  Coded caching is a technique for achieving increased throughput in cached
networks during peak hours. Placement delivery arrays (PDAs) capture both
placement and delivery scheme requirements in coded caching in a single array.
Lifting is a method of constructing PDAs, where entries in a small base PDA are
replaced with constituent PDAs that satisfy a property called
Blackburn-compatibility. We propose two new constructions for
Blackburn-compatible PDAs including a novel method for lifting
Blackburn-compatible PDAs to obtain new sets of Blackburn-compatible PDAs. Both
of these constructions improve upon previous tradeoffs between rate, memory and
subpacketization. We generalize lifting constructions by defining partial
Blackburn-compatibility between two PDAs w.r.t. a third PDA. This is a wider
notion of Blackburn-compatibility making the original definition a special
case. We show that some popular coded caching schemes can be defined as lifting
constructions in terms of this extended notion.
