Abstract
A minimax converse for the identification via channels is derived. By this converse, a general formula for the identification capacity, which coincides with the transmission capacity, is proved without the assumption of the strong converse property. Furthermore, the optimal second-order coding rate of the identification via channels is characterized when the type I error probability is non-vanishing and the type II error probability is vanishing. Our converse is built upon the so-called partial channel resolvability approach; however, the minimax argument enables us to circumvent a flaw reported in the literature.
Highlights
T HE identification is one of typical functions such that randomization significantly reduces the amount of communication necessary to compute those functions; e.g., see [26]
We have derived a minimax converse bound for the identification via channel
By using this converse bound, we have derived the general formula for the identification capacity without the assumption of the strong converse property; the problem has been unsolved for a long time
Summary
T HE identification is one of typical functions such that randomization significantly reduces the amount of communication necessary to compute those functions; e.g., see [26]. The identification capacity of general channels can be lower bounded by the spectral infmutual information rate maximized over input processes When those upper bound and lower bound coincide, which is termed the strong converse property, it was shown in [19] that the identification capacity and the optimal rate of the channel resolvability coincide with the transmission capacity of the same channels. The key difference between our argument and the argument in [35, Lemma 2] is as follows: in our argument, we consider a truncated channel induced from a fixed auxiliary output distribution; on the other hand, truncated channels are constructed from output distributions that depend on input distributions in [35, Lemma 2] In the former case, we can bound the number of messages of an identification code by the number of M -types without causing any trouble; this enables us to circumvent the flaw reported in [20, Remark 2].
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