K users caching two files: An improved achievable rate

Abstract

Abstract-Caching is an approach to smoothen the variability of traffic over time. Recently it has been proved that the local memories at the users can be exploited for reducing the peak traffic in a much more efficient way than previously believed. In this work we improve upon the existing results and introduce a novel caching strategy that takes advantage of simultaneous coded placement and coded delivery in order to decrease the worst case achievable rate with 2 files and K users. We will show that for any cache size 1 K < M < 1 our scheme outperforms the state of the art.Index Terms-Coded Caching, Content Delivery, Improved Achievable RateThe performance of content delivery services is highly dependent on the habits of the users and how well the servers model these habits and adapt their content distribution strategies to them. A basic observation of these habits is the temporal variability of the demands which in its simplest form can be formulated as high congestion during a particular time interval and low traffic for the rest of the day. One popular mechanism that the network can adapt to cope with this issue is caching: during the low traffic time interval, typically mornings, the servers store parts of the content in local memories of the users which may be helpful in the evenings, and hence reduce the peak traffic load. A notable challenge with this strategy is that typically the servers are not aware of which contents will be requested by the users in the peak time. Therefore, the caching of contents in local memories must be performed in such a way that regardless of what requests the users make, the contents are still helpful in reducing the traffic, as much as possible.Perhaps the simplest solution to this problem is to partially store every file at the local caches of the users and transfer the rest of the data uncoded according to the demands made in the delivery time. In their seminal works [1], [2] Maddah-Ali and Niesen have proved that by using network coding techniques this simple strategy can be significantly outperformed if one allows coding across different files on the server and jointly optimizes the caching and the delivery strategies.Despite its impressive potentials, the caching strategy introduced in [1] is known to perform poorly when the cache size is small, and in particular when the number of users is much larger than the number of files, K ≫ N . The applicability of this paradigm in real world scenarios is manifold. A good example is when the files on the server vary widely in their popularity. It has been proved [3] that a nearly optimal caching strategy is to group files with similar popularities and ignore caching opportunities among files from different groups. The cache of each user is then divided into several segments, each segment dedicated to one such group. If the number of groups is large, then the cache size dedicated to each group, as well as the number of files within each group will be small. Another case appears when there are few popular television hits, say on ...

Characterizing the rate-memory tradeoff in cache networks within a factor of 2

“…Note that the above characterization of R s exactly matches a characterization of R * for a caching system with N files and N e (s) users. Specifically, the lower bound of R s given by (109) exactly matches Theorem 2, and the upper bound R dec (M, s) defined in (111) exactly matches the upper bound R dec (M ) defined in (16). Thus, by reusing the same arguments in the proof of Theorem 1 for the peak rate, we can easily prove that R s ≥ R dec (M, s)/2.00884 holds for the general case, and R s ≥ R dec (M, s)/2 holds for large N when…”

The exact rate-memory tradeoff for caching with uncoded prefetching

“…There have also been several prior works considering caching designs with coded prefetching [10], [11], [13]- [15]. They focused on the centralized setting and showed that the peak communication rate achieved by uncoded prefetching schemes can be improved in some low capacity regimes.…”

Symmetry, Outer Bounds, and Code Constructions: A Computer-Aided Investigation on the Fundamental Limits of Caching

“…Subsequent works extended it to decentralized caching placements [7], caching with nonuniform demands [8], online caching placements [9], hierarchical caching [10], caching with random demands [11], among other things. There have been significant research activities recently [12][13][14][15][16][17][18][19][20][21] in both refining the outer bounds and finding stronger codes for caching. Despite these efforts, the fundamental tradeoff had not been fully characterized except for the case with only two users and two files [6] before our work.…”