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The Optimal Memory-Rate Trade-Off for the Non-Uniform Centralized Caching Problem With Two Files Under Uncoded Placement

Michael Christoph Gastpar, Pierre Victor Xavier Quinton, Saeid Sahraei

A new scheme for the problem of centralized coded caching with non-uniform demands is proposed. The distinguishing feature of the proposed placement strategy is that it admits equal sub-packetization for all files while allowing the users to allocate more cache to the files which are more popular. This creates natural broadcasting opportunities in the delivery phase which are simultaneously helpful for the users who have requested files of different popularities. For the case of two files, we propose a new delivery strategy based on interference alignment which enables each user to decode his desired file following a two-layer peeling decoder. Furthermore, we extend the existing converse bounds for uniform demands under uncoded placement to the nonuniform case. To accomplish this, we construct N! auxiliary users, corresponding to all permutations of the N files, each caching carefully selected sub-packets of the files. Each auxiliary user provides a different converse bound. The overall converse bound is the maximum of all these N! bounds. We prove that our achievable delivery rate for the case of two files meets this converse, thereby establishing the optimal expected memory-rate trade-off for the case of K users and two files with arbitrary popularities under uncoded placement.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

A Novel Centralized Strategy for Coded Caching with Non-uniform Demands

Michael Christoph Gastpar, Pierre Victor Xavier Quinton, Saeid Sahraei

Despite significant progress in the caching literature concerning the worst case and uniform average case regimes, the algorithms for caching with nonuniform demands are still at a basic stage and mostly rely on simple grouping and memory-sharing techniques. In this work we introduce a novel centralized caching strategy for caching with nonuniform file popularities. Our scheme allows for assigning more cache to the files which are more likely to be requested, while maintaining the same sub-packetization for all the files. As a result, in the delivery phase it is possible to perform linear codes across files with different popularities without resorting to zero-padding or concatenation techniques. We will describe our placement strategy for arbitrary range of parameters. The delivery phase will be outlined for a small example for which we are able to show a noticeable improvement over the state of the art.

2018