Bridging two extremes: Multi-antenna coded caching with reduced subpacketization and CSIT

Two long-standing bottlenecks of coded caching are the exponentially large file sizes that are needed to achieve a maximal caching gain, and - when multiple transmit antennas are involved - the large CSIT feedback costs needed for such caching gains to materialize. Recent results have addressed these two bottlenecks individually, allowing significant reductions in both. In the Multiple-Input-Single-Output (MISO) BC with $L$ antennas, the subpacketization constraint was shown to be as small as the L-th root of the single-antenna case, while maintaining the full Degrees-of-Freedom performance, but requiring feedback from all active users. On the other hand, another result showed that the feedback cost can be reduced to feedback from only $L$ users, but that method required a very high subpacketization. In this work we make progress towards combining the advantages of both worlds by proposing a near-optimal multiantenna coded caching algorithm that incurs a minimal feedback cost, untangled from the number of users, and simultaneously achieving an exponentially reduced subpacketization compared to the single-stream case. In particular - in the context of the L-antenna MISO BC with $K$ single-antenna receivers equipped with caches of normalized size $\gamma$ - the new algorithm achieves a DoF of $(L+K\gamma)(1-\gamma)$ using feedback from only $L$ users, while also reducing subpacketization by a multiplicative factor of $\left(\frac{L+K\gamma}{1+K\gamma}\right)^{K\gamma}$ compared to the single-antenna case, achieving subpacketization reductions exponential to the number of antennas.