NDLI: On linear index coding for random graphs

Content Provider	IEEE Xplore Digital Library
Author	Haviv, I. Langberg, M.
Copyright Year	2012
Description	Author affiliation: School of Computer Science, The Academic College of Tel Aviv-Yaffo, Israel (Haviv, I.) \|\| Department of Mathematics and Computer Science, The Open University of Israel (Langberg, M.)
Abstract	In the index coding problem, the goal is to transmit an n character word over a field F to n receivers (one character per receiver), where the receivers have side information represented by a graph G. The objective is to minimize the length of a codeword broadcasted to all receivers which allows each receiver to learn its character. For linear index coding, the minimum possible length is known to be equal to the minrank parameter. In this paper we initiate the study of the typical minimum length of a linear index code for the random graph G(n, p) over a field F. First, we prove that for every constant size field F and a constant p, the minimum length of a linear index code for G(n, p) over F is almost surely Ω(√n). Second, we introduce and study two special models of index coding and study their typical minimum length: Locally decodable index codes in which the receivers are required to query at most q characters from the encoded message (such codes naturally correspond to efficient decoding); and low density index codes in which every character of the broadcasted word affects at most q characters in the encoded message (such codes naturally correspond to efficient encoding procedures). We present enhanced results for these special models.
Starting Page	2231
Ending Page	2235
File Size	129551
Page Count	5
File Format	PDF
ISBN	9781467325806
ISSN	21578117
e-ISBN	9781467325790
e-ISBN	9781467325783
DOI	10.1109/ISIT.2012.6283850
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Indexes Vectors Receivers Generators Channel coding Hamming weight
Content Type	Text
Resource Type	Article

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