Random Coding Error Exponents for the Two-User Interference Channel

TL;DR

This paper derives improved lower bounds on the error exponents for the two-user interference channel using random coding, analyzing both i.i.d. codebooks with optimal decoding and superposition coding ensembles.

Contribution

It provides the first single-letter formulas for error exponents under optimal decoding for i.i.d. ensembles and extends the analysis to Han-Kobayashi superposition coding.

Findings

Our bounds are strictly better than existing lower bounds.

Single-letter formulas are derived for the first time for optimal decoding.

Error exponents are improved for superposition coding ensembles.

Abstract

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles, and find a lower bound on the error exponent associated with the celebrated Han-Kobayashi (HK) random coding ensemble, which is based on superposition coding.