Video on-demand streaming from Internetbased servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as "helpers"). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of 1 − (1 − 1/d) d , where d is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes.

Abstract-Video on-demand streaming from Internetbased servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as "helpers"). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of 1where d is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes.

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 A shorter version of this manuscript appeared in the 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2014 as an invited paper [1]. 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 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.

We present a novel upper bound for the optimal index coding rate. Our bound uses a graph theoretic quantity called the local chromatic number. We show how a good local coloring can be used to create a good index code. The local coloring is used as an alignment guide to assign index coding vectors from a general position MDS code. We further show that a natural LP relaxation yields an even stronger index code. Our bounds provably outperform the state of the art on index coding but at most by a constant factor.

This paper develops an unified framework to study finite-sample convergence guarantees of a large class of value-based asynchronous Reinforcement Learning (RL) algorithms. We do this by first reformulating the RL algorithms as Markovian Stochastic Approximation (SA) algorithms to solve fixed-point equations.We then develop a Lyapunov analysis and derive mean-square error bounds on the convergence of the Markovian SA. Based on this central result, we establish finite-sample mean-square convergence bounds for asynchronous RL algorithms such as Q-learning, n-step TD, TD(λ), and off-policy TD algorithms including V-trace. As a by-product, by analyzing the performance bounds of the TD(λ) (and n-step TD) algorithm for general λ (and n), we demonstrate a bias-variance trade-off, i.e., efficiency of bootstrapping in RL. This was first posed as an open problem in [37].

Coded caching is a problem where encoded broadcasts are used to satisfy users requesting popular files and having caching capabilities. Recent work by Maddah-Ali and Niesen showed that it is possible to satisfy a scaling number of users with only a constant number of broadcast transmissions by exploiting coding and caching. Unfortunately, all previous schemes required the splitting of files into an exponential number of packets before the significant coding gains of caching appeared. The question of what can be achieved with polynomial subpacketization (in the number of users) has been a central open problem in this area. We resolve this problem and present the first coded caching scheme with polynomial (in fact, linear) subpacketization. We obtain a number of transmissions that is not constant, but can be any polynomial in the number of users with an exponent arbitrarily close to zero. Our central technical tool is a novel connection between Ruzsa-Szeméredi graphs and coded caching.

Abstract-We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic factor from the chromatic number. This is in striking contrast to minrank since prior work has shown that it can outperform the chromatic number by a polynomial factor in some cases. The conclusion is that all known graph theoretic bounds are not much stronger than the chromatic number.

Coded multicasting has been shown to improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal performance require content items to be partitioned into a number of packets that grows exponentially with the number of users [1]. In this paper, we first extend the analysis of the achievable scheme in [2] to the case of heterogeneous cache sizes and demand distributions, providing an achievable scheme and an upper bound on the limiting average performance when the number of packets goes to infinity while the remaining system parameters are kept constant. We then show how the scheme achieving this upper bound can very quickly loose its multiplicative caching gain for finite content packetization. To overcome this limitation, we design a novel polynomial-time algorithm based on greedy local graph-coloring that, while keeping the same content packetization, recovers a significant part of the multiplicative caching gain. Our results show that the achievable schemes proposed to date to quantify the limiting performance, must be properly designed for practical finite system parameters.