Achieving positive rates with predetermined dictionaries

TL;DR

This paper demonstrates methods to achieve positive communication rates over complex channels by using predetermined dictionaries and specialized decoding techniques, extending results to channels with arbitrary alphabets.

Contribution

It introduces a novel approach for achieving positive rates with fixed dictionaries in non-stationary channels and extends the methodology to channels with arbitrary alphabets.

Findings

Positive rates are achievable with predetermined dictionaries in binary channels.

Conflict-set decoding enables positive rates for channels with arbitrary alphabets.

The approach generalizes to non-stationary and complex channel models.

Abstract

In the first part of the paper we consider binary input channels that are not necessarily stationary and show how positive rates can be achieved using codes constrained to be within predetermined dictionaries. We use a Gilbert-Varshamov-like argument to obtain the desired rate achieving codes. Next we study the corresponding problem for channels with arbitrary alphabets and use conflict-set decoding to show that if the dictionaries are contained within nice sets, then positive rates are achievable.