Coded Downlink Massive Random Access and a Finite de Finetti Theorem
Ryan Song, Kareem M. Attiah, Wei Yu
TL;DR
The paper addresses coded downlink transmission to a randomly active subset of users in a massive access setting, exploiting exchangeable source distributions to decouple header overhead from the pool size $n$. It introduces a two-stage codebook scheme that searches for the first matching codeword index in an urn-like, shared codebook and proves that the common message length concentrates around the joint source entropy $H(X_1, \dots,X_k)$ with an overhead that scales at most as $O(k)$ in general and as $O(\log k)$ for i.i.d. or finite-alphabet exchangeable sources. A KL-divergence version of the finite de Finetti theorem is developed, bounding the mismatch between exchangeable source distributions and i.i.d. mixtures, with tight, scalable bounds that match known optimal scaling. The framework covers applications such as scheduling, categorization, and resource allocation, and demonstrates that header overhead in downlink control can be made almost independent of the user pool size, which is significant for IoT and machine-type communications. Overall, the work unify downlink coding under symmetry with fundamental finite de Finetti bounds, offering practically relevant reductions in communication overhead for large-scale wireless systems.
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. This requires $H(X_1,\cdots,X_k) + k\log(n)$ bits, because the cost of specifying the identity of one out of $n$ users 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.