Bit-interleaved coded modulation revisited: a mismatched decoding perspective

We revisit the information-theoretic analysis of bit- interleaved coded modulation (BICM) by modeling the BICM decoder as a mismatched decoder. The mismatched-decoding model is well-defined for finite, yet arbitrary, block lengths, and captures the channel memory among the bits belonging to the same symbol. The generalized mutual information of the mismatched decoder coincides with the infinite-interleaver BICM capacity, where BICM is modeled as a set of independent parallel binary-input channels whose output is the bitwise log-likelihood ratio. The error exponent -and hence the cutoff rate- of the BICM mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite-interleaved model. For binary reflected Gray mapping in Gaussian channels the loss in error exponent is small.