[Paper Review] Bit-Interleaved Coded Modulation Revisited: A Mismatched Decoding Perspective

Alfonso García Martínez, Albert Guillén i Fàbregas+2 more|ArXiv.org|May 9, 2008

Advanced Wireless Communication Techniques16 references4 citations

TL;DR

This paper re-evaluates bit-interleaved coded modulation (BICM) through a mismatched decoding framework, showing that the generalized mutual information of the BICM decoder matches the BICM capacity derived under parallel independent channel modeling. It proves that the BICM error exponent is always upper-bounded by that of coded modulation, with only a negligible gap under binary reflected Gray mapping in Gaussian channels.

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.

Motivation & Objective

• To re-analyze bit-interleaved coded modulation (BICM) using a mismatched decoding framework valid for finite block lengths.
• To resolve the apparent paradox that BICM can achieve a higher cutoff rate than coded modulation despite being suboptimal.
• To clarify the operational meaning of mutual information in iterative decoding of BICM, particularly in EXIT chart analysis.
• To investigate how extrinsic side information affects the error exponent and generalized mutual information in BICM decoding.
• To establish conditions under which BICM can achieve the same error exponent as coded modulation, particularly with perfect side information.

Proposed method

• Models the classical BICM decoder as a mismatched decoder using a symbol-level metric based on the product of individual bit log-likelihood ratios.
• Uses typical sequences to prove achievability of the BICM capacity under the mismatched decoding model.
• Applies random coding error exponent theory with mismatched decoding to derive the generalized mutual information (GMI) of the BICM decoder.
• Compares the GMI of BICM to that of coded modulation, showing the BICM GMI is always upper-bounded by the coded modulation capacity.
• Analyzes the mutual information in EXIT charts for iterative BICM decoding, identifying it as a pseudo-generalized mutual information that may exceed capacity.
• Introduces a modified symbol metric where extrinsic information depends on the hypothesized symbol rather than the transmitted symbol, and derives its corresponding GMI.

Experimental results

Research questions

• RQ1 Does the mismatched decoding model of BICM achieve the same capacity as the parallel-channel model proposed by Caire et al.?
• RQ2 How does the error exponent of BICM compare to that of coded modulation under mismatched decoding?
• RQ3 What is the operational meaning of the mutual information used in EXIT chart analysis for iterative BICM decoding?
• RQ4 Can perfect extrinsic side information close the gap between BICM and coded modulation in terms of error exponent?
• RQ5 How does the choice of symbol decoding metric affect the generalized mutual information and achievable rate in BICM?

Key findings

• The generalized mutual information (GMI) of the mismatched BICM decoder coincides with the BICM capacity derived by Caire et al. under the parallel independent channel model.
• The error exponent of BICM under mismatched decoding is always upper-bounded by that of coded modulation, contrary to earlier results assuming independent parallel channels.
• For binary reflected Gray mapping in Gaussian channels, the loss in error exponent between BICM and coded modulation is negligible.
• The mutual information used in EXIT chart analysis of iterative BICM decoding is a pseudo-generalized mutual information, as it may exceed the channel capacity and thus lacks operational meaning as an achievable rate.
• When the extrinsic side information is based on the hypothesized symbol rather than the transmitted symbol, the resulting GMI is strictly lower than the coded modulation capacity.
• With perfect extrinsic side information, the error exponent of the BICM mismatched decoder equals that of coded modulation, demonstrating that the gap can be closed under ideal conditions.