By Topic

Nonlinear 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
$33 $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)
Eyal Lubetzky ; Theor. Group, Microsoft Res., Redmond, WA, USA ; Uri Stav

The following source coding problem was introduced by Birk and Kol: a sender holds a word x isin {0, 1}n, and wishes to broadcast a codeword to n receivers, Rn,..., 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 i j is an edge Ri 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 (FOCS'06). They introduced a graph parameter, minrk2(G), which completely characterizes the length of an optimal linear index code for G. They 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 Bar-Yossef, Birk, Jayram, and Kol in the following strong sense: for any epsiv > 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 nepsiv and yet a nonlinear index code for G has a word length of ne. This is achieved by an explicit construction, which extends Alon's variant of the celebrated Ramsey construction of Frankl and Wilson. In addition, we study optimal index codes in various, less restricted, natural models, and prove several related properties of the graph parameter minrk(G).

Published in:

IEEE Transactions on Information Theory  (Volume:55 ,  Issue: 8 )