Blind Updates in Coded Caching
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We consider the centralized coded caching system where a library of files is available at the server and their subfiles are cached at the clients as prescribed by a placement delivery array (PDA). We are interested in the problem where a specific file in the library is replaced with a new file at the server, the contents of which are correlated with the file being replaced, and this replacement needs to be communicated to the caches. The server loses the original file when the replacement is done and is unaware of the differences between the two files, whereas each cache has access to specific subfiles of the original file as dictated by the PDA. We model the correlation between the two files by assuming that they differ in at the most ϵ subfiles, and aim to reduce the number of bits broadcast by the server to update the caches. We design a new elegant coded transmission strategy for the server to update the caches blindly, and also identify another simple scheme that is based on MDS codes. We then derive converse bounds on the minimum cost ℓ^* among all linear strategies. Equipped with these results, we identify ℓ^* when the caching system uses a PDA of Yan et al. For two other families of PDAs – the Maddah-Ali-Niesen scheme and a scheme by Tang & Ramamoorthy and Yan et al. – we show that our new scheme has cost ℓ^*(1 + o(1)) when the updates are sufficiently sparse, while the scheme using MDS codes has order-optimal cost when the updates are dense.
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