Low Subpacketization Coded Caching via Projective Geometry for Broadcast and D2D Networks

Coded caching was introduced as a technique of systematically exploiting locally available storage at the clients to increase the channel throughput via coded transmissions. Most known coded caching schemes in literature enable large gains in terms of the rate, however at the cost of subpacketization that is exponential in K
^1/r
(K being the number of clients, r some positive integer). Building upon recent prior work for coded caching design via line graphs and finite-field projective geometries, we present a new scheme in this work which achieves a subexponential (in K) subpacketization of q
^{O((log(q) K)2)}
rate ⊖ (K/log(q) K)
²
) , for large K, and the cached fraction M/N being upper bounded by a constant 2/q
^α-1
(for some prime power q and constant α ≥ 2). Apart from this asymptotic improvement, we show that through some numerical comparisons that our present scheme has much lower subpacketization than previous comparable schemes, however with an increased rate and some increase in cache size required. For instance, we obtain practically relevant subpacketization levels such as 10
²
-10
⁷
-for 10
²
-10
⁴
number of clients. Leveraging prior results on adapting coded caching schemes for the error-free broadcast channel to device to device (D2D) networks, we obtain a low-subpacketization scheme for D2D networks also, and give numerical comparison for the same with prior work.