Min-Sum decoding of irregular LDPC codes with adaptive scaling based on mutual information

Min-Sum decoding (MS) is an alternative to belief propagation decoding with substantially lower complexity. MS often results in an overestimation of the log likelihood ratio (LLR) in particular in the early stage of the iterative process. A linear post-processing is usually performed as a compensation. With regular low density parity check codes (LDPC), a fixed scaling of the LLR yields sufficiently good results. In contrast, adaptive strategies are mandatory with irregular codes. It is well known that the scaling factor is an increasing function of the reliability of the LLR. In most of the publications, the scaling factor is envisioned as a function of both the iteration number and the signal-to-noise ratio. It is proposed here to use the mutual information between extrinsics as a measure of the reliability of the LLR. A practical implementation is derived with reasonable complexity. Compared to the literature, the proposed method yields slightly better results in terms of BER and a significant reduction in the number of iterations.