Structural Characteristics of TwoSender Index Coding
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 sideinformation, and requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is called twosender 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 subproblems 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 subproblems. 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 singlesender index coding. To adapt the confusion graph technique in TSUIC, we introduce a new graphcoloring approach that is different from the normal graph coloring, which we call twosender 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 sideinformation can be removed without affecting their optimal broadcast rates. Finally, we generalize the results of a class of TSUIC problems to multiple senders.
 Publication:

arXiv eprints
 Pub Date:
 November 2017
 arXiv:
 arXiv:1711.08150
 Bibcode:
 2017arXiv171108150T
 Keywords:

 Computer Science  Information Theory
 EPrint:
 Submitted for journal publication