  We consider the problem of designing decentralized schemes for coded caching.
In this problem there are $K$ users each caching $M$ files out of a library of
$N$ total files. The question is to minimize $R$, the number of broadcast
transmissions to satisfy all the user demands. Decentralized schemes allow the
creation of each cache independently, allowing users to join or leave without
dependencies. Previous work showed that to achieve a coding gain $g$, i.e. $R
\leq K (1-M/N)/g$ transmissions, each file has to be divided into number of
subpackets that is exponential in $g$.
  In this work we propose a simple translation scheme that converts any
constant rate centralized scheme into a random decentralized placement scheme
that guarantees a target coding gain of $g$. If the file size in the original
constant rate centralized scheme is subexponential in $K$, then the file size
for the resulting scheme is subexponential in $g$. When new users join, the
rest of the system remains the same. However, we require an additional
communication overhead of $O(\log K)$ bits to determine the new user's cache
state. We also show that the worst-case rate guarantee degrades only by a
constant factor due to the dynamics of user arrival and departure.
