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IEEE Transactions on Communications

Symbol Flipping Decoding Algorithms Based on Prediction for Non-Binary LDPC Codes

Shuai Wang, Qin Huang, Zulin Wang

Published Mar 2, 2017• 21 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2017.2677438

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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-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.
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 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.
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.
The main challenge for hardware implementation of non-binary LDPC decoding is the high computational complexity and large memory requirement. To address this challenge, five new low complexity LDPC decoding algorithms are proposed in this paper. The proposed algorithms are developed specifically towards the low complexity, yet effective, decoding of the NB LDPC codes. The proposed decoding algorithms update, iteratively, the hard decision received vector to search for the valid codeword in the vector space of Galois field (GF){(GF)}(GF) . The selection criterion for least reliable symbol positions is based on the information from the failed checks and the reliability information from the Galois field structure as well as from the received channel soft information. To choose the correct value for the candidate symbol, two methods are used. The first method is based on the prediction of the error symbol from the set of Galois field symbols which maximize an objective function. In the second method, individual bits are flipped based on the reliability information obtained from the channel. Algorithms 1 and 2 flip a single symbol per iteration whilst the other three algorithms 3, 4 and 5 flip multiple symbols in each iteration. The proposed voting based Algorithms 1, 2 and 5 first short list the unreliable positions using a majority voting scheme and then choose the candidate symbol value from the set of the symbols in GF(q){GF(q)}GF(q) while not violating the field order q{q}q . These methods simplify the decoding complexity in terms of computation and memory. Results and analysis of these algorithms show an appealing tradeoff between computational complexity and bit error rate performance for NB LDPC codes.