Mismatched identification via channels

The problem of identification via channels concerns a decoder that needs to provide a reliable answer to the question of whether or not a specific message (unknown in advance) was transmitted. The achievability result of Ahlswede and Dueck who introduced this problem, relied on a universal identification decoder. This decoder assigns a channel output vector yⁿ to a decision region D_m if the empirical mutual information between yⁿ and an input vector that could have been transmitted given message m exceeds a certain threshold. We study a generalized class of identification decoders that determine the decision regions by comparing a type-dependent 'metric' to a threshold. We introduce the notion of identification capacity with respect to a given decoding metric as the supremum of achievable normalized iterated logarithms of the number of messages that can be identified reliably using these metrics. We characterize achievable identification rates and error exponents using a type-dependent metric. In the case of an additive metric we show that the random coding achievable rate for classical mismatched decoding is an achievable identification rate.