Towards the Optimal Rate Memory Tradeoff in Caching With Coded Placement

The idea of coded caching for content distribution networks was introduced by Maddah-Ali and Niesen, who considered the canonical
$(N, K)$
cache network in which a server with
$N$
files satisfies the demands of
$K$
users (each equipped with an independent cache of size
$M$
). The optimal rate memory tradeoff for demands where all files are requested by at least one user has been characterized only for small caches where
$M\leq \frac {1}{K}$
and large caches where
$M\geq N-\frac {N}{K}$
. For the case
$N \leq K \leq 2N-1$
, we derive new lower bounds for small and large caches and propose a new coded caching scheme for large caches. Along with the scheme proposed by Gómez-Vilardebó, this leads to a characterization of the optimal rate memory tradeoff for
$M\leq \frac {1}{K}+\frac {1}{K(N-1)}$
and
$M\geq N-\frac {N}{K}-\frac {N-1}{K(K-1)}$
. For the case
$2N-1\leq K$
, we derive a new lower bound for large caches, which proves the optimality of the scheme proposed by Yu et al. and leads to a characterization of the optimal rate memory tradeoff for
$M\geq N-\frac {2N}{K}$
. We also derive a new lower bound for small caches, which improves upon previously known lower bounds.