Optimal Linear Broadcast Rates of Some Two-Sender Unicast Index Coding Problems

The two-sender unicast index coding problem consists of two senders, each having a different set of messages. Some messages may be common to both the senders. Each receiver demands a unique message and has a subset of messages known as its side-information. The senders transmit coded messages by availing the knowledge of the side-information of all the receivers, such that all the receivers are able to decode their demands. The aim is to find the optimal aggregate number of coded transmissions per message length (also called the optimal broadcast rate with finite length messages), and its limiting value as the message length tends to infinity (also called the optimal broadcast rate). In this paper, only linear coding schemes are considered. Optimal linear broadcast rate for any finite message length and optimal linear broadcast rate for a basic class of the two-sender unicast index coding problem are established. Optimal code-constructions are also provided. These results are given in terms of the corresponding results of three independent single-sender sub-problems of the two-sender unicast index coding problem. Proof techniques used to obtain the results for the two-sender problem are shown to be useful in obtaining the results for some classes of the multi-sender unicast index coding problem.

[1]  Alexandros G. Dimakis,et al.  FemtoCaching: Wireless Content Delivery Through Distributed Caching Helpers , 2013, IEEE Transactions on Information Theory.

[2]  Vaneet Aggarwal,et al.  Coded Caching With Distributed Storage , 2019, IEEE Transactions on Information Theory.

[3]  Lawrence Ong,et al.  Cooperative Multi-Sender Index Coding , 2019, IEEE Transactions on Information Theory.

[4]  Yucheng Liu,et al.  On the capacity for distributed index coding , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[5]  Yitzhak Birk,et al.  Coding on demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients , 2006, IEEE Transactions on Information Theory.

[6]  Syed A. Jafar,et al.  Interference Alignment: A New Look at Signal Dimensions in a Communication Network , 2011, Found. Trends Commun. Inf. Theory.

[7]  Min Li,et al.  Multi-Sender Index Coding for Collaborative Broadcasting: A Rank-Minimization Approach , 2019, IEEE Transactions on Communications.

[8]  Lawrence Ong,et al.  Graph-Theoretic Approaches to Two-Sender Index Coding , 2016, 2016 IEEE Globecom Workshops (GC Wkshps).

[9]  D. West.  Introduction to Graph Theory , 1995 .

[10]  Lawrence Ong,et al.  Structural Characteristics of Two-Sender Index Coding , 2019, Entropy.

[11]  Lawrence Ong,et al.  Improved bounds for multi-sender index coding , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[12]  B. Sundar Rajan,et al.  Optimal Scalar Linear Index Codes for Three Classes of Two-Sender Unicast Index Coding Problem , 2018, ArXiv.

[13]  Lawrence Ong,et al.  The Single-Uniprior Index-Coding Problem: The Single-Sender Case and the Multi-Sender Extension , 2016, IEEE Transactions on Information Theory.

[14]  Parastoo Sadeghi,et al.  Distributed index coding , 2016, 2016 IEEE Information Theory Workshop (ITW).

[15]  Parastoo Sadeghi,et al.  Instantly decodable network codes for cooperative index coding problem over general topologies , 2014, 2014 Australian Communications Theory Workshop (AusCTW).

[16]  Amin Gohari,et al.  Critical Graphs in Index Coding , 2013, IEEE Journal on Selected Areas in Communications.

[17]  Jae-Won Kim,et al.  Linear Index Coding With Multiple Senders and Extension to a Cellular Network , 2019, IEEE Transactions on Communications.

[18]  B. Sundar Rajan,et al.  On the Optimal Broadcast Rate of the Two-Sender Unicast Index Coding Problem With Fully-Participated Interactions , 2018, IEEE Transactions on Communications.