On AVCs with Quadratic Constraints

TL;DR

This paper demonstrates that in an AVC with quadratic constraints and an oblivious jammer, reliable communication at optimal rates is achievable without common randomness, matching theoretical bounds and improving proof techniques.

Contribution

It establishes the existence of stochastic codes for AVCs with quadratic constraints under maximum error, without shared randomness, matching outer bounds.

Findings

Reliable communication at optimal rates with no common randomness.

Existence of stochastic codes matching AWGN channel capacity.

More direct proof techniques of the main results.

Abstract

In this work we study an Arbitrarily Varying Channel (AVC) with quadratic power constraints on the transmitter and a so-called "oblivious" jammer (along with additional AWGN) under a maximum probability of error criterion, and no private randomness between the transmitter and the receiver. This is in contrast to similar AVC models under the average probability of error criterion considered in [1], and models wherein common randomness is allowed [2] -- these distinctions are important in some communication scenarios outlined below. We consider the regime where the jammer's power constraint is smaller than the transmitter's power constraint (in the other regime it is known no positive rate is possible). For this regime we show the existence of stochastic codes (with no common randomness between the transmitter and receiver) that enables reliable communication at the same rate as when the jammer is replaced with AWGN with the same power constraint. This matches known information-theoretic outer bounds. In addition to being a stronger result than that in [1] (enabling recovery of the results therein), our proof techniques are also somewhat more direct, and hence may be of independent interest.