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_1,... , x_n) of real numbers with (1/n){SIGMA x_i sup 2} < GAMMA and state sequences s = (s_1,... , S_n) of real numbers with (1/n) {SIGMA s_i sup 2} < GAMMA, the output sequence being x + s + V where V = (V_1, ... , V_n) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance ({LITTLE SIGMA} sup 2). We prove that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals 1/2 log ( 1 + r/(LAMBDA + {LITTLE SIGMA} sup 2)) if LAMBDA < GAMMA and is 0 otherwise.