Index coding via random coding

The index coding problem is a simple distributed source coding problem in which a sender broadcasts multiple messages to their respective receivers with side information about other messages. This problem arises in many applications such as content broadcasting, distributed caching, and wireless interference management. At the same time, it is a canonical instance of the multiple-unicast network coding problem that captures the essence of broadcasting multiple interfering streams. Reflecting the importance as well as the difficulty of the index coding problem, several coding schemes have been proposed that are built on tools from graph theory, linear network coding, combinatorial optimization, and interference alignment. This paper studies the composite coding scheme based on random coding in information theory. Despite its conceptual simplicity that allows for rather straightforward analysis, the scheme uniformly outperforms the existing coding schemes by Birk and Kol (1998), Blasiak, Kleinberg, and Lubetzky (2013), and Shanmugam, Dimakis, and Langberg (2013), and is optimal for all index coding problems with up to five messages.