We consider information-theoretic privacy in federated submodel learning, where a global server has multiple submodels. Compared to the considered conventional learning secure aggregation is adopted for ensuring privacy, provides stronger protection on selection by local machine. propose an achievable scheme that partially adopts private information retrieval (PIR) achieves minimum amount of do...

Assuming sparsity or compressibility of the underlying signals, compressed sensing or compressive sampling (CS) exploits the informational efficiency of under-sampled measurements for increased efficiency yet acceptable accuracy in information gathering, transmission and processing, though it often incurs extra computational cost in signal reconstruction. Shannon information quantities and theo...

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

We study the problem of Private Information Retrieval (PIR) in the presence of prior side information. The problem setup includes a database of K independent messages possibly replicated on several servers, and a user that needs to retrieve one of these messages. In addition, the user has some prior side information in the form of a subset of M messages, not containing the desired message and u...

Information-theoretic studies on the fundamental limits of communication over wireless fading channels typically rely on simplifying assumptions, such as perfect channel state information (CSI), infinite blocklength, and vanishing probability of error. Although these assumptions are reasonable for most of the current wireless communication systems, they may be inaccurate for next-generation wir...

A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that collection structures can be embedded, via a map they call Stone pairing, in space measures, where desired computed. We show closely related but finer grained (finitely additive) measures arises -- Stone-Priestley duality notion types from model enrichi...

This paper considers the linear inverse problem Y = AX ⊕ Z, where A is the incidence matrix of an Erdős-Rényi graph, Z is an i.i.d. noise vector, and X is the vector of unknown variables, assumed to be Boolean. This model is motivated by coding, synchronization, and community detection problems. Without noise, exact recovery is possible if and only the graph is connected, with a sharp threshold...

The advantages of adaptivity and feedback are of immense interest in signal processing and communication with many positive and negative results. Although it is established that adaptivity does not offer substantial reductions in minimax mean square error for a fixed number of measurements, existing results have shown several advantages of adaptivity in complexity of reconstruction, accuracy of...