Codeword-Independent Performance of Nonbinary Linear Codes Under Linear-Programming and Sum-Product Decoding

TL;DR

This paper proves that for certain symmetric modulator-channel combinations, the error rate performance of nonbinary linear codes remains independent of the transmitted codeword, applicable to LP and sum-product decoding over common channels.

Contribution

It establishes a symmetry condition ensuring codeword-independent performance for nonbinary codes with LP and sum-product decoders, applicable to PSK modulation over memoryless channels.

Findings

Performance independence holds under specific symmetry conditions.

Applicable to PSK modulation over AWGN and fading channels.

Valid for both LP and sum-product decoding methods.

Abstract

A coded modulation system is considered in which nonbinary coded symbols are mapped directly to nonbinary modulation signals. It is proved that if the modulator-channel combination satisfies a particular symmetry condition, the codeword error rate performance is independent of the transmitted codeword. It is shown that this result holds for both linear-programming decoders and sum-product decoders. In particular, this provides a natural modulation mapping for nonbinary codes mapped to PSK constellations for transmission over memoryless channels such as AWGN channels or flat fading channels with AWGN.