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

Abstract

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.

Memory-Rate Tradeoff for Caching with Uncoded Placement under Nonuniform Random Demands

“…The gap between the achievable rate of either the CCS or the MCCS and the optimal caching with uncoded placement remains unknown. Most recently, the exact memory-rate tradeoff under uncoded placement for the case of two files was characterized [31]. However, the caching scheme proposed in [31] is only designed for two files, which is not extendable to general scenarios.…”

“…Most recently, the exact memory-rate tradeoff under uncoded placement for the case of two files was characterized [31]. However, the caching scheme proposed in [31] is only designed for two files, which is not extendable to general scenarios.…”

“…One possible solution to avoid this loss is to create as many subfiles of equal size as possible during the placement phase. Coincidentally, such an approach was exploited in [31] for N = 2 files, where a placement scheme was proposed to create equal subfile size and was shown to be an optimal caching scheme with uncoded placement for two files.…”

“…However, these gaps are still large for practical concerns. Only recently, for two files of nonuniform popularity, a coded caching scheme was proposed [31], which achieves the lower bound for caching with uncoded placement. For the MCCS, existing studies are scarce, and only [32] studied the cache placement optimization under nonuniform file popularity.…”

Content Caching for Shared Medium Networks Under Heterogeneous Users' Behaviours

“…, and therefore we do not need to broadcast it and the delivery rate reduces to 2/3. Authors in [33] generalized this idea to propose a new coded caching strategy under uncoded placement to handle non-uniform demands. This strategy uses equal subpacketization for all contents while allowing to allocate more cache to more popular content.…”