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Optical Fiber Communication Conference

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

Shuai Wang, Zulin Wang, Lei Jing, Qin Huang

Published Jan 1, 2017• 0 citations
Publisher

Abstract

This paper proposes a symbol flipping decoding algorithm based on prediction for non-binary LDPC codes, considering not only soft reliability, but also hard reliability. It provides 2.6 dB improvement compared with the weighted Algorithm B.
DOI
10.1364/ofc.2017.w2a.49

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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.
In this letter, a new algorithm to decode non-binary LDPC (NB-LDPC) codes is proposed. This algorithm is inspired from very low complexity decoders that have been proposed recently, in which only syndrome computations at the check node update are used, while performing symbol-flipping based update at the variable node. Usually, the low complexity decoders based on symbol flipping suffer from a non-negligible performance degradation compared to soft-decision NB-LDPC decoders. Our improved decoder makes use of a list of syndrome computations instead of a single one based on hard-decision, and builds soft information at the variable node input by assigning votes weighted by different amplitudes. Simulations show that using multiple votes with multiple weights yields better performance, while still maintaining the low complexity feature.
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.
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.