On Coded Caching with Correlated Files
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This paper studies the fundamental limits of the shared-link caching problem with correlated files, where a server with a library of N files communicates with K users who can store M files. Given an integer r∈[N], correlation is modelled as follows: each r-subset of files contains a common block. The tradeoff between the cache size and the average transmitted load is considered. We first propose a converse bound under the constraint of uncoded cache placement (i.e., each user directly caches a subset of the library bits). We then propose an interference alignment scheme for the cases where users have different requests. The proposed scheme achieves the optimal average load under uncoded cache placement when users demand distinct files. In addition, an extension of the proposed scheme achieves an optimal average load among all possible demands (i.e., not necessarily distinct demands) for KrM ≤ 2N or KrM ≥ (K-1)N or r ∈{1,2,N-1,N}. As a by-product, we show that the proposed scheme reduces the load of existing schemes for the caching problem with multi-requests, and reduces the required finite field size for the distributed computation problem.
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