Simultaneous communication and detection over compound channels

Consider a compound channel W with L component discrete memoryless channels (DMCs). We seek a channel code which serves two purposes: the code must achieve a communication rate R over every DMC in W, and the decoder must accurately detect which of the DMCs in W is in effect. These two objectives are clearly conflicting: accurate detection of the channel is possible only if the code consists of relatively few codewords; such codes though convey little information. Suppose we measure detection performance using the hypothesis testing error exponent r. We ask the following question: what communication rates R and error exponents r are simultaneously achievable on W? For the case L=2 and a Neyman-Pearson detection approach, we establish single-letter bounds and prove a strong converse