A Case Where Interference Does Not Affect The Channel Dispersion

TL;DR

This paper demonstrates that in a specific interference channel model with strict conditions, the channel's dispersion remains unaffected by interference, extending Carleial's 1975 findings to second-order coding rates.

Contribution

It characterizes the second-order coding rates of the Gaussian interference channel under strict very strong interference conditions, showing dispersions are unaffected by interference.

Findings

Dispersions are unaffected by interference in the specified channel model.

Second-order coding rates are characterized in terms of error probability and information density variances.

The results extend classical capacity results to second-order analysis in interference channels.

Abstract

In 1975, Carleial presented a special case of an interference channel in which the interference does not reduce the capacity of the constituent point-to-point Gaussian channels. In this work, we show that if the inequalities in the conditions that Carleial stated are strict, the dispersions are similarly unaffected. More precisely, in this work, we characterize the second-order coding rates of the Gaussian interference channel in the strictly very strong interference regime. In other words, we characterize the speed of convergence of rates of optimal block codes towards a boundary point of the (rectangular) capacity region. These second-order rates are expressed in terms of the average probability of error and variances of some modified information densities which coincide with the dispersion of the (single-user) Gaussian channel. We thus conclude that the dispersions are unaffected by interference in this channel model.