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IEEE Open Journal of the Communications Society

Dynamic Multi-Symbol Flipping Decoding of Non-Binary LDPC Codes

Xiuwen Bao, Ming Jiang, Dongli Fan, Mingyang Zhu

Published Jan 1, 2022• 2 citations
Publisher

Abstract

A dynamic multi-symbol (DM) flipping scheme is proposed for various symbol flipping decodings of non-binary low-density parity-check (NB-LDPC) codes. This new approach divides the whole decoding process into multiple stages according to the number of iterations and allows a different maximum number of symbols to be flipped in each stage. Numerical analysis reveals that the proposed multi-symbol flipping scheme can yield a higher probability of correct flipping with the dynamic flipping threshold. The proposed DM scheme can be highly parallelized, extensively improving the decoder throughput over existing symbol flipping decoding algorithms based on prediction (SFDP). Numerical results show that the DM scheme can significantly enhance the error correction capability and achieve faster convergence speed with little increase in average computational complexity.

DOI
10.1109/ojcoms.2022.3211418

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A dynamic multi-symbol (DM) flipping scheme is proposed for various symbol flipping decodings of non-binary low-density parity-check (NB-LDPC) codes. This new approach divides the whole decoding process into multiple stages according to the number of iterations and allows a different maximum number of symbols to be flipped in each stage. Numerical analysis reveals that the proposed multi-symbol flipping scheme can yield a higher probability of correct flipping with the dynamic flipping threshold. The proposed DM scheme can be highly parallelized, extensively improving the decoder throughput over existing symbol flipping decoding algorithms based on prediction (SFDP). Numerical results show that the DM scheme can significantly enhance the error correction capability and achieve faster convergence speed with little increase in average computational complexity.
A novel decoding algorithm for non-binary low density parity check (NB-LDPC) codes is proposed. The algorithm builds on the recently designed parallel symbol-flipping decoding (PSFD) algorithm and combines a technique of error estimation and a method of multiple voting levels from each unsatisfied check-sum to the corresponding variable nodes. Simulations results, performed on a number of NB-LDPC codes of various lengths and column weights constructed using several methods, show that the new algorithm not only avoids using code-dependent voting threshold but also improves the error rate performance of the PSFD algorithm, particularly for low column weight parity-check matrices.
The symbol flipping decoding algorithms based on prediction (SFDP) for non-binary LDPC codes perform well in terms of error performances but converge slowly when compared to other symbol flipping decoding algorithms. In order to improve the convergence rate, we design new flipping rules with two phases for the SFDP algorithms. In the first phase, two or more symbols are flipped at each iteration to allow a quick increase of the objective function. While in the second phase, only one symbol is flipped to avoid the oscillation of the decoder when the objective function is close to its maximum. Simulation results show that the SFDP algorithms with the proposed flipping rules can reduce the average number of iterations significantly, whereas having similar performances when compared to the original SFDP algorithms.
Symbol flipping decoding (SFD) of non-binary low-density parity-check (NB-LDPC) codes has lower implementation complexity at a cost of performance degradation, when compared with other belief propagation decoding algorithms. This paper proposes modified SFD algorithms based on prediction (SFDP) for NB-LDPC codes by introducing random penalty items into the flipping metrics. Two types of noise with uniform and Gaussian distributions are considered. A probabilistic analysis shows theoretically that the randomly penalized SFDP algorithms can be advantageous in the correct flipping probability over their original versions. Simulation results show that the proposed penalizing methods exhibit significant performance gains for both regular and irregular NB-LDPC codes with different rates and alphabet sizes in both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC).
A properly designed stopping criterion for iterative decoding algorithms can save a number of iterations and lead to a considerable reduction of system latency. The symbol flipping decoding algorithms based on prediction (SFDP) have been proposed recently for efficient decoding of non-binary low-density parity-check (LDPC) codes. To detect the decoding frames with slow convergence or even non-convergence, we track the number of oscillations on the value of objective function during the iterations. Based on this tracking number, we design a simple stopping criterion for the SFDP algorithms. Simulation results show that the proposed stopping criterion can significantly reduce the number of iterations at low signal-to-noise ratio regions with slight error performance degradation.
This paper investigates the application of gradient descent with momentum in symbol flipping decoding algorithms based on prediction (SFDP) for non-binary low-density parity-check (NB-LDPC) codes. The momentum added in the objective function of SFDP algorithms can provide inertia to the decoding process by considering the flipping states in the past iterations. Simulation results show that the proposed momentum-based SFDP algorithms perform significantly better than the original SFDP algorithms with low extra complexity. Furthermore, to lower the error floor of momentum-based SFDP algorithms, we also introduce artificial noises into the objective functions of momentum-based SFDP algorithms to help the iterative decoding escape from local optimum.