On the Asymptotic Performance of Bit-Wise Decoders for Coded Modulation

TL;DR

This paper analyzes the asymptotic performance of bit-wise decoders in coded modulation, showing a bounded loss compared to maximum likelihood decoding, with zero loss for many linear codes over Gaussian channels.

Contribution

It provides a theoretical analysis of the asymptotic loss of bit-wise decoders, quantifying the maximum loss and identifying conditions for zero loss.

Findings

Asymptotic loss bounded by 1.25 dB for any code

Zero asymptotic loss for many linear codes over Gaussian channels

Performance gap between decoders is limited at high SNR

Abstract

Two decoder structures for coded modulation over the Gaussian and flat fading channels are studied: the maximum likelihood symbol-wise decoder, and the (suboptimal) bit-wise decoder based on the bit-interleaved coded modulation paradigm. We consider a 16-ary quadrature amplitude constellation labeled by a Gray labeling. It is shown that the asymptotic loss in terms of pairwise error probability, for any two codewords caused by the bit-wise decoder, is bounded by 1.25 dB. The analysis also shows that for the Gaussian channel the asymptotic loss is zero for a wide range of linear codes, including all rate-1/2 convolutional codes.