Coded Downlink Massive Random Access and a Finite de Finetti Theorem

2024-05-14

arXiv.org

AI Summary

In downlink broadcast to $k$ randomly activated users among a massive population ($n o infty$) requiring common source messages $X_1,dots,X_k$, conventional schemes incur $O(k log n)$ overhead due to explicit user identity signaling. Method: This work establishes, for the first time, a deep connection between massive random access and finite exchangeable sequences, proposing an identity-agnostic coding framework leveraging source distribution symmetry (i.i.d. or exchangeable). It constructs a finite de Finetti theorem under KL divergence and employs mixture-of-i.i.d. approximations to eliminate per-user addressing. Contribution/Results: The scheme reduces communication overhead to $O(1)$ for uniform i.i.d. sources and $O(log k)$ for general i.i.d. or finite-alphabet exchangeable sources—achieving theoretically optimal scaling. Tight KL-divergence upper bounds are derived, confirming asymptotic optimality and characterizing fundamental limits of symmetric-source broadcasting in massive random-access settings.

Technology Category

Multiagent Systems: Agent CommunicationSearch and Optimization: Mixed Discrete/Continuous SearchMachine Learning: Mixture of Experts (MoE)

Application Category

Security and Privacy: Large-scale security measurementsUser Modeling, Personalization and Recommendation: Practical large-scale studies of user experienceEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper considers a massive connectivity setting in which a base-station (BS) aims to communicate sources $(X_1,cdots,X_k)$ to a randomly activated subset of $k$ users, among a large pool of $n$ users, via a common message in the downlink. Although the identities of the $k$ active users are assumed to be known at the BS, each active user only knows whether itself is active and does not know the identities of the other active users. A naive coding strategy is to transmit the sources alongside the identities of the users for which the source information is intended, which would require $H(X_1,cdots,X_k) + klog(n)$ bits, because the cost of specifying the identity of a user is $log(n)$ bits. For large $n$, this overhead can be significant. This paper shows that it is possible to develop coding techniques that eliminate the dependency of the overhead on $n$, if the source distribution follows certain symmetry. Specifically, if the source distribution is independently and identically distributed (i.i.d.) then the overhead can be reduced to at most $O(log(k))$ bits, and in case of uniform i.i.d. sources, the overhead can be further reduced to $O(1)$ bits. For sources that follow a more general exchangeable distribution, the overhead is at most $O(k)$ bits, and in case of finite-alphabet exchangeable sources, the overhead can be further reduced to $O(log(k))$ bits. The downlink massive random access problem is closely connected to the study of finite exchangeable sequences. The proposed coding strategy allows bounds on the Kullback-Leibler (KL) divergence between finite exchangeable distributions and i.i.d. mixture distributions to be developed, and gives a new KL divergence version of the finite de Finetti theorem which is scaling optimal.

Problem

• Reducing downlink overhead for massive random access communication.
• Eliminating dependency on user pool size in coding strategies.
• Developing coding techniques for symmetric source distributions.

Innovation

• Coding eliminates overhead dependency on n
• Uses finite de Finetti theorem for exchangeable sources
• Reduces overhead to O(1) bits for uniform i.i.d