Adding Transmitters Dramatically Boosts Coded-Caching Gains for Finite File Sizes

In the context of coded caching in the K-user broadcast channel, 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 suhpacketization. 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 manages for the first time to virtually decompose the fully connected cache-aided channel into L parallel channels. The scheme is practical; it works for all the values of K and L and all cache sizes, and its 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 is, while have needed subpacketization S-1= ((K)(G)) = ((100)(10)) > 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 = (G/L-K/L) = ((100/5)(10/5)) = 190. The work extends to the multi-server and cache-aided IC settings, while the scheme's performance, given subpacketization S-L = ((K/L)(G/L)), is within a factor of 2 from the optimal linear sum-DoE.