Resolvability on Continuous Alphabets

TL;DR

This paper characterizes the resolvability region for continuous alphabet channels, demonstrating the existence of effective codebooks and extending previous results with probabilistic bounds adapted for the continuous case.

Contribution

It provides a comprehensive characterization of resolvability for continuous channels, including both existence proofs and converse results, using probabilistic bounds.

Findings

Existence of good resolvability codebooks for continuous channels

Doubly exponentially small probability of unsuitable codebooks

Extension of elementary resolvability results to continuous alphabets

Abstract

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse part, we show that our previous elementary result carries over to the continuous case easily under some mild continuity assumption.