Optimal Broadcast Rate of a Class of TwoSender Unicast Index Coding Problems The twosender unicast index coding problem consists of two senders collectively having all the demanded messages of a set of receivers, where each receiver demands a unique message. The senders avail the knowledge of the sideinformation present at all the receivers to reduce the total number of broadcast transmissions. This problem is relevant in many practical communication problems like multisource satellite communication, multiuser coded cooperative data exchange, and other related problems. In this paper, the twosender unicast index coding problem is analyzed using three independent singlesender subproblems. Optimal broadcast rate (total number of transmitted bits per message bit as the message length tends to infinity) for all the unsolved instances of a special class of the twosender unicast index coding problem is provided in terms of those of the three associated subproblems. The optimal broadcast rate established in this work serves as a lower bound for the optimal broadcast rate of any general associated twosender unicast index coding problem. An achievable broadcast rate (total number of transmitted bits per message bit) with finite length messages for any finite length, is given for a subclass of the twosender unicast index coding problem by providing a codeconstruction. This serves as a tighter upper bound when compared to the prior state of art.

Embedded Index Coding Motivated by applications in distributed storage and distributed computation, we introduce embedded index coding (EIC). EIC is a type of distributed index coding in which nodes in a distributed system act as both senders and receivers of information. We show how embedded index coding is related to index coding in general, and give characterizations and bounds on the communication costs of optimal embedded index codes. We also define taskbased EIC, in which each sending node encodes and sends data blocks independently of the other nodes. Taskbased EIC is more computationally tractable and has advantages in applications such as distributed storage, in which senders may complete their broadcasts at different times. Finally, we give heuristic algorithms for approximating optimal embedded index codes, and demonstrate empirically that these algorithms perform well.