Non-linear index coding outperforming the linear optimum

Eyal Lubetzky, Uri Stav

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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 R1 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 large n, there is an n-vertex graph G so that every linear index code for G requires codewords of length at least n 1-ε, and yet a non-linear index code for G has a word length of nε. This is achieved by an explicit construction, which extends Alon's variant of the celebrated Ramsey construction of Frankl and Wilson.

Original languageEnglish (US)
Title of host publicationProceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007
Pages161-168
Number of pages8
DOIs
StatePublished - 2007
Event48th Annual Symposium on Foundations of Computer Science, FOCS 2007 - Providence, RI, United States
Duration: Oct 20 2007Oct 23 2007

Other

Other48th Annual Symposium on Foundations of Computer Science, FOCS 2007
CountryUnited States
CityProvidence, RI
Period10/20/0710/23/07

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Directed graphs

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Lubetzky, E., & Stav, U. (2007). Non-linear index coding outperforming the linear optimum. In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007 (pp. 161-168). [4389489] https://doi.org/10.1109/FOCS.2007.4389489

Non-linear index coding outperforming the linear optimum. / Lubetzky, Eyal; Stav, Uri.

Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007. 2007. p. 161-168 4389489.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lubetzky, E & Stav, U 2007, Non-linear index coding outperforming the linear optimum. in Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007., 4389489, pp. 161-168, 48th Annual Symposium on Foundations of Computer Science, FOCS 2007, Providence, RI, United States, 10/20/07. https://doi.org/10.1109/FOCS.2007.4389489
Lubetzky E, Stav U. Non-linear index coding outperforming the linear optimum. In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007. 2007. p. 161-168. 4389489 https://doi.org/10.1109/FOCS.2007.4389489
Lubetzky, Eyal ; Stav, Uri. / Non-linear index coding outperforming the linear optimum. Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007. 2007. pp. 161-168
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