State constraints and list decoding for the AVC

TL;DR

This paper explores list decoding for arbitrarily varying channels with state constraints, demonstrating achievable rates near capacity and analyzing the impact of list size and symmetrizability on capacity.

Contribution

It introduces new bounds and insights into list decoding capacities for AVCs with state constraints, highlighting differences from unconstrained scenarios.

Findings

Rates within epsilon of capacity are achievable with list decoding.

Bounds depend on different notions of symmetrizability.

Capacity can be positive but less than randomized coding capacity with list size L.

Abstract

List decoding for arbitrarily varying channels (AVCs) under state constraints is investigated. It is shown that rates within $\epsilon$ of the randomized coding capacity of AVCs with input-dependent state can be achieved under maximal error with list decoding using lists of size $O(1/\epsilon)$. Under average error an achievable rate region and converse bound are given for lists of size $L$. These bounds are based on two different notions of symmetrizability and do not coincide in general. An example is given that shows that for list size $L$ the capacity may be positive but strictly smaller than the randomized coding capacity. This behavior is different than the situation without state constraints.