Random Coding Error Exponents for the Two-User Interference Channel

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.

Mismatched Multi-Letter Successive Decoding for the Multiple-Access Channel

“…Currently, no examples are known where such an improvement is obtained. Moreover, while the analysis techniques of [20] extend to the mismatched case, doing so leads to the same achievable rate region as ours; the only potential improvement is in the exponent. Finally, we note that while our focus is solely on codebooks with independent codewords, error exponents were also given for the Han-Kobayashi construction in [20].…”

“…As discussed in Section I-A, this exponent is closely related to a parallel work on the error exponent of the interference channel [20].…”

“…In a work that developed independently of ours, the interference channel perspective was pursued in depth in the matched case in [20], with a focus on error exponents. The error exponent of [20] is similar to that derived in the present paper, but also contains an extra maximization term that, at least in principle, could improve the exponent. Currently, no examples are known where such an improvement is obtained.…”

Gaussian Intersymbol Interference Channels With Mismatch

“…Specifically, to obtain ensemble-tight results, the only step in our proof that should be modified is the application of the truncated union-bound, which is not necessarily tight in the multi-user settings. To this end, one can use the tighter union bounds that were derived in [44,45].…”

“…It turns out that a byproduct of our analysis is an ensemble-tight characterization of the random coding error exponent. Exponentially tight analysis of the average probability of error was extensively studied before (see, e.g., [21][22][23][24]) mainly for discrete memoryless sources and channels. Here, on the other hand, as we deal with sources and channels with memory defined over infinite alphabets, the same methods cannot be applied.…”