A hybrid network coding technique for single-hop wireless networks
IEEE Journal on Selected Areas in Communications - Special issue on network coding for wireless communication networks
Nonlinear index coding outperforming the linear optimum
IEEE Transactions on Information Theory
Index coded repetition-based MAC in vehicular ad-hoc networks
CCNC'09 Proceedings of the 6th IEEE Conference on Consumer Communications and Networking Conference
Gaussian broadcast channels with receiver message side information
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
A new construction method for networks from matroids
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
On broadcast stability of queue-based dynamic network coding over erasure channels
IEEE Transactions on Information Theory
On the index coding problem and its relation to network coding and matroid theory
IEEE Transactions on Information Theory
An adaptive network coded retransmission scheme for single-hop wireless multicast broadcast services
IEEE/ACM Transactions on Networking (TON)
Linear index coding via semidefinite programming
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Wireless Personal Communications: An International Journal
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Motivated by a problem of transmitting data over broadcast channels (Birk and Kol, INFOCOM 1998), we study the following coding problem: a sender communicates with n receivers R_1, . . . , R_n. He holds an input x \in {0, 1}^n and wishes to broadcast a single message so that each receiver R_i can recover the bit x_i. Each R_i has prior side information about x, induced by a directed graph G on n nodes; R_i knows the bits of x in the positions {j | (i, j) is an edge of G}. We call encoding schemes that achieve this goal INDEX codes for {0, 1}^n with side information graph G. In this paper we identify a measure on graphs, the minrank, which we conjecture to exactly characterize the minimum length of INDEX codes. We resolve the conjecture for certain natural classes of graphs. For arbitrary graphs, we show that the minrank bound is tight for both linear codes and certain classes of non-linear codes. For the general problem, we obtain a (weaker) lower bound that the length of an INDEX code for any graph G is at least the size of the maximum acyclic induced subgraph of G.