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An Achievable Rate-Distortion Region of Joint Identification and Sensing for Multiple Access Channels

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

TL;DR

The paper addresses joint identification and sensing over a state‑dependent MAC with noiseless strictly causal feedback. It extends ID with feedback to a K‑SD‑MAC and derives lower bounds on the deterministic and randomized ID capacity‑distortion regions, showing that a joint design can outperform a separation approach. The proofs adapt IDF coding to the multi‑user setting using common randomness, typical sequences, and coloring techniques, and an example with a binary adder MAC illustrates the performance gains. These results have implications for future 6G networks by enabling efficient joint transmission and sensing and point to future work on converses and Gaussian channel extensions.

Abstract

In contrast to Shannon transmission codes, the size of identification (ID) codes for discrete memoryless channels (DMCs) experiences doubly exponential growth with the block length when randomized encoding is used. Additional enhancements within the ID paradigm can be realized through supplementary resources such as quantum entanglement, common randomness (CR), and feedback. Joint transmission and sensing demonstrate significant benefits over separation-based methods. Inspired by the significant impact of feedback on the ID capacity, our work delves into the realm of joint ID and sensing (JIDAS) for state-dependent multiple access channels (SD-MACs) with noiseless strictly casual feedback. Here, the senders aim to convey ID messages to the receiver while simultaneously sensing the channel states. We establish a lower bound on the capacity-distortion region of the SD-MACs. An example shows that JIDAS outperforms the separation-based approach.

An Achievable Rate-Distortion Region of Joint Identification and Sensing for Multiple Access Channels

TL;DR

The paper addresses joint identification and sensing over a state‑dependent MAC with noiseless strictly causal feedback. It extends ID with feedback to a K‑SD‑MAC and derives lower bounds on the deterministic and randomized ID capacity‑distortion regions, showing that a joint design can outperform a separation approach. The proofs adapt IDF coding to the multi‑user setting using common randomness, typical sequences, and coloring techniques, and an example with a binary adder MAC illustrates the performance gains. These results have implications for future 6G networks by enabling efficient joint transmission and sensing and point to future work on converses and Gaussian channel extensions.

Abstract

In contrast to Shannon transmission codes, the size of identification (ID) codes for discrete memoryless channels (DMCs) experiences doubly exponential growth with the block length when randomized encoding is used. Additional enhancements within the ID paradigm can be realized through supplementary resources such as quantum entanglement, common randomness (CR), and feedback. Joint transmission and sensing demonstrate significant benefits over separation-based methods. Inspired by the significant impact of feedback on the ID capacity, our work delves into the realm of joint ID and sensing (JIDAS) for state-dependent multiple access channels (SD-MACs) with noiseless strictly casual feedback. Here, the senders aim to convey ID messages to the receiver while simultaneously sensing the channel states. We establish a lower bound on the capacity-distortion region of the SD-MACs. An example shows that JIDAS outperforms the separation-based approach.
Paper Structure (7 sections, 4 theorems, 34 equations, 2 figures, 1 table)

This paper contains 7 sections, 4 theorems, 34 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Main Results
  3. Proof
  4. Proof of Theorem \ref{['thm.JdIDAS']}
  5. Sketch of Proof of Theorem \ref{['thm.JrIDAS']}
  6. Example
  7. Conclusions

Key Result

Theorem 6

If all senders can transmit with positive rates, then the deterministic ID capacity-distortion region $\mathcal{C}_{ID}^d(\boldsymbol{D})$ of a K-SD-MAC $W_S$ is lower-bounded by where $\boldsymbol{\mathcal{X}}^{D}=\mathcal{X}_{1}^{D_{1}}\times \cdots \times\mathcal{X}_{K}^{D_{K}}$, and $\mathcal{X}_{k}^{D_k}=\left\{x_k\in\mathcal{X}_k|d_k^*(x_k)\le D_k\right\}$ representing the sets of admissibl

Figures (2)

  • Figure 1: K-SD-MAC with noiseless causal feedback
  • Figure 2: Joint approach vs. separation-based approach

Theorems & Definitions (11)

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