Robustness, Security, Privacy, and Linear Function Retrieval From Coded Servers for Users With Multiple-Cache Accessibility

The model considered in this work consists ofHservers where the file library is Maximum Distance Separable (MDS) coded and stored. Each server is connected toKusers through a dedicated shared link, and each user has access to a unique set ofrout ofCcaches. For every set ofrcaches, there is a user. Each user aims to retrieve an arbitrary linear combination of files. All the users should be able to retrieve their demands using the signals from anyLout ofHservers. In addition, the following conditions must be satisfied: (a) content-security from an eavesdropper, b) demand-privacy against non-colluding users and any colluding set of servers. We propose two schemes, one of which satisfies both the above conditions and the other satisfies only the security condition. Over a certain range in the low memory region, our schemes are within a constant multiplicative factor from the optimal. As special cases, our schemes recover some of the previous works in the literature. One of our schemes is extended to a more general setup where different users are connected to different numbers of caches, and multiple users are connected to the same subset of caches.