Capacity of the Gaussian arbitrarily varying channel

The Gaussian arbitrarily varying channel with input constraint r and state constraint 2 admits input sequences x = ( x l , , x , ~ ) of real numbers with Cxf 5 nT and state sequences s = ( 5 ,. , T , ~ ) of real numbers with L Y ~ 5 H A ; the output sequence x + s + V , where V = ( VI, , y , ) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance c’. It is proved that the capacity of this arbitrarily varying channel for deterministic codes and the average probability of error criterion equals l o g ( l + r/( 2 t c2) ) if Z < r and is 0 otherwise. Index Terms -Arbitrarily varying channel, Gaussian, capacity.