In this paper, we propose CodedSketch, as a distributed straggler-resistant scheme to compute an approximation of the multiplication of two massive matrices. The objective is to reduce the recovery threshold, defined as the total number of worker nodes that we need to wait for to be able to recover the final result. To exploit the fact that only an approximated result is required, in reducing the recovery threshold, some sorts of pre-compression are required. However, compression inherently involves some randomness that would lose the structure of the matrices. On the other hand, considering the structure of the matrices is crucial to reduce the recovery threshold. In CodedSketch, we use count-sketch, as a hash-based compression scheme, on the rows of the first and columns of the second matrix, and a structured polynomial code on the columns of the first and rows of the second matrix. This arrangement allows us to exploit the gain of both in reducing the recovery threshold. To increase the accuracy of computation, multiple independent count-sketches are needed. This independency allows us to theoretically characterize the accuracy of the result and establish the recovery threshold achieved by the proposed scheme. To guarantee the independency of resulting count-sketches in the output, while keeping its cost on the recovery threshold minimum, we use another layer of structured codes.
We propose SwiftAgg+, a novel secure aggregation protocol for federated learning systems, where a central server aggregates local models of N ∈ N distributed users, each of size L ∈ N, trained on their local data, in a privacypreserving manner. SwiftAgg+ can significantly reduce the communication overheads without any compromise on security, and achieve the optimum communication load within a diminishing gap. Specifically, in presence of at most D dropout users, SwiftAgg+ achieves average per-user communication load of (1 + O( 1 N ))L and the server communication load of (1 + O( 1 N ))L, with a worst-case information-theoretic security guarantee, against any subset of up to T semi-honest users who may also collude with the curious server. The proposed SwiftAgg+ has also a flexibility to reduce the number of active communication links at the cost of increasing the the communication load between the users and the server. In particular, for any K ∈ N, SwiftAgg+ can achieve the uplink communication load of (1 + T K )L, and per-user communication load of up to (1 − 1 N )(1 + T +D K )L, where the number of pair-wise active connections in the network is N 2 (K + T + D + 1).
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