NDLI: Bounding multiple unicasts through index coding and Locally Repairable Codes

Content Provider	IEEE Xplore Digital Library
Author	Shanmugam, K. Dimakis, A.G.
Copyright Year	2014
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Univ. of Texas at Austin, Austin, TX, USA (Shanmugam, K.; Dimakis, A.G.)
Abstract	We establish a duality result between linear index coding and Locally Repairable Codes (LRCs). Specifically, we show that a natural extension of LRCs we call Generalized Locally Repairable Codes (GLCRs) are exactly dual to linear index codes. In a GLRC, every node is decodable from a specific set of other nodes and these sets induce a recoverability directed graph. We show that the dual linear subspace of a GLRC is a solution to an index coding instance where the side information graph is this GLRC recoverability graph. We show that the GLRC rate is equivalent to the complementary index coding rate, i.e. the number of transmissions saved by coding. Our second result uses this duality to establish a new upper bound for the multiple unicast network coding problem. In multiple unicast network coding, we are given a directed acyclic graph and r sources that want to send independent messages to r corresponding destinations. Our new upper bound is efficiently computable and relies on a strong approximation result for complementary index coding. We believe that our bound could lead to an approximation guarantee for multiple unicast network coding if a plausible connection we state is verified.
Starting Page	296
Ending Page	300
File Size	928951
Page Count	5
File Format	PDF
ISBN	9781479951864
ISSN	21578117
DOI	10.1109/ISIT.2014.6874842
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Indexes Unicast Channel coding Network coding Vectors
Content Type	Text
Resource Type	Article

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