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.

翻译：编码缓存是一种在高峰时段实现缓存网络吞吐量提升的技术。放置传输阵列（PDA）通过单一阵列同时捕捉编码缓存中的放置与传输方案需求。提升是一种构建PDA的方法，其中小型基阵中的条目被替换为满足布莱克本兼容性这一属性的构成型PDA。我们提出了两种新的布莱克本兼容型PDA构造方法，包括一种通过提升布莱克本兼容型PDA来获得新布莱克本兼容型PDA集合的创新方法。这两种构造均改进了速率、内存与子包化程度之间的现有权衡。通过定义两个PDA相对于第三个PDA的部分布莱克本兼容性，我们对提升构造进行了推广。这是布莱克本兼容性的广义概念，使得原始定义成为其特例。我们证明了若干主流编码缓存方案可依据这一扩展概念被定义为提升构造。