Competitive Analysis of Arbitrary Varying Channels

TL;DR

This paper analyzes arbitrary varying channels (AVCs) using competitive analysis, revealing that adaptive input distributions outperform fixed ones, challenging traditional worst-case rate optimization methods.

Contribution

It introduces a competitive analysis framework for AVCs and shows that adaptive input strategies can outperform fixed distributions, contrasting with classical capacity results.

Findings

Single input distribution codes are suboptimal in competitive performance.

Adaptive input distribution strategies improve communication rates.

Contrasts with classical single-letter capacity formulas for AVCs.

Abstract

Arbitrary varying channels (AVC) are used to model communication settings in which a channel state may vary arbitrarily over time. Their primary objective is to circumvent statistical assumptions on channel variation. Traditional studies on AVCs optimize rate subject to the worst-case state sequence. While this approach is resilient to channel variations, it may result in low rates for state sequences that are associated with relatively good channels. This paper addresses the analysis of AVCs through the lens of competitive analysis, where solution quality is measured with respect to the optimal solution had the state sequence been known in advance. Our main result demonstrates that codes constructed by a single input distribution do not achieve optimal competitive performance over AVCs. This stands in contrast to the single-letter capacity formulae for AVCs, and it indicates, in our setting, that even though the encoder cannot predict the subsequent channel states, it benefits from varying its input distribution as time proceeds.