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Enhancing Sum Capacity via Quantum and No-Signaling Cooperation Between Transmitters

Seung-Hyun Nam, Hyun-Young Park, Jiyoung Yun, Ashutosh Rai, Si-Hyeon Lee, Joonwoo Bae

TL;DR

The paper addresses when transmitter cooperation via quantum or no-signaling resources can increase the sum capacity of discrete memoryless interference/multiple-access channels. It introduces a broad class of game-based channels that become less noisy and decompose into parallel weakly symmetric sub-channels when the input satisfies the winning condition of a pseudo-telepathy game, enabling a provable increase in the sum capacity using quantum or no-signaling strategies. The authors derive a converse upper bound on the $r$-sum capacity and show achievability by constructing cooperative encoders aligned with a winning strategy, establishing $\, ext{C}_s^{ ext{C}} < \, ext{C}_s^{ ext{Q}}$ or $\text{C}_s^{ ext{C}} < \, ext{C}_s^{ ext{NS}}$ for $r \\in \{\text{Q},\text{NS}\}$ when the underlying game is $r$-pseudo-telepathy. This framework generalizes prior results and provides a unified approach to identifying channels where quantum/no-signaling cooperation yields a concrete sum-capacity advantage, with future directions including computation of sum capacities, Gaussian-channel extensions, and potential single-letter characterizations.

Abstract

We consider a communication scenario over a discrete memoryless interference channel or multiple access channel without feedback, where transmitters exploit classical, quantum, or no-signaling cooperation. In this scenario, several previous works have shown that the sum capacities of channels involving pseudo-telepathy games can be enhanced by quantum or no-signaling cooperation. However, a full characterization of which channels admit such an improvement remains open. By focusing on the common characteristics of previously studied channels, we propose a broader class of channels for which quantum or no-signaling cooperation increases the sum capacity. Channels in this class are associated with a pseudo-telepathy game, with channel inputs specified as tuples of questions and answers from the game. In addition, when the channel inputs satisfy the winning condition of the game, the channel decomposes into parallel weakly symmetric sub-channels and is less noisy compared to the case when the inputs do not meet the winning condition.

Enhancing Sum Capacity via Quantum and No-Signaling Cooperation Between Transmitters

TL;DR

The paper addresses when transmitter cooperation via quantum or no-signaling resources can increase the sum capacity of discrete memoryless interference/multiple-access channels. It introduces a broad class of game-based channels that become less noisy and decompose into parallel weakly symmetric sub-channels when the input satisfies the winning condition of a pseudo-telepathy game, enabling a provable increase in the sum capacity using quantum or no-signaling strategies. The authors derive a converse upper bound on the -sum capacity and show achievability by constructing cooperative encoders aligned with a winning strategy, establishing or for when the underlying game is -pseudo-telepathy. This framework generalizes prior results and provides a unified approach to identifying channels where quantum/no-signaling cooperation yields a concrete sum-capacity advantage, with future directions including computation of sum capacities, Gaussian-channel extensions, and potential single-letter characterizations.

Abstract

We consider a communication scenario over a discrete memoryless interference channel or multiple access channel without feedback, where transmitters exploit classical, quantum, or no-signaling cooperation. In this scenario, several previous works have shown that the sum capacities of channels involving pseudo-telepathy games can be enhanced by quantum or no-signaling cooperation. However, a full characterization of which channels admit such an improvement remains open. By focusing on the common characteristics of previously studied channels, we propose a broader class of channels for which quantum or no-signaling cooperation increases the sum capacity. Channels in this class are associated with a pseudo-telepathy game, with channel inputs specified as tuples of questions and answers from the game. In addition, when the channel inputs satisfy the winning condition of the game, the channel decomposes into parallel weakly symmetric sub-channels and is less noisy compared to the case when the inputs do not meet the winning condition.

Paper Structure

This paper contains 11 sections, 5 theorems, 24 equations, 1 figure.

Table of Contents

  1. Introduction
  2. System model & Preliminaries
  3. Communication over IC without transmitter cooperation
  4. Communication over IC with transmitter cooperation
  5. Non-local games
  6. Main results
  7. DM-ICs from non-local games
  8. Enhancing sum capacity
  9. Converse
  10. Achievability
  11. Conclusion & Discussions

Key Result

Lemma 1

If $P_{Y|Q}$ is weakly symmetric, then the point-to-point channel capacity of $P_{Y|Q}$ is given by for all $q \in \mathcal{Q}$. Moreover, the maximum is achieved when $P_Q$ is the uniform distribution on $\mathcal{Q}$, and $P_Y$ becomes the uniform distribution on $\mathcal{Y}$ when $P_Q$ is the uniform distribution on $\mathcal{Q}$.

Figures (1)

  • Figure 1: A schematic diagram of the proposed achievability scheme over a single use $(n=1)$ of a game channel $P^G_{Y_{[K]}|X_{[K]}}$, which exploits a winning strategy $P_{A_{[K]}|Q_{[K]}}$ for a pseudo-telepathy game $G$. For $n \geq 2$, the part in the dash-dot line is copied $n$ times, i.e., $P_{Y_{[K]}|Q_{[K]}}$ is replaced by $P_{Y_{[K]}^n|Q_{[K]}^n} = P_{Y_{[K]}|Q_{[K]}}^{\otimes n}$.

Theorems & Definitions (12)

  • Definition 1
  • Remark 1
  • Definition 2
  • Lemma 1
  • Definition 3
  • Example 1
  • Remark 2
  • Theorem 2
  • Proposition 3
  • Lemma 4
  • ...and 2 more