Non-Linear Index Coding Outperforming the Linear Optimum

The following source coding problem was introduced by Birk and Kol: a sender holds a word x ∈ {0, 1}n , and wishes to broadcast a codeword to n receivers, R1, . . . , Rn. The receiver Ri is interested in xi, and has prior side information comprising some subset of the n bits. This corresponds to a directed graph G on n vertices, where ij is an edge iff Ri knows the bit xj. An index code for G is an encoding scheme which enables each Ri to always reconstruct xi, given his side information. The minimal word length of an index code was studied by Bar-Yossef, Birk, Jayram and Kol [4]. They introduced a graph parameter, minrk2(G), which completely characterizes the length of an optimal linear index code for G. The authors of [4] showed that in various cases linear codes attain the optimal word length, and conjectured that linear index coding is in fact always optimal. In this work, we disprove the main conjecture of [4] in the following strong sense: for any ε > 0 and sufficiently l...

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Eyal Lubetzky, Uri Stav
• Keywords: FOCS 2007, Index Codes, Linear Index Code, Theoretical Computer Science, Word Length