On the Optimum Achievable Rates of a Coded Caching Scheme with Small Cache Memory

In the coded caching scheme proposed by Maddah-Ali and Niesen, we usually consider the setup where K users have the cache memory of size MF and require arbitrary one of N files. Finding the optimum achievable rate of a codeword is one of the fundamental problems of the coded cashing scheme. In this paper, we first consider the case of M = 1/K and give a simplified proof on the achievability part. This result can be extended to the case where the users have cash memory of unequal sizes. We can obtain the optimum achievable rate for this case under a certain assumption. Finally, we consider a new problem on the coded caching where an additional user wants to recover all the files from a codeword and the content of his/her cache memory. We clarify the optimum achievable size of the cash memory of this additional user.