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

Network Codes for Real-Time Applications

We consider the scenario of broadcasting for real-time applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications that have strict deadlines. In this work, we are interested in finding a code that is instantly decodable by the maximum number of users. First, we prove that this problem is NP-Hard in the general case. Then we consider the practical probabilistic scenario, where users have i.i.d. loss probability and the number of packets is linear or polynomial in the number of users. In this scenario, we provide a polynomial-time (in the number of users) algorithm that finds the optimal coded packet. The proposed algorithm is evaluated using both simulation and real network traces of a real-time Android application. Both results show that the proposed coding scheme significantly outperforms the state-of-the-art baselines: an optimal repetition code and a COPE-like greedy scheme.Comment: ToN 2013 Submission Versio

A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Machine Learning for Multimedia Communications

Machine learning is revolutionizing the way multimedia information is processed and transmitted to users. After intensive and powerful training, some impressive efficiency/accuracy improvements have been made all over the transmission pipeline. For example, the high model capacity of the learning-based architectures enables us to accurately model the image and video behavior such that tremendous compression gains can be achieved. Similarly, error concealment, streaming strategy or even user perception modeling have widely benefited from the recent learningoriented developments. However, learning-based algorithms often imply drastic changes to the way data are represented or consumed, meaning that the overall pipeline can be affected even though a subpart of it is optimized. In this paper, we review the recent major advances that have been proposed all across the transmission chain, and we discuss their potential impact and the research challenges that they raise