Security, Privacy, and Linear Function Retrieval in Combinatorial Multi-Access Coded Caching with Private Caches

We consider combinatorial multi-access coded caching with private caches, where users are connected to two types of caches: private caches and multi-access caches. Each user has its own private cache, while multi-access caches are connected in the same way as caches are connected in a combinatorial topology. A scheme is proposed that satisfies the following three requirements simultaneously: (a) Linear Function Retrieval (LFR), (b) content security against an eavesdropper, and (c) demand privacy against a colluding set of users. It is shown that the private caches included in this work enable the proposed scheme to provide privacy against colluding users. For the same rate, our scheme requires less total memory accessed by each user and less total system memory than the existing scheme for multi-access combinatorial topology (no private caches) in the literature. We derive a cut-set lower bound and prove optimality when r≥C−1. For r<C−1, we show a constant gap of 5 under certain conditions. Finally, the proposed scheme is extended to a more general setup where different users are connected to different numbers of multi-access caches, and multiple users are connected to the same subset of multi-access caches.