Designs, Codes and Cryptography
An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
XORs in the air: practical wireless network coding
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
Index Coding with Side Information
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Network Coding Theory (Foundations and Trends(R) in Communications and Information Theory)
Network Coding Theory (Foundations and Trends(R) in Communications and Information Theory)
Non-Linear Index Coding Outperforming the Linear Optimum
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Symbol-level network coding for wireless mesh networks
Proceedings of the ACM SIGCOMM 2008 conference on Data communication
Broadcasting with Side Information
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Network Coding Fundamentals
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On Witsenhausen's zero-error rate for multiple sources
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
Networks, Matroids, and Non-Shannon Information Inequalities
IEEE Transactions on Information Theory
Network coding-based reliable multicast in wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Wireless Personal Communications: An International Journal
Hi-index | 754.84 |
The index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks. An instance of the index coding problem includes a sender that holds a set of information messages X = {x1,..., xk} and a set of receivers R. Each receiver ρ = (x, H) in R needs to obtain a message x ∈ X and has prior side information consisting of a subset H of X. The sender uses a noiseless communication channel to broadcast encoding of messages in X to all clients. The objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers. In this paper, we analyze the relation between the index coding problem, the more general network coding problem, and the problem of finding a linear representation of a matroid. In particular, we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem. Our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem. Specifically, we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions.