Capacity of the Gaussian arbitrarily varying channel

• Authors: I. Csiszar;P. Narayan
• Venue: IEEE Transactions on Information Theory
• Year: 2006

The Gaussian arbitrarily varying channel with input constraint Γ and state constraint Λ admits input sequences x=(x1,---,Xn) of real numbers with Σxi2⩽nΓ and state sequences s=(S1,---,sn ) of real numbers with Σsi2⩽nΛ; the output sequence x+s+V, where V=(V1,---,Vn) is a sequence of independent and identically distributed Gaussian random variables with mean 0 and variance σ2. 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+Γ/(Λ+σ2)) if Λ<Γ and is 0 otherwise