  We consider the coded caching problem with shared caches where several users
share a cache, but each user has access to only a single cache. For this
network, the fundamental limits of coded caching are known for centralized and
decentralized settings under uncoded placement. In the centralized case, to
achieve the gains offered by coded caching, one requires a sub-packetization
which increases exponentially with the number of caches. The dedicated cache
networks had a similar issue, and placement delivery arrays (PDAs) were
introduced as a solution to it. Using the PDA framework, we propose a procedure
to obtain new coded caching schemes for shared caches with lower
sub-packetization requirements. The advantage of this procedure is that we can
transform all the existing PDA structures into coded caching schemes for shared
caches, thus resulting in low sub-packetization schemes. We also show that the
optimal scheme given by Parrinello, Unsal and Elia (Fundamental Limits of Coded
Caching with Multiple Antennas, Shared Caches and Uncoded Prefetching) can be
recovered using a Maddah-Ali Niesen PDA.
