Bit-Interleaved Coded Modulation Revisited: A Mismatched Decoding Perspective

TL;DR

This paper revisits the information-theoretic analysis of BICM by modeling it as a mismatched decoder, providing new proofs of capacity achievability, and analyzing error exponents and mutual information in iterative decoding.

Contribution

It offers two independent proofs of BICM capacity achievability under mismatched decoding and explores the implications for error exponents and iterative decoding mutual information.

Findings

The generalized mutual information matches the infinite-interleaver BICM capacity.

The error exponent of the mismatched decoder is upper bounded by that of coded modulation.

The EXIT chart mutual information can be represented as a pseudo-generalized mutual information.

Abstract

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 naturally captures the channel memory among the bits belonging to the same symbol. We give two independent proofs of the achievability of the BICM capacity calculated by Caire et al. where BICM was modeled as a set of independent parallel binary-input channels whose output is the bitwise log-likelihood ratio. Our first achievability proof uses typical sequences, and shows that due to the random coding construction, the interleaver is not required. The second proof is based on the random coding error exponents with mismatched decoding, where the largest achievable rate is the generalized mutual information. We show that the generalized mutual information of the mismatched decoder coincides with the infinite-interleaver BICM capacity. We also show that 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. We also consider the mutual information appearing in the analysis of iterative decoding of BICM with EXIT charts. We show that the corresponding symbol metric has knowledge of the transmitted symbol and the EXIT mutual information admits a representation as a pseudo-generalized mutual information, which is in general not achievable. A different symbol decoding metric, for which the extrinsic side information refers to the hypothesized symbol, induces a generalized mutual information lower than the coded modulation capacity.