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.
Highlights
Consider a communication scenario over a noiseless channel where a sender is required to broadcast messages to multiple receivers, each caching some messages requested by other receivers a priori
This paper investigates the structural characteristics of two-sender unicast index coding (TSUIC) problems for the same purpose by studying the interactions among D1, D2 and D3 of D
The results are established by utilizing existing Single-sender unicast index coding (SSUIC)’s results and our proposed coloring of confusion graphs for TSUIC, which we discuss in the subsequent sections
Summary
Consider a communication scenario over a noiseless channel where a sender is required to broadcast messages to multiple receivers, each caching some messages requested by other receivers a priori. The messages cached at each receiver is known as its side-information In this scenario, if the sender is informed about the side-information available at all receivers, it can leverage that information whilst encoding to reduce the required number of broadcast transmissions, in comparison with a naive approach of transmitting all requested messages uncoded and separately. If the sender is informed about the side-information available at all receivers, it can leverage that information whilst encoding to reduce the required number of broadcast transmissions, in comparison with a naive approach of transmitting all requested messages uncoded and separately Such an encoding process is called index coding, and the resulting sequence of coded messages is known as an index code. Index coding was introduced by Birk and Kol [1,2], and further studied in subsequent works [3,4,5,6,7,8,9,10,11,12,13]
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