Coded Caching with Low Subpacketization Levels

Abstract

Abstract-Caching is popular technique in content delivery networks that allows for reductions in transmission rates from the content-hosting server to the end users. Coded caching is a generalization of conventional caching that considers the possibility of coding in the caches and transmitting coded signals from the server. Prior results in this area demonstrate that huge reductions in transmission rates are possible and this makes coded caching an attractive option for the next generation of content-delivery networks. However, these results require that each file hosted in the server be partitioned into a large number (i.e., the subpacketization level) of non-overlapping subfiles. From a practical perspective, this is problematic as it means that prior schemes are only applicable when the size of the files is extremely large. In this work, we propose a novel coded caching scheme that enjoys a significantly lower subpacketization level than prior schemes, while only suffering a marginal increase in the transmission rate. In particular, for a fixed cache size, the scaling with the number of users is such that the increase in transmission rate is negligible, but the decrease in subpacketization level is exponential.

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

“…Similar conclusions were also drawn in [19] [20] which took a hyper-graph theoretic approach to show that there do not exist caching algorithms that achieve a constant T (T is independent of K) with subpacketization that grows linearly 3 with K. This work also provided constructions which nicely tradeoff performance with subpacketization, which require though (Construction 6) that K > 4/γ 2 (approximately) in order 4 to have gains bigger than 1. Another milestone of a more theoretical nature was the very recent work in [21] which employed the Ruzsa-Szeméredi graphs to show for the first time that, under the assumption of (an unattainably) large K, one can get a (suboptimal) gain that scales with K, with a subpacketization that scales with K 1+δ for some arbitrarily small positive δ.…”

“…Finally, similar multiplicative boosts of the caching gain will be achieved when we apply the ideas here in conjunction with a variety of different underlying coded caching algorithms (see Section IV-F) like the ones in [18], [19].…”

“…New coded caching algorithms with reduced subpacketization: This subpacketization bottleneck sparked significant interest in designing coded caching algorithms which can provide further caching gains under reduced subpacketization costs. A first breakthrough came with the work in [18] (see also [19]) which reformulated the coded caching problem into a placement-delivery array (PD) combinatorial design problem, and which exploited interesting connections between coded caching and distributed storage to design an algorithm that provided a maximum theoretical caching gain of G 1,pd = Kγ − 1 (treating a total of Kγ, rather than Kγ + 1, users at a time), at a reduced subpacketization of…”

“…We recall that the scheme that we have presented, involved 'elevating' the original MN algorithm in [1], from the single-stream scenario (L = 1) with K = K/L users, to the L-antenna case with K groups of L-users per group. This same idea can apply directly to other centralized coded caching algorithms like those in [18], [19], [21], in which case the steps are almost identical:…”

“…Hence we recall that when 12 elevating the MN algorithm -which, for the single-stream K -user case, treats d 1 (γ) = K γ + 1 users at a time -we treated d 1 = K γ + 1 groups at a time, thus treating a total of d L (γ) = L · d 1 (γ) = L + Kγ users at a time. On the other hand, when elevating for example the algorithms in [18], [19], we would naturally have to change the cache placement and the sequence of XORs, and we would have to account for the fact that -for the single stream K -user case -the algorithm treats d 1,pd = K γ users at a time (not K γ + 1), and thus for L ≥ 1, we would treat d 1,pd = K L γ groups at a time (L ≤ Kγ), thus treating a total of d L,pd (γ) = L · d 1,pd = Kγ users at a time (not Kγ + L).…”