Precoding for the AWGN Channel with Discrete Interference

TL;DR

This paper investigates optimal precoding strategies for transmitting over an AWGN channel with discrete interference known causally at the transmitter, deriving capacity bounds and proposing a general structure for optimal communication systems.

Contribution

It introduces a precoding scheme that achieves channel capacity with discrete interference and extends the approach to continuous input alphabets.

Findings

Capacity can be achieved using at most MQ-Q+1 input symbols.

A sufficient condition for achieving maximum rate independent of interference.

Proposed a general structure for optimal precoding systems.

Abstract

$M$-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. Shannon's theorem for channels with side information at the transmitter is used to formulate the capacity of the channel. It is shown that by using at most $MQ-Q+1$ out of $M^Q$ input symbols of the \emph{associated} channel, the capacity is achievable. 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. The extension of the proposed precoding scheme to continuous channel input alphabet is also investigated.