Cache-Aided Interference Management with Subexponential Subpacketization
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Consider an interference channel consisting of K_T transmitters and K_R receivers with AWGN noise and complex channel gains, and with N files in the system. The one-shot DoF for this channel is the maximum number of receivers which can be served simultaneously with vanishing probability of error as the SNR grows large, under a class of schemes known as one-shot schemes. Consider that there exists transmitter and receiver side caches which can store fractions M_T/N and M_R/N of the library respectively. Recent work for this cache-aided interference channel setup shows that, using a carefully designed prefetching(caching) phase, and a one-shot coded delivery scheme combined with a proper choice of beamforming coefficients at the transmitters, we can achieve a DoF of t_T+t_R, where t_T=M_T K_T/N and t_R=M_R K_R/N, which was shown to be almost optimal. The existing scheme involves splitting the file into F subfiles (the parameter F is called the subpacketization), where F can be extremely large (in fact, with constant cache fractions, it becomes exponential in K_R, for large K_R). In this work, our first contribution is a scheme which achieves the same DoF of t_T+t_R with a smaller subpacketization than prior schemes. Our second contribution is a new coded caching scheme for the interference channel based on projective geometries over finite fields which achieves a one-shot DoF of Θ(log_qK_R+K_T), with a subpacketization F=q^O(K_T+(log_qK_R)^2) (for some prime power q) that is subexponential in K_R, for small constant cache fraction at the receivers. To the best of our knowledge, this is the first coded caching scheme with subpacketization subexponential in the number of receivers for this setting.
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