By Topic

Non-Linear Index Coding Outperforming the Linear Optimum

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)

The following source coding problem was introduced by Birk and Kol: a sender holds a word x epsi {0,1}n, and wishes to broadcast a codeword to n receivers, R1,..., Rnmiddot. The receiver Ri is interested in x;, 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 Xj, given his side information. The minimal word length of an index code was studied by Bar-Yossef Birk, Jay ram and Kol. Thev introduced a graph parameter, minrk2(G), which completely characterizes the length of an optimal linear index code for G. The authors of (Z. Bar-Yossef, 2006) 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 (Z. Bar-Yossef, 2006) in the following strong sense: for any epsiv > 0 and sufficiently large n, there is an n-vertex graph G so that evety linear index code for G requires codewords of length at least n1-epsiv and yet a non-linear index code for G has a word length of nepsiv. This is achieved by an explicit construction, which extends Alon's variant of the celebrated Ramsey construction of Frankl and Wilson.

Published in:

Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on

Date of Conference:

21-23 Oct. 2007