Capacity bounds for identification via broadcast channels that are optimal for the determination broadcast channel

An inner bound to the capacity region for identification via a broadcast channel with feedback and a soft outer bound to the capacity region of a general broadcast channel without feedback are established, allowing randomized encoding in both cases. These results can be combined to determine the identification capacity region for the deterministic broadcast channel; the set of achievable second-order rate pairs (R₁,R₂) for the deterministic broadcast channel is given by the constraints 0⩽R ₁⩽H(Y₁) and 0⩽R ₂⩽H(Y_Z), where (Y ₁,Y₂) are the channel outputs of some input random variable X. These results are the first multiuser results obtained for identification. The important corollary for the deterministic case shows that the region of achievable identification rates can exceed the region of achievable identification rates, both in the presence and absence of feedback. Indeed, in the description of the identification capacity region for a deterministic broadcast channel, one observes that the rate-sum constraint R ₁+R₂⩽H(Y₁ ,Y₂) occurring in M.S. Pinsker´s (1978) transmission region does not appear