Design of Placement Delivery Arrays for Coded Caching with Small Subpacketizations and Flexible Memory Sizes

TL;DR

This paper introduces a new construction of placement delivery arrays using proper orthogonal arrays to achieve low subpacketization levels and flexible memory sizes in coded caching, improving efficiency.

Contribution

It proposes a novel PDA construction based on proper orthogonal arrays, enabling flexible memory sizes and reduced subpacketization in coded caching schemes.

Findings

Lower subpacketization levels compared to existing schemes

Reduced transmission rates with the new PDA construction

Enhanced flexibility in memory size configurations

Abstract

Coded caching is an emerging technique to reduce the data transmission load during the peak-traffic times. In such a scheme, each file in the data center or library is usually divided into a number of packets to pursue a low broadcasting rate based on the designed placements at each user's cache. However, the implementation complexity of this scheme increases as the number of packets increases. It is crucial to design a scheme with a small subpacketization level, while maintaining a relatively low transmission rate. It is known that the design of caches in users (i.e., the placement phase) and broadcasting (i.e., the delivery phase) can be unified in one matrix, namely the placement delivery array (PDA). This paper proposes a novel PDA construction by selecting proper orthogonal arrays (POAs), which generalizes some known constructions but with a more flexible memory size. Based on the proposed PDA construction, an effective transformation is further proposed to enable a coded caching scheme to have a smaller subpacketization level. Moreover, two new coded caching schemes with the coded placement are considered. It is shown that the proposed schemes yield a lower subpacketization level and transmission rate over some existing schemes.