In the recent past, several application scenarios have emerged that require large-scale deployment of communication network infrastructure such as packet-switched wireline networks, mobile cellular wireless networks, and distributed sensor networks. In this project, the problem of efficient communication of information in multiterminal systems, where a multiuser channel must be shared among several users in the network is addressed. The new coding methods developed in this project shed light on intricate structural aspects of abstract groups. The development of efficient coding techniques has broad impact on the next generation of communication networks.
In this project, the development of a unified framework to address a class of network communication problems based on new multiuser code ensembles constructed from nested linear codes is studied. In particular, the problem of transmission of information over general discrete memoryless broadcast channels is considered. This problem has received a great deal of attention in the last thirty years. This approach is then applied to other multiuser channels such as the interference channel. For these problems, the average performance of nested linear code ensembles is strictly better than that of the standard unstructured code ensembles. The development of a methodology to compute the performance limits of such coding schemes (which are finite dimensional yet non-convex optimization problems) efficiently with current technology is considered. This project also considers the development of practical constructions of codes with computationally efficient encoding and decoding algorithms and procedures. This is accomplished by putting additional sparsity constraints on the generator and parity-check matrices of these codes.