Multi-Antenna Coded Caching From a Placement Delivery Array for Shared Caches

Abstract

The coded caching problem with shared caches where the server is equipped with multiple transmit antennas is considered. In a shared cache network, several users share a cache, but each user can access only a single cache. The fundamental limits of coded caching are known for the above setting under centralized uncoded placement. In the centralized case, to achieve the gains offered by coded caching, one requires a sub-packetization level which increases exponentially with the number of caches. The dedicated cache networks too had a similar issue, and placement delivery arrays (PDAs) were introduced as a solution to address the sub-packetization bottleneck of coded caching in the dedicated cache network. Our objective is to design coded caching schemes for shared caches with lower sub-packetization requirements than the existing schemes. By leveraging the PDA constructions, we propose a procedure to obtain new coded caching schemes for shared caches with reduced sub-packetization levels than the known schemes in both single and multi-antenna settings. The advantage of the proposed procedure is that all the existing PDA constructions can be transformed into coded caching schemes for shared caches, thereby reducing the sub-packetization level requirement. In addition, the proposed procedure also recovers the optimal caching schemes given by Parinello <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> by using a PDA corresponding to the Maddah-Ali Niesen scheme.