完全参与交互作用下两点单播索引编码问题的最优线性广播速率
Optimal Linear Broadcast Rates of the Two-Sender Unicast Index Coding Problem with Fully-Participated Interactions
摘要：
两个发送者的单播索引编码问题包括从两个共同知道所有接收者所需的消息的发送者中找到最佳编码传输。每个接收者都需要一个唯一的消息。该问题的一个重要类别包括在接收器处的消息集和在接收器处的边信息满足\emph{fully-participated interactions}。本文提供了最佳的线性广播速率和相应的代码结构的所有可能的情况下，两个发送者的单播索引编码问题的完全参与的相互作用。最佳线性广播速率和相应的代码的两个发送者的问题给出的三个单发送者的单播问题与两个发送者的问题。具有完全参与交互作用的两发送者问题的最优线性广播速率提供了许多相关的具有\emph{partially-participated interactions}的两发送者问题的最优线性广播速率的下界。证明技术用于获得两个发送者的问题的结果被证明是有用的，在某些情况下的多发送者单播索引编码问题的结果。
英文摘要：
The two-sender unicast index coding problem consists of finding optimal coded transmissions from the two senders which collectively know the messages demanded by all the receivers. Each receiver demands a unique message. One important class of this problem consists of the message sets at the senders and the side-information at the receivers satisfying \emph{fully-participated interactions}. This paper provides optimal linear broadcast rates and corresponding code constructions for all the possible cases of the two-sender unicast index coding problem with fully-participated interactions. The optimal linear broadcast rate and the corresponding code for the two-sender problem are given in terms of those of the three single-sender unicast problems associated with the two-sender problem. Optimal linear broadcast rates of two-sender problems with fully-participated interactions provide lower bounds for the optimal linear broadcast rates of many related two-sender problems with \emph{partially-participated interactions}. Proof techniques used to obtain the results for the two-sender problem are shown to be useful in obtaining the results for some cases of the multi-sender unicast index coding problem.
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