Abstract
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.
Highlights
Non-binary low density parity check (NB-LDPC) codes defined over Galois field (GF)(q > 2) are an extension of binary LDPC codes [1], [2]
NON-BINARY LDPC CODES Consider a regular parity check matrix H with dimension m× n defined over the Galois field (GF) size q > 2 where each element hi,j(1 ≤ i ≤ m, 1 ≤ j ≤ n) of H is an element over the GF(q) where q = 2r such that q = 2r and r shows the number of bits in each symbol
The log likelihood ration (LLR) for NB-LDPC codes corresponding to the jth symbol, is computed as follows for the binary phase shift keying (BPSK) signalling in additive white Gaussian noise (AWGN) channel [31]
Summary
Non-binary low density parity check (NB-LDPC) codes defined over GF(q > 2) are an extension of binary LDPC codes [1], [2]. As research in the literature is focused mostly on low column or ultra-low column weight LDPC codes, we have chosen to use low/ultra-low column weight In the literature, those symbol flipping NB-LDPC decoders, showing better BER performances for low column weight, are considered as good decoding algorithms LDPC codes using high column weight increase the decoding computational complexity and contribute towards error floor [7], [13], [25]. NON-BINARY LDPC CODES Consider a regular parity check matrix H with dimension m× n defined over the Galois field (GF) size q > 2 where each element hi,j(1 ≤ i ≤ m, 1 ≤ j ≤ n) of H is an element over the GF(q) where q = 2r such that q = 2r and r shows the number of bits in each symbol.
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