Adding Transmitters Allows Unbounded Coded-Caching Gains with Bounded File Sizes
Eleftherios Lampiris, Petros Elia · 2018
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 longstanding 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 multiantenna 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 , while if extra transmitting antennas were added, the subpacketization was previously known to match or exceed S1. Now for L=5, our scheme offers the theoretical (unconstrained) cumulative DoF dI = L+G = 5 +10 = 15, with subpacketization SL=\binomK/LG/L=\binom100/510/5=190. The scheme's performance, given, subpacketization sL=\binomK/LG/L, is within a factor of 2 from the optimal linear sum-DoF. The gains stemming from this work come by a virtual decomposition of the fully connected cache-aided channel into parallel ones, which significantly reduces the required subpacketization