Precoding for the AWGN Channel with Discrete Interference

TL;DR

This paper investigates optimal precoding strategies for channels with discrete interference known causally at the transmitter, achieving capacity with limited input symbols and analyzing special cases like zero noise.

Contribution

It introduces a method to achieve capacity using a subset of input symbols and characterizes optimal precoding for channels with discrete interference and side information.

Findings

Capacity achievable with at most |X||S|-|S|+1 input symbols

Zero-noise case capacity equals 2 log2 M bits per channel use

Optimal precoding structure proposed for uniform input distribution under interference constraints

Abstract

For a state-dependent DMC with input alphabet $\mathcal{X}$ and state alphabet $\mathcal{S}$ where the i.i.d. state sequence is known causally at the transmitter, it is shown that by using at most $|\mathcal{X}||\mathcal{S}|-|\mathcal{S}|+1$ out of $|\mathcal{X}|^{|\mathcal{S}|}$ input symbols of the Shannon's \emph{associated} channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, $M$-ary signal transmission over AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. For the special case where the Gaussian noise power is zero, a sufficient condition, which is independent of interference, is given for the capacity to be $\log_2 M$ bits per channel use. The problem of maximization of the transmission rate under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet is investigated. For this setting, the general structure of a communication system with optimal precoding is proposed.