Identification via Gaussian Multiple Access Channels in the Presence of Feedback

TL;DR

This paper explores message identification over multi-user Gaussian channels with feedback, establishing capacity regions and demonstrating the benefits of feedback and additional resources for improved communication efficiency.

Contribution

It determines the capacity regions for K-sender Gaussian MACs with feedback and extends the analysis to state-dependent channels, highlighting feedback's role in capacity enhancement.

Findings

Capacity region of K-GMAC with feedback established

Infinite capacity achieved for single-user Gaussian channel with feedback

Feedback and resources like quantum entanglement improve identification performance

Abstract

We investigate message identification over a K-sender Gaussian multiple access channel (K-GMAC). Unlike conventional Shannon transmission codes, the size of randomized identification (ID) codes experiences a doubly exponential growth in the code length. Improvements in the ID approach can be attained through additional resources such as quantum entanglement, common randomness (CR), and feedback. It has been demonstrated that an infinite capacity can be attained for a single-user Gaussian channel with noiseless feedback, irrespective of the chosen rate scaling. We establish the capacity region of both the K-sender Gaussian multiple access channel (K-GMAC) and the K-sender state-dependent Gaussian multiple access channel (K-SD-GMAC) when strictly causal noiseless feedback is available.