Paper Info
Title
Broadcasting With Side Information: Bounding and Approximating the Broadcast Rate
Abstract
Index coding has received considerable attention recently motivated in part by applications such as fast video-on-demand and efficient communication in wireless networks and in part by its connection to network coding. Optimal encoding schemes and efficient heuristics were studied in various settings, while also leading to new results for network coding such as improved gaps between linear and non-linear capacity as well as hardness of approximation. The problem of broadcasting with side information, a generalization of the index coding problem, begins with a sender and sets of users and messages. Each user possesses a subset of the messages and desires an additional message from the set. The sender wishes to broadcast a message so that on receipt of the broadcast each user can compute her desired message. The fundamental parameter of interest is the broadcast rate, $\\beta $, the average communication cost for sufficiently long broadcasts. Though there have been many new nontrivial bounds on $\\beta $ by Bar-Yossef (2006), Lubetzky and Stav (2007), Alon (2008), and Blasiak (2011) there was no known polynomial-time algorithm for approximating $\\beta $ within a nontrivial factor, and the exact value of $\\beta $ remained unknown for all nontrivial instances. Using the information theoretic linear program introduced in Blasiak (2011), we give a polynomial-time algorithm for recognizing instances with $\\beta = 2$ and pinpoint $\\beta $ precisely for various classes of graphs (e.g., various Cayley graphs of cyclic groups). Further, extending ideas from Ramsey theory, we give a polynomial-time algorithm with a nontrivial approximation ratio for computing $\\beta $. Finally, we provide insight into the quality of previous bounds by giving constructions showing separations between $\\beta $ and the respective bounds. In particular, we construct graphs where $\\beta $ is uniformly bounded while its upper bound derived from the naïve encoding scheme is polynomially worse.
Year
DOI
Venue
2013
10.1109/TIT.2013.2264472
IEEE Transactions on Information Theory
Keywords
Field
DocType
network coding,radio broadcasting,approximation theory,graph theory,communication complexity,linear programming
Graph theory,Linear network coding,Discrete mathematics,Approximation algorithm,Combinatorics,Upper and lower bounds,Computer science,Hardness of approximation,Communication complexity,Theoretical computer science,Linear code,Linear programming
Journal
Volume
Issue
ISSN
59
9
0018-9448
Citations 
PageRank 
References 
32
1.19
6
Authors
3
Name
Order
Citations
PageRank
Anna Blasiak11227.05
Robert Kleinberg22886202.55
Eyal Lubetzky335528.87