Finite length analysis of caching-aided coded multicasting

Abstract

In this work, we study a noiseless broadcast link serving K users whose requests arise from a library of N files. Every user is equipped with a cache of size M files each. It has been shown that by splitting all the files into packets and placing individual packets in a random independent manner across all the caches, it requires at most N/M file transmissions for any set of demands from the library. The achievable delivery scheme involves linearly combining packets of different files following a greedy clique cover solution to the underlying index coding problem.This remarkable multiplicative gain of random placement and coded delivery has been established in the asymptotic regime when the number of packets per file F scales to infinity.In this work, we initiate the finite-length analysis of random caching schemes when the number of packets F is a function of the system parameters M, N, K. Specifically, we show that existing random placement and clique 2 cover delivery schemes that achieve optimality in the asymptotic regime can have at most a multiplicative gain of 2 if the number of packets is sub-exponential. Further, for any clique cover based coded delivery and a large class of random caching schemes, that includes the existing ones, we show that the number of packets required to get a multiplicative gain of 4 3 g is at least O((N/M ) g ). We exhibit a random placement and an efficient clique cover based coded delivery scheme that approximately achieves this lower bound. We also provide tight concentration results thatshow that the average (over the random caching involved) number of transmissions concentrates very well requiring only polynomial number of packets in the rest of the parameters.

Speeding Up Future Video Distribution via Channel-Aware Caching-Aided Coded Multicast

“…In this context, recent information theoretic studies have shown that the use of network coding over the wireless backhaul can significantly improve the performance of wireless caching networks by creating cache-enabled coded multicast transmissions useful for multiple users (access points) even if requesting different content. In fact, is has been shown that the use of wireless edge caching and coded multicasting enables multiplicative caching gains, in the sense that the per-user throughput scales linearly with the local cache size [4]- [11]. However, the underlying assumption in existing information theoretic literature on caching networks is that the channels between the content source and the users either exhibit the same qualities or follow a shared error-free deterministic model.…”

“…While a number of studies have characterized this fundamental tradeoff under error-free channel conditions [4]- [11], only a few recent works have provided first steps towards the characterization of the rate-memory region under a degraded broadcast channel [21], [22]. These studies are however limited to scenarios with only two receivers and unrealistic constraints such as requiring the worst channel receiver to have larger storage capacity.…”

“…These algorithms build on generalizations of existing caching-aided coded multicast schemes to the case of noisy broadcast channels. Specifically, Section VI-A describes CA-CIC as the channel aware extension of the chromatic index coding scheme [6,7,22], and Section VI-B describes CA-HgC as the channel-aware extension of the polynomial-time hierarchical greedy coloring algorithm [9,11].…”

“…If the subroutine returns a nonempty set G, then we color the vertices in G with the same color (lines 6-10). Otherwise, we move the uncolored vertex v to the next hierarchy, i.e., H i−1 (lines [11][12]. This procedure is iteratively applied for any hierarchy, until all the vertices in 8 With a slight abuse of notation, we denote by cu = Cu({v ∈ G : µ(v ) = u}) the codeword obtained by coding the Bsu source bits associated to the packets {ρ(v ) : µ(v ) = u}.…”

“…By construction, each vertex in the conflict graph has an associated receiver, hence we denote by Ω the set of receivers associated to the vertices in G. If G < i, i.e., if we were not able to select at least i vertices, then we return two empty sets (lines [19][20]. Otherwise, we proceed by trying to select, for each receiver µ(v ) ∈ Ω, at most d µ(v ) − 1 additional lowest-cardinality vertices in H i having no links with the vertices in G associated to receivers different from µ(v ) (lines [10][11][12][13][14][15][16][17]. Once this is done (or if the considered hierarchy is 1, meaning that we have no further hierarchies to explore), then we return the set of selected vertices G as well as the set of associated receivers Ω (line 18).…”