4 research outputs found
The Optimal Memory-Rate Trade-off for the Non-uniform Centralized Caching Problem with Two Files under Uncoded Placement
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 auxiliary users, corresponding to
all permutations of the 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 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
users and two files with arbitrary popularities under uncoded placement