An Algebraic Framework for Multi-Terminal Communication.

We consider the problem of developing coding techniques and characterizing information-theoretic achievable rate regions for the following three multi-terminal communication channels. Firstly, we study an interference channel with three transmitter receiver pairs (3-IC). Secondly, we consider a broadcast channel with three receivers (3-BC), wherein three independent information streams are to be communicated to the three receivers. Thirdly, we consider a two user multiple access channel (MAC) with channel state information distributed at the transmitters (MAC-DSTx). The above channels are assumed discrete, memoryless and used without feedback. Current known coding technique for a general instance of these channels are based on independent unstructured codes. Recognizing the need for codes endowed with algebraic closure properties, we identify three ensembles of coset codes. We propose coding techniques based on these ensembles that exploit their algebraic closure property. We develop tools to characterize information-theoretic performance of the proposed coding techniques. These enable us derive achievable rate regions for a general instance of the above channels. The current known achievable rate regions can be enlarged by gluing together current known coding techniques and the ones proposed herein. Moreover, such an enlargement, as indicated below, is proven to be strict for certain instances. We identify additive and non-additive instances of 3-IC for which the derived achievable rate region is analytically proven to be strictly larger than current known largest. Moreover, for these channels, the proposed coding techniques based on coset codes is capacity achieving. We also identify a vector 3-BC for which the achievable rate region derived herein is analytically proven to be strictly larger than the current known largest. This vector 3-BC is the first known broadcast channel, for which superposition and binning of unstructured independent codes, proposed over three decades ago, can be strictly improved upon. We also identify non-additive and non-symmetric instances of MAC-DSTx for which the proposed coding technique is verified, through computation, to yield strictly larger achievable rate regions. Finally, we develop a coding technique based on nested coset codes to characterize a weaker set of sufficient conditions for the problem of computing sum of sources over a discrete memoryless MAC.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107264/1/arunpr_1.pd

Achievable rate region for three user discrete broadcast channel based on coset codes

We present an achievable rate region for the general three user discrete memoryless broadcast channel, based on nested coset codes. We characterize 3-to-1 discrete broadcast channels, a class of broadcast channels for which the best known coding technique\footnote{We henceforth refer to this as Marton's coding for three user discrete broadcast channel.}, which is obtained by a natural generalization of that proposed by Marton for the general two user discrete broadcast channel, is strictly sub-optimal. In particular, we identify a novel 3-to-1 discrete broadcast channel for which Marton's coding is \textit{analytically} proved to be strictly suboptimal. We present achievable rate regions for the general 3-to-1 discrete broadcast channels, based on nested coset codes, that strictly enlarge Marton's rate region for the aforementioned channel. We generalize this to present achievable rate region for the general three user discrete broadcast channel. Combining together Marton's coding and that proposed herein, we propose the best known coding technique, for a general three user discrete broadcast channel.Comment: A non-additive 3-user discrete broadcast channel is identified for which achievable rate region based on coset codes is analytically proven to be strictly larger than that achievable using unstructured iid codes. This version is submitted to IEEE Transactions on Information Theor

Achievable Rate Regions for Two-Way Relay Channel using Nested Lattice Coding

This paper studies Gaussian Two-Way Relay Channel where two communication nodes exchange messages with each other via a relay. It is assumed that all nodes operate in half duplex mode without any direct link between the communication nodes. A compress-and-forward relaying strategy using nested lattice codes is first proposed. Then, the proposed scheme is improved by performing a layered coding : a common layer is decoded by both receivers and a refinement layer is recovered only by the receiver which has the best channel conditions. The achievable rates of the new scheme are characterized and are shown to be higher than those provided by the decode-and-forward strategy in some regions.Comment: 27 pages, 13 figures, Submitted to IEEE Transactions on Wireless Communications (October 2013