Finite Blocklength and Dispersion Bounds for the Arbitrarily-Varying Channel

TL;DR

This paper develops finite blocklength and dispersion bounds for the arbitrarily-varying channel, providing new achievability bounds and analyzing their tightness for various channel models, especially without shared randomness.

Contribution

It introduces a novel finite blocklength achievability bound for the AVC and derives tight dispersion bounds for channels without shared randomness.

Findings

Bounds are tight for many channels, including binary symmetric AVC.

Finite blocklength bounds are analogous to the random coding union bound.

Bounds are not tight when deterministic and random code capacities differ.

Abstract

Finite blocklength and second-order (dispersion) results are presented for the arbitrarily-varying channel (AVC), a classical model wherein an adversary can transmit arbitrary signals into the channel. A novel finite blocklength achievability bound is presented, roughly analogous to the random coding union bound for non-adversarial channels. This finite blocklength bound, along with a known converse bound, is used to derive bounds on the dispersion of discrete memoryless AVCs without shared randomness, and with cost constraints on the input and the state. These bounds are tight for many channels of interest, including the binary symmetric AVC. However, the bounds are not tight if the deterministic and random code capacities differ.