Comments on `Bit Interleaved Coded Modulation'

TL;DR

This paper critically examines the validity of the expurgated bound in bit interleaved coded modulation analysis, providing a new, tighter upper bound and discussing implications for square QAM with Gray labeling.

Contribution

It identifies flaws in the original proof of the expurgated bound and introduces a new upper bound that is numerically tighter for certain modulation schemes.

Findings

The original expurgated bound proof is flawed.

A new upper bound is derived and shown to be slightly tighter.

The validity of the original bound for square QAM with Gray labeling remains uncertain.

Abstract

Caire, Taricco and Biglieri presented a detailed analysis of bit interleaved coded modulation, a simple and popular technique used to improve system performance, especially in the context of fading channels. They derived an upper bound to the probability of error, called the expurgated bound. In this correspondence, the proof of the expurgated bound is shown to be flawed. A new upper bound is also derived. It is not known whether the original expurgated bound is valid for the important special case of square QAM with Gray labeling, but the new bound is very close to, and slightly tighter than, the original bound for a numerical example.