Channel Code Design with Causal Side Information at the Encoder

TL;DR

This paper develops a new code design criterion for the M-ary input AWGN channel with causal interference knowledge at the encoder, simplifying the design for binary cases by reducing it to binary symmetric channel coding.

Contribution

It introduces a new distance measure for code design and shows that for binary input channels, only two symbols are needed, simplifying the coding problem.

Findings

High SNR code design criterion based on a new distance measure.

Binary input case reduces to binary symmetric channel code design.

Use of only two symbols in encoding for binary case simplifies code construction.

Abstract

The problem of channel code design for the $M$-ary input AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the encoder is considered. The code design criterion at high SNR is derived by defining a new distance measure between the input symbols of the Shannon's \emph{associated} channel. For the case of binary-input channel, i.e., M=2, it is shown that it is sufficient to use only two (out of $2^Q$) input symbols of the \emph{associated} channel in the encoding as far as the distance spectrum of code is concerned. This reduces the problem of channel code design for the binary-input AWGN channel with known interference at the encoder to design of binary codes for the binary symmetric channel where the Hamming distance among codewords is the major factor in the performance of the code.