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Establishing code equivalences between index coding and network coding provides important insights for code design. Previous works showed an equivalence relation between any index-coding instance and a network-coding instance, for which a code for one instance can be translated to a code for the other instance with the same decoding-error performance. The equivalence also showed a surprising result that any network-coding instance can be mapped to an index-coding instance with a properly designed code translation.

We consider three different variants of differential privacy (DP), namely approximate DP, Rényi DP (RDP), and hypothesis test DP. In the first part, we develop a machinery for optimally relating approximate DP to RDP based on the joint range of two $f$ -divergences that underlie the approximate DP and RDP. In particular, this enables us to derive the optimal approximate DP parameters of a mechanism that satisfies a given level of RDP.

Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In particular, the overhead of the state-of-the-art protocols for secure model aggregation grows quadratically with the number of users.