On the correlation between error weights and syndrome weights for belief propagation decoding of LDPC codes

This paper analyzes the correlation between the error weights and the syndrome weights during the sum product algorithm (SPA) decoding process of low density parity check codes (LDPC) in order to improve the error performance and the decoding speed. In this paper, we propose a modified SPA decoding algorithm to improve the decoding performance of the non-decoded codewords and investigate if this new algorithm takes indeed the best decoding decision for each codeword. The effect of the averaged decoding over the error weights and syndrome weights are analyzed as well as their correlation. The correlation coefficients between them are computed and a weight enumerator polynomial is used to jointly represent the error and syndrome weight distribution for each codeword.