Channel-code detection by a third-party receiver via the likelihood ratio test

Channel codebook detection is of interest in cognitive paradigm or security applications. A binary hypothesis testing problem is considered, where a receiver has to detect the channel-code from two possible choices upon observing noise-affected codewords through a communication channel. For analytical tractability, it is assumed that the two channel-codes are linear block codes with identical block-length. In a first, this work studies the likelihood ratio test for minimizing the error probability in this detection problem. In an asymptotic setting, where a large number of noise-affected codewords are available for detection, the Chernoff information characterizes the error probability. A lower bound on the Chernoff information, based on the parameters of the two hypothesis, is established. Further, it is shown that if likelihood based efficient (generalized distributive law or BCJR) bit-decoding algorithms are available for the two codes, then the likelihood ratio test for the code-detection problem can be performed in a computationally feasible manner.