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This paper considers the secure aggregation problem for federated learning under an information theoretic cryptographic formulation, where distributed training nodes (referred to as users) train models based on their own local data and a curious-but-honest server aggregates the trained models without retrieving other information about users’ local data. Secure aggregation generally contains two phases, namely key sharing phase and model aggregation phase. Due to the common effect of user dropouts in federated learning, the model aggregation phase should contain two rounds, where in the first round the users transmit masked models and, in the second round, according to the identity of surviving users after the first round, these surviving users transmit some further messages to help the server decrypt the sum of users’ trained models. The objective of the considered information theoretic formulation is to characterize the capacity region of the communication rates from the users to the server in the two rounds of the model aggregation phase, assuming that key sharing has already been performed offline in prior. In this context, Zhao and Sun completely characterized the capacity region under the assumption that the keys can be arbitrary random variables. More recently, an additional constraint, known as “uncoded groupwise keys,” has been introduced. This constraint entails the presence of multiple independent keys within the system, with each key being shared by precisely $\mathsf S$ users, where $\mathsf S$ is a defined system parameter. The capacity region for the information theoretic secure aggregation problem with uncoded groupwise keys was established in our recent work subject to the condition ${\mathsf S}\gt {\mathsf K}-{\mathsf U}$ , where $\mathsf K$ is the number of total users and $\mathsf U$ is the designed minimum number of surviving users (which is another system parameter). In this paper we fully characterize the capacity region for this problem by matching a new converse bound and an achievable scheme. Experimental results over the Tencent Cloud show the improvement on the model aggregation time compared to the original secure aggregation scheme.

Physically accurate and mathematically tractable models are presented to characterize the scattering and reflection properties of reconfigurable intelligent surfaces (RISs). We describe a single metallic patch and patch array, as well as their interactions with multiple incident electromagnetic (EM) waves using continuous and discrete strategies. Our models take into account the effect of the incident and scattered angles, polarization features, and the topology and geometry of RISs. In particular, we propose a simple system of linear equations to characterize the multiple-input multiple-output (MIMO) behaviors of RISs under appropriate assumptions. This model can be used as a fundamental tool for analyzing and optimizing the performance of RIS-aided systems in the far-field regime. Using the proposed models, we identify the advantages and limitations of three typical configurations. An important discovery is that the popular phase compensation designs cannot provide complicated beam reshaping functionality. A possible solution is the simultaneous configurations of collecting area and phase shifting. Numerical simulations validate the effectiveness of the proposed configuration schemes.

A notion of sparse dual frames for a given non-exact frame is introduced. The sparse dual frame is motivated in a study of compressed sensing problems where signal are sparse with respect to a redundant and coherent dictionary (frames). A sparse-dual-based 1-analysis is thereby proposed. We show that sparse dual frames are locally stable. An error bound ensuring the correct signal recovery is obtained. More importantly, solutions to very hard problems in compressed sensing with redundant dictionaries that are otherwise completely unsuccessful by known algorithms of 1-synthesis and the 1-analysis are seen as satisfactory, by the new sparse-dual-based approach and an alternating iterative algorithm that we propose. Examples are provided.