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Identification via Gaussian Multiple Access Channels in the Presence of Feedback

Yaning Zhao, Wafa Labidi, Holger Boche, Eduard Jorswieck, Christian Deppe

TL;DR

This paper shows that for a K-user Gaussian MAC with noiseless strictly causal feedback, each user can achieve an infinite identification rate under average power constraints when using double-exponential ID codes. The authors construct a two-stage coding scheme that first generates common randomness via the feedback-enabled channel output, then maps common randomness to identities using random binning and a standard transmission code, ensuring exponentially small type-I errors and vanishing type-II errors as the block length grows. The main contributions are the identification of the IDF capacity region as unbounded ($R_k$ can be infinite for all $k$) for both the K-GMAC and the K-SD-GMAC, along with a concrete common randomness based proof strategy that extends to state-dependent Gaussian MACs. The results imply that, in such feedback-enabled Gaussian networks, identification tasks can achieve dramatically higher growth in the number of identifiable messages than conventional transmission, with potential implications for secure and scalable ID protocols in 6G-like systems. $N=2^{2^{nR}}$, $R_k<+ finite$, and $P_{total}>0$ are central quantities underpinning the infinite-ID-rate conclusion.

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.

Identification via Gaussian Multiple Access Channels in the Presence of Feedback

TL;DR

This paper shows that for a K-user Gaussian MAC with noiseless strictly causal feedback, each user can achieve an infinite identification rate under average power constraints when using double-exponential ID codes. The authors construct a two-stage coding scheme that first generates common randomness via the feedback-enabled channel output, then maps common randomness to identities using random binning and a standard transmission code, ensuring exponentially small type-I errors and vanishing type-II errors as the block length grows. The main contributions are the identification of the IDF capacity region as unbounded ( can be infinite for all ) for both the K-GMAC and the K-SD-GMAC, along with a concrete common randomness based proof strategy that extends to state-dependent Gaussian MACs. The results imply that, in such feedback-enabled Gaussian networks, identification tasks can achieve dramatically higher growth in the number of identifiable messages than conventional transmission, with potential implications for secure and scalable ID protocols in 6G-like systems. , , and are central quantities underpinning the infinite-ID-rate conclusion.

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.
Paper Structure (8 sections, 6 theorems, 41 equations, 3 figures)

This paper contains 8 sections, 6 theorems, 41 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Model and Main Results
  4. Proof
  5. Common Randomness Generation
  6. Proof of Theorem \ref{['thm:GMAC']}
  7. Sketch proof of Theorem \ref{['thm:SD-GMAC']}
  8. Discussion and Conclusions

Key Result

Theorem 3

labidi2021identification Let $P>0$. Then there exists for all $R>0$ a blocklength $n_0$ such that for every $n\ge n_0$ there exists a deterministic IDF code for $W_{\sigma^2}$ of blocklength $n$ with $N=2^{2^{nR}}$ identities and with $\lambda\in\left(0,\frac{1}{2}\right)$, i.e., $C(W_{\sigma^2},P)=

Figures (3)

  • Figure 1: IDF via single-user Gaussian channel with feedback
  • Figure 2: K-GMAC with noiseless feedback
  • Figure 3: K-SD-GMAC with noiseless feedback

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Theorem 3
  • Definition 4
  • Definition 5
  • Theorem 6
  • Definition 7
  • Theorem 8
  • Remark 9
  • Lemma 10
  • ...and 3 more