Conference Paper

Index Coding with Side Information

Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa
DOI: 10.1109/FOCS.2006.42 Conference: Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on
Source: IEEE Xplore

ABSTRACT Motivated by a problem of transmitting data over broadcast channels (BirkandKol, INFOCOM1998), we study the following coding problem: a sender communicates with n receivers Rl,.., Rn. He holds an input x isin {0, 1}n and wishes to broadcast a single message so that each receiver Ri can recover the bit xi. Each Ri has prior side information about x, induced by a directed graph G on n nodes; Ri knows the bits of x in the positions {j | (i, j) is anedge 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

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    ABSTRACT: In the original index coding problem, each user has a set of uncoded packets as side information, and wants to decode some other packets from the source node. Shum et al, (2013) considered the more general problem where side information can be also coded. We refer to this class of problems as index coding with coded side-information (ICCSI). We describe a generalized min-rank for the ICCSI problem, and obtain bounds on this quantity taking an algebraic approach rather than one from graph theory. We also consider error correction for the ICCSI problem, both for the Hamming and rank metric and address the question of the main index coding problem for error correcting index codes (ECIC).

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