On error exponents in hypothesis testing

The classical result of Blahut, which characterizes achievable error exponents in binary hypothesis testing, is generalized in two different directions. First, in M-ary hypothesis testing, the tradeoff of all M(M - 1) types of error exponents and corresponding optimal decision schemes are explored. Then, motivated by a power-constrained distributed detection scenario, binary hypothesis testing is revisited, and the tradeoff of power consumption versus error exponents is fully characterized. In the latter scenario, sensors are allowed to make random decisions as to whether they should remain silent and save power, or transmit and improve detection quality. It is then shown by an example that optimal sensor decisions may indeed be random.