The Optimal Memory-Rate Trade-off for the Non-uniform Centralized Caching Problem with Two Files under Uncoded Placement
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We propose a novel caching strategy for the problem of centralized coded caching with non-uniform demands. Our placement strategy can be applied to an arbitrary number of users and files, and can be easily adapted to the scenario where file popularities are user-specific. The distinguishing feature of the proposed placement strategy is that it allows for equal sub-packetization for all files while requiring the users to allocate more cache to the more popular files. This creates natural broadcasting opportunities in the delivery phase which are simultaneously helpful for users who have requested files of different popularities. For the case of two files, we propose a delivery strategy which meets a natural extension of the existing converse bounds under uncoded placement to non-uniform demands, thereby establishing the optimal expected memory-rate trade-off for the case of two files with arbitrary popularities under the restriction of uncoded placement.
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