding low-density parity-check (LDPC) codes, which offers a good tradeoff between decoding performance and complexity. Unfortunately, the decoding performance of GDBF algorithm degenerates dramatically for structured LDPC codes due to their large column weight. To address the above issue, we propose to improve GDBF algorithm by introducing a weighted parameter in the energy function of each bit. Specifically, this parameter compensates for the computational error of the energy function due to the large column weight of the parity-check matrices of structured LDPC codes. Moreover, the flipping number of each bit in the iterative process is included in the energy function to avoid consecutive bit flips in the decoding. Simulation results on typical structured LDPC codes indicate that the performance of the proposed algorithm is better than the standard GDBF algorithm at the cost of slight increment in the algorithmic complexity. The increase operations can be easily implemented, which indicates the proposed algorithm is suitable for practical purposes.
An improved bit-flipping(BF) algorithm with low complexity for decoding structured low-density parity-check codes(LDPC) is proposed to improve the performance of the hard-decision BF algorithm.The hard-decision bits are divided into two groups based on the magnitudes of the received symbols,and at each iteration,the proposed algorithm can flip more than one bit with using two thresholds,and the flipping error probability is effectively decreased.The improved BF algorithm requires some real number comparisons before iterations and requires only logical operations during the iterations.Compared with the weighted bit-flipping algorithm and its modifications,the new method is with significantly lower complexity.Simulations show that the proposed algorithm is provided with very fast convergence speed and excellent performance with significantly low complexity.
An improved iterative bit-flipping(BF) algorithm adapted for decoding low-density parity-check(LDPC) codes is proposed to improve the performance of the hard-decision BF decoding algorithm.The new algorithm uses an alternating threshold pattern to determine the bits whether to be flipped or not,and the flipping error probability is effectively decreased.Simulation results show that compared with BF algorithm,the improved BF algorithm improves both the error-correction performance and the convergence speed while maintaining the low computational complexity.