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Covert Multi-Access Communication with a Non-Covert User

Abdelaziz Bounhar, Mireille Sarkiss, Michèle Wigger

TL;DR

This work analyzes a three-user discrete memoryless MAC where two users must communicate covertly to a common receiver in the presence of a warden, while a third user communicates openly. It develops a phase-m multiplexing coding scheme that concatenates covert and non-covert codes across multiple phases, achieving vanishing error and vanishing warden detectability while characterizing the optimal trade-off between covert rates, non-covert rates, and secret-key rates. The key finding is that covert bits scale on the order of $\sqrt{n}$ and that introducing a non-covert user can boost the covert capacity under tight secret-key constraints, with the entire region described by explicit single-letter expressions and a converse proof. Numerical examples on binary channels illustrate tangible gains from phase-based multiplexing and the presence of a non-covert user, offering guidance for covert IoT communications and physical-layer security design.

Abstract

In this paper, we characterize the fundamental limits of a communication system with three users (i.e., three transmitters) and a single receiver where communication from two covert users must remain undetectable to an external warden. Our results show a tradeoff between the highest rates that are simultaneously achievable for the three users. They further show that the presence of a non-covert user in the system can enhance the capacities of the covert users under stringent secret-key constraints. To derive our fundamental limits, we provide an information-theoretic converse proof and present a coding scheme that achieves the performance of our converse result. Our coding scheme is based on multiplexing different code phases, which seems to be essential to exhaust the entire tradeoff region between the rates at the covert and the two non-covert users. This property is reminiscent of the setup with multiple non-covert users, where multiplexing is also required to exhaust the entire rate-region.

Covert Multi-Access Communication with a Non-Covert User

TL;DR

This work analyzes a three-user discrete memoryless MAC where two users must communicate covertly to a common receiver in the presence of a warden, while a third user communicates openly. It develops a phase-m multiplexing coding scheme that concatenates covert and non-covert codes across multiple phases, achieving vanishing error and vanishing warden detectability while characterizing the optimal trade-off between covert rates, non-covert rates, and secret-key rates. The key finding is that covert bits scale on the order of and that introducing a non-covert user can boost the covert capacity under tight secret-key constraints, with the entire region described by explicit single-letter expressions and a converse proof. Numerical examples on binary channels illustrate tangible gains from phase-based multiplexing and the presence of a non-covert user, offering guidance for covert IoT communications and physical-layer security design.

Abstract

In this paper, we characterize the fundamental limits of a communication system with three users (i.e., three transmitters) and a single receiver where communication from two covert users must remain undetectable to an external warden. Our results show a tradeoff between the highest rates that are simultaneously achievable for the three users. They further show that the presence of a non-covert user in the system can enhance the capacities of the covert users under stringent secret-key constraints. To derive our fundamental limits, we provide an information-theoretic converse proof and present a coding scheme that achieves the performance of our converse result. Our coding scheme is based on multiplexing different code phases, which seems to be essential to exhaust the entire tradeoff region between the rates at the covert and the two non-covert users. This property is reminiscent of the setup with multiple non-covert users, where multiplexing is also required to exhaust the entire rate-region.
Paper Structure (10 sections, 2 theorems, 15 equations, 6 figures)

This paper contains 10 sections, 2 theorems, 15 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Problem statement
  4. Coding Scheme, Main Result, and Numerical Simulations
  5. Coding Scheme
  6. Generalization of the Coding Scheme
  7. Main Results
  8. Numerical examples
  9. Proof of Converse to Theorem \ref{['th:asymp_result']}
  10. Summary and Discussion

Key Result

Theorem 1

Choose an arbitrary set of For any $\epsilon>0$, arbitrary small positive numbers $\xi_m \in (0,1)$ for all $m \in \{1,\ldots,6\}$, and sufficiently large blocklength $n$, it is possible to find codes, $\mathcal{C}_{1,t}, \mathcal{C}_{2,t}, \mathcal{C}_{3,t}$ of blocklengths $n_t=\lfloor n \cdot P_T(t)\rfloor$, for $t=1, \ldo so that the encoding/decoding scheme described in the previous subsecti

Figures (6)

  • Figure 1: MAC setup with 2 covert users and a non-covert user in the presence of an external warden.
  • Figure 2: Our encoding process under $\mathcal{H}=1$ for binary input alphabets at all users. Under $\mathcal{H}=0$, the covert users 1 and 2 send the all-zero sequence.
  • Figure 3: Under $\mathcal{H}=1$, the non-covert message $W_3$ is decoded first, followed by parallel decoding of the covert messages using an Interference as Noise scheme. Under $\mathcal{H}=0$, we decode only $W_3$.
  • Figure 4: Rate-region $(r_2,R_3)$ for secret-key rates $k_1\leq 0.8, k_2\leq 0.8$ and $r_1=0.5$ (solid line) and a degenerate region when restricting to $|\mathcal{T}|=1$ (dashed line).
  • Figure 5: Covert rate $r_2$ as function of secret-key rate $k_2$ when optimizing over $P_{X_3T}$ (solid line) and when choosing $X_3=0$ or $X_3=1$ deterministically (dashed and dash-dotted lines) for a covert rate $r_1=0.1$ and a secret-key rate $k_1 \leq 0.8$.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Theorem 2