The Capacity Region of the Multiple Access Channel with Non-Signaling Assistance

2026-08-13

AI Summary

This study addresses the characterization of the capacity region for k-user discrete memoryless multiple-access channels (MACs) without signaling assistance. By extending the two-sender outer bound to the k-user scenario and integrating information-theoretic analysis with non-signaling resource modeling, this work fully characterizes the capacity region under arbitrarily correlated inputs. The results demonstrate that the derived capacity region structure aligns with classical formulations and establish a tight upper bound of k for the multiplicative capacity gain. Consequently, this research not only resolves the open problem of capacity region characterization for multi-user non-signaling-assisted MACs but also confirms that the maximum capacity gain can reach k, thereby providing a fundamental theoretical benchmark for evaluating the efficacy of non-signaling resources in multiple-access communications.

Abstract

The capacity region of the $K$-sender discrete memoryless multiple access channel (MAC) is fully characterized when non-signaling (NS) assistance is available to all $K$ transmitters and the receiver. It is shown to have the same form as the classical capacity region of the MAC, except that the input distribution is allowed to be arbitrarily dependent across the senders. In particular, the NS-assisted capacity region matches the natural generalization to $K$ senders of an outer bound that was previously established by Fawzi and Fermé for $K=2$ senders. Additionally, we provide examples of $K$-sender MACs where the multiplicative gain in capacity from NS-assistance is arbitrarily close to $K$. Combined with an upper bound from prior work, this establishes $K$ as the extremal value of the multiplicative gain from NS-assistance across all $K$-sender MAC settings.

Problem

• Multiple Access Channel
• Non-Signaling Assistance
• Capacity Region
• Discrete Memoryless Channel

Innovation

• Non-Signaling Assistance
• Multiple Access Channel
• Capacity Region
• Arbitrary Input Dependence
• Multiplicative Gain