Multiple-Antenna Placement Delivery Array for Cache-Aided MISO Systems
Ting Yang, Kai Wan, Minquan Cheng, Robert C. Qiu, Giuseppe Caire · IEEE Transactions on Information Theory · 2023
We consider the cache-aided multiple-input single-output (MISO) broadcast channel, which consists of a server with$L$antennas and$K$single-antenna users, where the server contains$N$files of equal length and each user is equipped with a local cache of size$M$files. Each user requests an arbitrary file from library. The objective is to design a coded caching scheme based on uncoded placement and one-shot linear delivery, to achieve the maximum sum Degree-of-Freedom (sum-DoF) with low subpacketization. It was shown in the literature that under the constraint of uncoded placement and one-shot linear delivery, the maximum sum-DoF is$\min \left\{{L+\frac {KM}{N},K}\right\}$. However, previously proposed schemes for this setting incurred either an exponential subpacketization order in$K$, or required specific conditions in the system parameters$L$,$K$,$M$and$N$. In this paper, we propose a new combinatorial structure called multiple-antenna placement delivery array (MAPDA). Based on MAPDA and Latin square, the first proposed scheme achieves the maximum sum-DoF$\min \left\{{L+\frac {KM}{N},K}\right\}$with the subpacketization of$K$when$\frac {KM}{N}+L=K$. Subsequently, for the general case we propose a transformation approach to construct an MAPDA from any$g$-regular PDA (a class of placement delivery arrays for the shared link caching problem where each integer in the array occurs$g$times). When$g$-regular PDA corresponds to the Maddah-Ali and Niesen scheme, the resulting MAPDA yields the maximum sum-DoF$\min \left\{{L+\frac {KM}{N},K}\right\}$with reduced subpacketization compared to the existing schemes. The general scheme can be extended to the multiple independent single-antenna transmitters (servers) corresponding to the cache-aided interference channel proposed by Naderializadeh et al. and the scenario of transmitters equipped with multiple antennas.