Identification in the presence of feedback-a discovery of new capacity formulas

A study is made of the identification problem in the presence of a noiseless feedback channel, and the second-order capacity C_f (resp. C_F) for deterministic (resp. randomized) encoding strategies is determined. Several important phenomena are encountered. (1) Although feedback does not increase the transmission capacity of a discrete memoryless channel (DMC), it does increase the (second-order) identification capacity; (2) noise increases C_f; (3) the structure of the new capacity formulas is simpler than C.E. Shannon´s (1948) familiar formula. This has the effect that proofs of converses become easier than in the authors´ previous work