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Structural Characteristics of Two-Sender Index Coding

1
CSIRO Data61, Marsfield, NSW 2122, Australia
2
School of Electrical Engineering and Computing, The University of Newcastle, Callaghan, NSW 2308, Australia
3
College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 615; https://doi.org/10.3390/e21060615
Received: 29 March 2019 / Revised: 18 June 2019 / Accepted: 19 June 2019 / Published: 21 June 2019
(This article belongs to the Special Issue Multiuser Information Theory II)
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Abstract

This paper studies index coding with two senders. In this setup, source messages are distributed among the senders possibly with common messages. In addition, there are multiple receivers, with each receiver having some messages a priori, known as side-information, and requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is called two-sender unicast index coding (TSUIC). The main goal is to find the shortest aggregate normalized codelength, which is expressed as the optimal broadcast rate. In this work, firstly, for a given TSUIC problem, we form three independent sub-problems each consisting of the only subset of the messages, based on whether the messages are available only in one of the senders or in both senders. Then, we express the optimal broadcast rate of the TSUIC problem as a function of the optimal broadcast rates of those independent sub-problems. In this way, we discover the structural characteristics of TSUIC. For the proofs of our results, we utilize confusion graphs and coding techniques used in single-sender index coding. To adapt the confusion graph technique in TSUIC, we introduce a new graph-coloring approach that is different from the normal graph coloring, which we call two-sender graph coloring, and propose a way of grouping the vertices to analyze the number of colors used. We further determine a class of TSUIC instances where a certain type of side-information can be removed without affecting their optimal broadcast rates. Finally, we generalize the results of a class of TSUIC problems to multiple senders. View Full-Text
Keywords: index coding; multi-sender index coding; confusion graphs; graph coloring; optimal broadcast rate; network coding index coding; multi-sender index coding; confusion graphs; graph coloring; optimal broadcast rate; network coding
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Thapa, C.; Ong, L.; Johnson, S.J.; Li, M. Structural Characteristics of Two-Sender Index Coding. Entropy 2019, 21, 615.

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