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IEEE Transactions on Vehicular Technology

Symbol Flipping Algorithm With Self-Adjustment Strategy for LDPC Codes Over GF($q$)

Bin Dai, Rongke Liu, Chenyu Gao, Zhen Mei

Published May 9, 2019• 8 citations
Publisher

Abstract

Compared with the non-prediction algorithm, the prediction-based symbol flipping decoding algorithm of non-binary, low-density, parity-check codes over GF(q) can significantly improve the error performance. To escape from undesirable local maximum, this paper proposes a self-adjustment strategy to redesign the flipping metric. Combined with the prediction mechanism, our proposed algorithm provides a good tradeoff between the complexity and the error correction performance. Simulation results for the additive white Gaussian noise channel and the binary symmetric channel verify the effectiveness of the proposed algorithm.

DOI
10.1109/tvt.2019.2915802

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Symbol Flipping Algorithm With Self-Adjustment Strategy for LDPC Codes Over GF(qqq)
Compared with the non-prediction algorithm, the prediction-based symbol flipping decoding algorithm of non-binary, low-density, parity-check codes over GF(q) can significantly improve the error performance. To escape from undesirable local maximum, this paper proposes a self-adjustment strategy to redesign the flipping metric. Combined with the prediction mechanism, our proposed algorithm provides a good tradeoff between the complexity and the error correction performance. Simulation results for the additive white Gaussian noise channel and the binary symmetric channel verify the effectiveness of the proposed algorithm.
This paper constructs an objective function for symbol flipping decoding algorithms, considering not only soft reliability, but also hard reliability. The maximization of this objective function indicates that the flipping metric should involve both the information before and after symbol flipping, while the existing algorithms consider the information before symbol flipping. Theoretical analysis shows that such prediction mechanism, together with hard reliability, can significantly improve the error performance of symbol flipping algorithms. Simulation results show that the proposed algorithms provide effective tradeoff between error performance and complexity for decoding non-binary LDPC codes.
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).
In this paper, we present two low complexity algorithms to decode non-binary LDPC codes. The proposed decoding algorithms update iteratively the hard decision received vector to search for a valid codeword in the vector space of Galois field (GF). The selection criterion for the position of unreliable symbols is based on failed checks and the information from the Galois field structure. In the first proposed algorithm, the flipping function is calculated for all symbols of the received sequence and multiple symbols are flipped in each iteration while in the second proposed algorithm, a single symbol is flipped per iteration. In the second method, unreliable positions are short-listed by using a majority voting scheme, and then the flipping function is computed to predict candidate symbols from the set of symbols in GF(q) while not violating the field order q. The proposed methods reduce the decoding complexity and memory use. The results of the algorithms show appealing tradeoffs between complexity and bit error rate performance for non-binary LDPC codes.
Symbol flipping-based hard decision decoding for non-binary low-density parity check (LDPC) codes has attracted much attention due to low decoding complexity even though the error performance of the symbol flipping decoder is inferior to that of the soft decision decoders. Standard symbol flipping decoding involves two steps, selection of the symbol position to be flipped and selection of the flipped symbol value. In this paper, an improved symbol value selection algorithm is developed for symbol flipping-based non-binary LDPC decoding. The key idea of the proposed algorithm is to use the complete information on correlation among the code symbols, in addition to their initial reliabilities when value of the flipped symbol is decided. The proposed algorithm offers improved error performance over the existing approaches of flipped symbol value selection which are solely based on the initial symbol reliabilities, with only a non-significant increase in complexity. At the same time, the proposed algorithm is low in complexity compared to other symbol flipping-based LDPC decoding algorithms which use the information on correlation among the code symbols in selecting the flipped symbol value.
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.
To speed up the convergence rate of non-binary low-density parity check codes and reduce decoding computational complexity of decoding algorithm, a weighted symbol flipping decoding algorithm based on iterative stopping criteria is proposed. The algorithm determines the position and amplitude of the flipped symbol according to the weight of the information node and the flipping function in the check equation, and selects the optimal value of the weighting factor through simulation. At the same time, the iteration stop criterion is introduced, and the iteration is stopped by setting the number of parity equations without satisfying the different signal-to-noise ratio. The simulation results show that the channel additive white Gauss noise, the algorithm ensures the invariant properties of weighted symbol flipping decoding algorithm under the condition that can accelerate the convergence speed, reduce the average number of iterations, so the decoding performance and complexity trad-off between effective.