A Mutual Information Approach for Comparing LLR Metrics for Iterative Decoders

We develop an approach to compare different log-likelihood ratio (LLR) metrics for iterative soft decoding. We show that an LLR metric for a function of the received signals is a sufficient statistic to this function about the binary channel input. We also prove that when the function belongs to a set of specific mappings, the corresponding LLR metric can feed the maximal mutual information to the decoder. For decoding low density parity check codes with the belief-propagation decoder, we develop a method to estimate the minimal average number of iterations. The results are applied to compare the Gaussian metric in and the two-symbol-observation-interval LLR metric in. The latter is shown to be superior.