Adding transmitters dramatically boosts coded-caching gains for finite file sizes
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In the context of coded caching in the K-user BC, our work reveals the surprising fact that having multiple (L) transmitting antennas, dramatically ameliorates the long-standing subpacketization bottleneck of coded caching by reducing the required subpacketization to approximately its Lth root, thus boosting the actual DoF by a multiplicative factor of up to L. In asymptotic terms, this reveals that as long as L scales with the theoretical caching gain, then the full cumulative (multiplexing + full caching) gains are achieved with constant subpacketization. This is the first time, in any known setting, that unbounded caching gains appear under finite file-size constraints. The achieved caching gains here are up to L times higher than any caching gains previously experienced in any single- or multi-antenna fully-connected setting, thus offering a multiplicative mitigation to a subpacketization problem that was previously known to hard-bound caching gains to small constants. The proposed scheme is practical and it works for all values of K,L and all cache sizes. The scheme's gains show in practice: e.g. for K=100, when L=1 the theoretical caching gain of G=10, under the original coded caching algorithm, would have needed subpacketization S_1 = KG= 10010 > 10^13, while if extra transmitting antennas were added, the subpacketization was previously known to match or exceed S_1. Now for L=5, our scheme offers the theoretical (unconstrained) cumulative DoF d_L = L+G = 5+10=15, with subpacketization S_L=K/LG/L =100/510/5 = 190. The work extends to the multi-server and cache-aided IC settings, while the scheme's performance, given subpacketization S_L=K/LG/L, is within a factor of 2 from the optimal linear sum-DoF.
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