Deterministic Identification Over Channels With Power Constraints

TL;DR

This paper characterizes the deterministic identification capacity of Gaussian and discrete memoryless channels without randomization, showing it can be significantly higher than transmission capacity, with detailed proofs provided.

Contribution

It provides the first explicit proof of the deterministic identification capacity for Gaussian and DMC channels, establishing their capacities without local randomness.

Findings

DI capacity of Gaussian channel is infinite regardless of noise

Deterministic identification capacity scales exponentially with block length

Achievable rates can surpass traditional transmission rates

Abstract

The identification capacity is developed without randomization at neither the encoder nor the decoder. In particular, full characterization is established for the deterministic identification (DI) capacity for the Gaussian channel and for the general discrete memoryless channel (DMC) with and without constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness given at the encoder, resulting in a double exponential number of messages in the block length. In the deterministic setup, the number of messages scales exponentially, as in Shannon's transmission paradigm, but the achievable identification rates can be significantly higher than those of the transmission rates. Ahlswede and Dueck further stated a capacity result for the deterministic setting of a DMC, but did not provide an explicit proof. In this paper, a detailed proof is given for both the Gaussian channel and the general DMC. The DI capacity of a Gaussian channel is infinite regardless of the noise.