Decoding of iterative Non-Binary LDPC codes using a near Maximum Likelihood approach

This paper investigates the decoding of rate 1/2 Non-Binary LDPC codes using a non-iterative approach based on the Maximum-Likelihood (ML) principle. The iterative decoding approach based on the well known Extended-Min-Sum (EMS) algorithm, considered as the most efficient decoding algorithm to decode NB-LDPC codes, executes the decoding process iteratively. The main operations of this algorithm are the variable and check node updates which are performed at least eight times requiring a long decoding time to achieve good performance in terms of Frame Error Rate (FER). The proposed decoding near ML approach is based on ML search where the number of candidates is highly reduced using a technique privileging the most reliable and nearest codewords. Then, a new decision making rule is proposed permitting to stop the ML search and select the decoded codeword. Simulation results show that the proposed algorithm achieves, at a reduced list of 5 searched candidates in average at 3 dB, the performance offered by the EMS algorithm. We also show that by slightly increasing the list of candidates, the proposed algorithm outperforms the EMS algorithm.