Identification over Additive Noise Channels in the Presence of Feedback

TL;DR

This paper investigates deterministic message identification over additive white noise channels with feedback, demonstrating infinite feedback capacity for identification regardless of power constraints and coding schemes.

Contribution

It introduces a coding scheme leveraging common randomness and feedback to achieve arbitrarily large deterministic identification codes with infinite capacity.

Findings

Deterministic identification capacity is infinite with feedback.

Common randomness enables large identification codes.

Results hold under various power constraints and coding schemes.

Abstract

We analyze deterministic message identification via channels with non-discrete additive white noise and with a noiseless feedback link under both average power and peak power constraints. The identification task is part of Post Shannon Theory. The consideration of communication systems beyond Shannon's approach is useful in order to increase the efficiency of information transmission for certain applications. We propose a coding scheme that first generates infinite common randomness between the sender and the receiver. If the channel has a positive message transmission feedback capacity, for given error thresholds and sufficiently large blocklength this common randomness is then used to construct arbitrarily large deterministic identification codes. In particular, the deterministic identification feedback capacity is infinite regardless of the scaling (exponential, doubly exponential, etc.) chosen for the capacity definition. Clearly, if randomized encoding is allowed in addition to the use of feedback, these results continue to hold.