Capacity of the Gaussian Arbitrarily-Varying Channel with List Decoding

Abstract

This paper considers list-decoding for the Gaussian arbitrarily-varying channel under the average probability of error criterion, where both the legitimate transmission and the state (or adversarial signal) are power limited. For list size L, the capacity is equivalent to the capacity of a standard Gaussian with the noise power raised by the adversary power, if the ratio of the adversary power to the transmitter power is less than L; otherwise, the capacity is zero. The converse proof involves showing that with enough power, an adversary can confuse the decoder by transmitting a superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof uses a novel variant of the Csiszar-Narayan method for the arbitrarily-varying channel.