Predictive Syndrome Based Low Complexity Joint Iterative Detection-Decoding Algorithm for Non-Binary LDPC Codes

This paper addresses the problem of decoding non-binary low density parity check codes(LDPC) over finite field $GF(q)$ using symbol flipping approach. To achieve low complexity reliable communication, three new algorithms for improving the bit error rate performance of the non-binary LDPC decoder are presented. The first type is the symbol flipping decoding algorithm using a flipping function based on the channel reliability to identify the least reliable symbol position. In this algorithm, if the predicted symbol value satisfies the check sum, then the value is declared as correct otherwise the value is adjusted and sent back to the QAM detector. Algorithms 2 in this paper is an improvement to iterative joint detection-decoding algorithm by using the method of iterative hard decision based majority logic to select the new candidate symbol value. The feedback value to the QAM detector is adjusted by using Euclidean distance between the current symbol and the newly selected symbol value. Algorithm 3 is a low complexity version of Algorithm 2 which is derived by applying a majority voting scheme. In the majority voting scheme, symbols are short listed first by voting and all the computation are carried out only for the short listed least reliable symbols which significantly lowers the processing complexity. Numerical results and complexity analysis show that the proposed methods have good bit error rate versus complexity trade-off for various applications when compared with some existing algorithms.