Coded Downlink Massive Random Access and a Finite de Finetti Theorem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918019512401920 |
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| author | Song, Ryan Attiah, Kareem M. Yu, Wei |
| author_facet | Song, Ryan Attiah, Kareem M. Yu, Wei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_08301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coded Downlink Massive Random Access and a Finite de Finetti Theorem Song, Ryan Attiah, Kareem M. Yu, Wei Information Theory 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. |
| title | Coded Downlink Massive Random Access and a Finite de Finetti Theorem |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.08301 |