Finite Length Analysis of Caching-Aided Coded Multicasting

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 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 $\frac{4}{3}g$ 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 that show 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.Comment: A shorter version appeared in the 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 201

An Efficient Coded Multicasting Scheme Preserving the Multiplicative Caching Gain

Coded multicasting has been shown to be a promis- ing approach to significantly improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, achievable schemes proposed to date have been shown to achieve the proved order-optimal performance only in the asymptotic regime in which the number of packets per requested item goes to infinity. In this paper, we first extend the asymptotic analysis of the achievable scheme in [1], [2] to the case of heterogeneous cache sizes and demand distributions, providing the best known upper bound on the fundamental limiting performance when the number of packets goes to infinity. We then show that the scheme achieving this upper bound quickly loses its multiplicative caching gain for finite content packetization. To overcome this limitation, we design a novel polynomial-time algorithm based on random greedy graph- coloring that, while keeping the same finite content packetization, recovers a significant part of the multiplicative caching gain. Our results show that the order-optimal coded multicasting schemes proposed to date, while useful in quantifying the fundamental limiting performance, must be properly designed for practical regimes of finite packetization.Comment: 6 pages, 7 figures, Published in Infocom CNTCV 201

Distortion-Memory Tradeoffs in Cache-Aided Wireless Video Delivery

Mobile network operators are considering caching as one of the strategies to keep up with the increasing demand for high-definition wireless video streaming. By prefetching popular content into memory at wireless access points or end user devices, requests can be served locally, relieving strain on expensive backhaul. In addition, using network coding allows the simultaneous serving of distinct cache misses via common coded multicast transmissions, resulting in significantly larger load reductions compared to those achieved with conventional delivery schemes. However, prior work does not exploit the properties of video and simply treats content as fixed-size files that users would like to fully download. Our work is motivated by the fact that video can be coded in a scalable fashion and that the decoded video quality depends on the number of layers a user is able to receive. Using a Gaussian source model, caching and coded delivery methods are designed to minimize the squared error distortion at end user devices. Our work is general enough to consider heterogeneous cache sizes and video popularity distributions.Comment: To appear in Allerton 2015 Proceedings of the 53rd annual Allerton conference on Communication, control, and computin

Algorithms for Asynchronous Coded Caching

The original formulation of the coded caching problem assumes that the file requests from the users are synchronized, i.e., they arrive at the server at the same time. Several subsequent contributions work under the same assumption. Furthermore, the majority of prior work does not consider a scenario where users have deadlines. In our previous work we formulated the asynchronous coded caching problem where user requests arrive at different times. Furthermore, the users have specified deadlines. We proposed a linear program for obtaining its optimal solution. However, the size of the LP (number of constraints and variables) grows rather quickly with the number of users and cache sizes. In this work, we explore a dual decomposition based approach for solving the LP under consideration. We demonstrate that the dual function can be evaluated by equivalently solving a number of minimum cost network flow algorithms. Minimum cost network flow algorithms have been the subject of much investigation and current solvers routinely solve instances with millions of nodes in minutes. Our proposed approach leverages these fast solvers and allows us to solve several large scale instances of the asynchronous coded caching problem with manageable time and memory complexity