Cross-entropy and iterative decoding

In this correspondence, the relationship between iterative decoding and techniques for minimizing cross-entropy is explained. It is shown that minimum cross-entropy (MCE) decoding is an optimal lossless decoding algorithm but its complexity limits its practical implementation. Use of a maximum a posteriori (MAP) symbol estimation algorithm instead of the true MCE algorithm provides practical algorithms that are identical to those proposed in the literature. In particular, turbo decoding is shown to be equivalent to an optimal algorithm for iteratively minimizing cross-entropy under an implicit independence assumption.