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IEEE International Conference on Computer and Communications (ICCC)

An Improved Syndrome Bit Flipping Decoder with Narrowed Flipping Set for LDPC Codes

Wenlin Zhao, Jie Zhang, Li Li, Haitong Jiang

Published Dec 8, 2023• 0 citations
Publisher

Abstract

In this paper, we propose an improved Syndrome Bit Flipping (SBF) decoding algorithm that utilizes narrowed flipping set. The narrowed flipping set is prone to contain all error bit positions with high probability. To construct the narrowed flipping set, part of its elements are selected according to channel information, and the rest are constructed by random selections. The narrowed flipping set mitigates possible error propagation by avoiding some non-error bits being unnessary flipped, thereby further improving the decoding performance of the original SBF algorithm. The simulation results show that the proposed algorithm can achieve about 1.2 dB bit error rate gain compared with the original SBF algorithm, with a modest increase in computational complexity.

DOI
10.1109/iccc59590.2023.10507492

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In this paper, we propose an improved Syndrome Bit Flipping (SBF) decoding algorithm that utilizes narrowed flipping set. The narrowed flipping set is prone to contain all error bit positions with high probability. To construct the narrowed flipping set, part of its elements are selected according to channel information, and the rest are constructed by random selections. The narrowed flipping set mitigates possible error propagation by avoiding some non-error bits being unnessary flipped, thereby further improving the decoding performance of the original SBF algorithm. The simulation results show that the proposed algorithm can achieve about 1.2 dB bit error rate gain compared with the original SBF algorithm, with a modest increase in computational complexity.
Performance of LDPC decoders at high SNR is dominated by trapping sets that induce an error floor in the performance curve. We propose a new algorithm that resolves trapping sets and lowers the error floor. The new algorithm, called Syndrome Bit Flipping (SBF), computes the sum of adjacent parity violations at each symbol node. Bits are flipped by comparing the syndrome sum against a time-varying threshold called the decoding key. SBF is compared to other bit-flipping decoders on the Binary Symmetric Channel (BSC), and is demonstrated as a post-processing step for a Noisy Gradient Descent Bit-Flipping (NGDBF) hardware decoder. We demonstrate the post-processing method for an LDPC code defined in the 802.3an standard, and find that the frame error rate is improved by at least two orders of magnitude, even as the required iterations are reduced by 33%.
Gradient descent bit flipping (GDBF) algorithm is an important low-complexity method for decoding LDPC codes. In particular, the multi-bit GDBF decoding has the best decoding performance among BF algorithms if a suitable threshold is prescribed. However, extensive computer searches are needed to find such a threshold for a specific LDPC code. In this paper, we propose a syndrome-aided GDBF (SAGDBF) algorithm to address the problem. The thresholds in our algorithm are adaptively adjusted according to the syndrome values in the iterative process. Simulation results for different LDPC codes suggest that the error performances of the proposed SAGDBF algorithm are close to and even better than the original multi-bit GDBF algorithm at a relatively small number of iterations. In addition, the complexity increased in our proposed algorithm is negligible compared with the original multi-bit GDBF algorithm. Hence, the proposed algorithm is suitable for practical purposes.
The Bit-Flipping (BF) algorithm is considered as a hard decoding method for LDPC codes. It is much simpler than the probabilistic methods like Sum Product Algorithm (SPA), and can be efficiently implemented by electronic circuits. In this paper, we propose a new Bit Flipping algorithm for Low-Density Parity-Check codes (LDPC) called Single Bit-Flipping (SBF). Compared to the Gallager Bit-Flipping algorithm, the proposed algorithm employs criteria of flipping single bit chosen carefully. This method eliminates the risk for flipping more than one bit at a time that can induce additional error bits and propagate the errors to the later iterations. We present some results obtained by applying this new method that provides a gain in performance in comparison to the standard Gallager Bit-Flipping with low complexity.
The gradient descent bit-flipping (GDBF) decoding algorithm offers an attractive tradeoff between performance and complexity compared with the other bit-flipping (BF) decoding algorithms. However, the performance of GDBF decoding is seriously effected by infinite decoding loop, which always results in decoding failure when maximal iteration number is reached. To avoid the decoding loop and improve the performance, an efficient escaping scheme is proposed for the GDBF algorithm in this paper. This scheme firstly introduces syndrome weight to detect the decoding loop. If a decoding loop is detected, the escaping mechanism works, where only the bit which can decrease the syndrome weight most efficiently is selected to be flipped. In addition, the excluding set is introduced to further prevent the local maximum. Simulation results show that the GDBF algorithm can obtain about 1 dB code gain by utilizing this scheme. Compared with noise GDBF, it has 0.1dB performance loss as well as lower complexity.
This work presents a high-performance bit-flipping (BF) algorithm utilizing a proposed syndrome vote technique of a defined culprit bit set, named CVBF algorithm for LDPC decoding. It can achieve significant decoding performance improvements by about 0.9 dB over the most efficient BF algorithm, owing to the introduced an additional syndrome vote procedure after updating the flipping reliabilities of all the received bits in each iteration. Moreover, its performance is comparable to the min-sum algorithm (MSA) under the condition of same iteration number, but with much lower complexity per iteration. The proposed syndrome vote scheme only costs little overhead in hardware realization. Besides, an early termination strategy suited for the proposed algorithm is also devised to further reduce the iteration number.
In this study, we propose a “New Reliability Ratio Weighted Bit Flipping” (NRRWBF) algorithm for Low‐Density Parity‐Check (LDPC) codes. This algorithm improves the “Reliability Ratio Weighted Bit Flipping” (RRWBF) algorithm by modifying the reliability ratio. It surpasses the RRWBF in performance, reaching a 0.6 dB coding gain at a Binary Error Rate (BER) of 10−4 over the Additive White Gaussian Noise (AWGN) channel, and presents a significant reduction in the decoding complexity. Furthermore, we improved NRRWBF using the sum of the syndromes as a criterion to avoid the infinite loop. This will enable the decoder to attain a more efficient and effective decoding performance.