Kai Wan

On the optimality of uncoded cache placement

Caching is an effective way to reduce peak-hour network traffic congestion by storing some contents at users local cache. Maddah-Ali and Niesen (MAN) initiated a fundamental study of caching systems by proposing a scheme (with uncoded cache placement and linear network coding delivery) that is provably optimal to within a factor 4.7. In this paper, when the cache contents and the user demands are fixed, we connect the caching problem to an index coding problem and show the optimality of the MAN scheme under the conditions that (i) the cache placement phase is restricted to be uncoded (i.e, pieces of the files can only copied into the users cache), and (ii) the number of users is no more than the number of files. As a consequence, further improvements to the MAN scheme are only possible through the use of coded cache placement.

On caching with more users than files

Caching is an efficient way to reduce peak hour network traffic congestion by storing some content at the users cache without knowledge of later demands. Recently, Maddah-Ali and Niesen proposed a two-phase, placement and delivery phase, coded caching strategy for centralized systems (where coordination among users is possible in the placement phase), and for decentralized systems. This paper investigates the same setup under the assumption that the number of users is larger than the number of files. By using the same uncoded placement strategy of Maddah-Ali and Niesen, a novel coded delivery strategy is proposed to profit from the multicasting opportunities that arise because a file may be demanded by multiple users. The proposed delivery method is proved to be optimal under the constraint of uncoded cache placement for centralized systems with two files. Moreover it is shown to outperform known caching strategies for both centralized and decentralized systems.

Novel delivery schemes for decentralized coded caching in the finite file size regime

This paper analyzes the achievable tradeoff between cache size and download rate in decentralized caching systems with the uncoded cache placement originally proposed by Maddah-Ali and Niesen. It proposes two novel delivery schemes that take advantage of the multicasting opportunities that arise when a file is demanded by multiple users. These delivery schemes are extensions of known ones to the regime where the file size is finite. Numerical evaluations for the case of file uniform popularity show that the proposed schemes outperform previous ones for all value of the cache size.

Novel outer bounds for combination networks with end-user-caches

This paper studies the tradeoff between the memory size M and the download time / rate R∗ for networks where a server with N files is connected to H relays (without caches), which in turns are connected to K users equipped with caches of size M files. When each user is connected to a different subset of r relays, i.e., K = (Hr), the system is referred to as a combination network with end-user-caches. In this work, outer bounds are derived for the practically motivated case of uncoded cache contents, that is, bits of the various files are directly copied in the user caches without any coding. In this case, once the cache contents and the user demands are known, the problem reduces to a general index coding problem. This paper shows that relying on a well known “acyclic index coding outer bound” results in bounds that are not tight for combination networks with enduser-caches (as opposed to the case without relays) and provides two novel ways to derive the tightest known outer bounds to date. As a result of independent interest, an inequality that generalizes the well-known sub-modularity of entropy is derived.

A novel index coding scheme and its application to coded caching

This paper proposes a novel achievable scheme for the index problem and applies it to the caching problem. Index coding and caching are noiseless broadcast channel problems where receivers have message side information. In the index coding problem the side information sets are fixed, while in the caching problem the side information sets correspond the cache contents, which are under the control of the system designer. The proposed index coding scheme, based on distributed source coding and non-unique decoding, is shown to strictly enlarge the rate region achievable by composite coding. The novel index coding scheme applied to the caching problem is then shown to match an outer bound (previously proposed by the authors and also based on known results for the index coding problem) under the assumption of uncoded cache placement/prefetching.

Novel inner bounds with uncoded cache placement for combination networks with end-user-caches

This paper considers combination networks with end-user-caches, where a server with N files communicates through H relays (without caches) to K = (Hr) users equipped with caches of size M files. In this setting, each user is connected to a different subset of r relays. The tradeoff between the cache size and the worst-case download time is studied. Several novel caching schemes are proposed, which leverage the symmetries of combination networks and interference elimination at the end-users. The proposed schemes are proved: (i) to be optimal for some choices of the parameters (N, M, H, r) under the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations.