  Coded caching is a technique where multicasting and coding opportunities are
utilized to achieve better rate-memory tradeoff in cached networks. A crucial
parameter in coded caching is subpacketization, which is the number of parts a
file is to be split into for coding purposes. The original Maddah-Ali-Niesen
scheme has order-optimal rate at a subpacketization growing exponentially with
the number of users. In contrast, placement and delivery schemes in coded
caching, designed using placement delivery arrays (PDAs), can have linear
subpacketization with a penalty in rate. In this work, we propose several
constructions of efficient PDAs through lifting, where a base PDA is expanded
by replacing each entry by another PDA. By proposing and using the notion of
Blackburn-compatibility of PDAs, we provide multiple lifting constructions with
increasing coding gains. We compare the constructed coded caching schemes with
other existing schemes for moderately high number of users and show that the
proposed constructions are versatile and achieve a good rate-memory tradeoff at
low subpacketizations.
