Modified fast Hadamard transform based belief propagation decoding algorithm

In this paper, we propose a new fast Hadamard transform based the belief-propagation (BP) decoding algorithm over GF (2^p) with a modification of the permutations between the check nodes and variable nodes. This scheme is mathematically equivalent to the conventional BP decoding algorithm, but complexity of the proposed scheme is lower. We show by simulation that the non-binary regular and irregular LDPC codes in GF (2^p) have good performance with our proposed modified BP decoding algorithm.