Capacity of the Gaussian arbitrarily varying channel

Abstract

The Gaussian arbitrarily varying channel with input constraint Gamma and state constraint Lambda admits input sequences x=(x/sub 1/,---,X/sub n/) of real numbers with Sigma x/sub i//sup 2/<or=n Gamma and state sequences s=(S/sub 1/,---,s/sub n/) of real numbers with Sigma s/sub i//sup 2/<or=n Lambda ; the output sequence x+s+V, where V=(V/sub 1/,---,V/sub n/) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance sigma /sup 2/. It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log (1+ Gamma /( Lambda + sigma /sup 2/)) if Lambda < Gamma and is 0 otherwise.<<ETX>>