An Optimal Linear Error Correcting Scheme for Shared Caching with Small Cache Sizes

Coded caching is a technique which enables the server to reduce the peak traffic rate by making use of the caches available at each user. In the classical coded caching problem, a centralized server is connected to many users through an error free link. Each user have a dedicated cache memory. This paper considers the shared caching problem which is an extension of the coded caching problem in which each cache memory could be shared by more than one user. An existing prefetching and delivery scheme for the shared caching problem with better rate-memory tradeoff than the rest is studied and the optimality of the scheme is proved by using techniques from index coding. The worst case rate of the coded caching problem is also obtained by using cut-set bound techniques. An optimal linear error correcting delivery scheme is obtained for the shared caching problem satisfying certain conditions.