Lower Bounds on the Minimum Pseudodistance for Linear Codes with $q$-ary PSK Modulation over AWGN

TL;DR

This paper derives lower bounds on the minimum pseudodistance for linear codes with q-ary PSK modulation over AWGN, providing insights into error performance for coded modulation systems.

Contribution

It introduces new lower bounds on pseudodistance applicable to both binary and nonbinary coded modulation over AWGN channels.

Findings

Lower bounds on pseudodistance are established.

Bounds can predict error performance for LP and message-passing decoders.

Results are applicable to direct modulation mapping systems.

Abstract

We present lower bounds on the minimum pseudocodeword effective Euclidean distance (or minimum "pseudodistance") for coded modulation systems using linear codes with $q$-ary phase-shift keying (PSK) modulation over the additive white Gaussian noise (AWGN) channel. These bounds apply to both binary and nonbinary coded modulation systems which use direct modulation mapping of coded symbols. The minimum pseudodistance may serve as a first-order measure of error-correcting performance for both linear-programming and message-passing based receivers. In the case of a linear-programming based receiver, the minimum pseudodistance may be used to form an exact bound on the codeword error rate of the system.