Nonasymptotic Oblivious Relaying and Variable-Length Noisy Lossy Source Coding

TL;DR

This paper investigates finite-blocklength limits of oblivious relay channels, deriving new second-order and variable-length coding results using advanced nonasymptotic information theory techniques.

Contribution

It introduces novel nonasymptotic achievability bounds for oblivious relay channels, including a new variable-length noisy lossy source coding theorem.

Findings

Derived second-order coding rates for fixed-length and variable-length relay coding.

Established a new nonasymptotic variable-length noisy lossy source coding result.

Utilized advanced nonasymptotic techniques like the Poisson matching lemma.

Abstract

The information bottleneck channel (or the oblivious relay channel) concerns a channel coding setting where the decoder does not directly observe the channel output. Rather, the channel output is relayed to the decoder by an oblivious relay (which does not know the codebook) via a rate-limited link. The capacity is known to be given by the information bottleneck. We study finite-blocklength achievability results of the channel, where the relay communicates to the decoder via fixed-length or variable-length codes. These two cases give rise to two different second-order versions of the information bottleneck. Our proofs utilize the nonasymptotic noisy lossy source coding results by Kostina and Verd\'{u}, the strong functional representation lemma, and the Poisson matching lemma. Moreover, we also give a novel nonasymptotic variable-length noisy lossy source coding result.