Multiple-antenna Placement Delivery Array for Cache-aided MISO Systems
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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 phases, to achieve the maximum worst-case sum Degree-of-Freedom (sum-DoF) with low subpacketization. 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 sum-DoF L+KM/N with the subpacketization of K when 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 PDA where each integer in the array occurs g times) for the original shared-link coded caching problem. If the original PDA is the seminal coded caching scheme proposed by Maddah-Ali and Niesen, the resulting scheme can achieve the sum-DoF L+KM/N with reduced subpacketization than the existing schemes.The work 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.
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