Pre-Decoder Processing Functions for a DMC with Mismatched Decoding

TL;DR

This paper investigates how pre-decoder processing functions can enhance the performance of mismatched decoders over discrete memoryless channels, providing bounds, optimal strategies, and separation principles.

Contribution

It introduces the analysis of symbolwise and vectorwise pre-processing functions, establishing bounds, optimality of deterministic functions, and a separation principle for mismatched decoding.

Findings

Pre-processing functions enable reliable transmission at positive rates.

Optimal pre-processing functions for random coding are deterministic.

A separation principle holds for vectorwise pre-processing functions.

Abstract

This paper analyzes the effect of adding a pre-decoder processing function to a receiver that contains a fixed mismatched decoder at the output of a discrete memoryless channel. We study properties of the symbolwise pre-processing function and show that it is a simple yet very powerful tool which enables to obtain reliable transmission at a positive rate for almost every metric. We present lower and upper bounds on the capacity of a channel with mismatched decoding and symbolwise(scalar-to-scalar) pre-processing, and show that the optimal pre-processing function for random coding is deterministic. We also characterize achievable error exponents. Finally, we prove that a separation principle holds for vectorwise(vector-to-vector) pre-processing functions and further, that deterministic functions maximize the reliably transmitted rate in this case.