Capacity regions of Wireless Network Coding with Hierarchical Decode & forward strategy applied on Impulse Radio UWB technology

Abstract

This paper addresses a cooperative communication scheme in a simple multi-node network of two mutually independent sources communicating over a common shared relay. We assume an Impulse Radio Ultra-Wideband (UWB) communication technique employed by all network nodes which influences used model of a channel impulse response. The signal received at the relay is processed by a Hierarchical Decode & Forward (HDF) strategy. Due to properties of a Hierarchical eXclusive Code (HXC) it is sufficient for the relay to fully decode only hierarchical symbols. The capacity region of the HDF strategy has a rectangular shape and exceeds the capacity region of a Joint Decode & Forward (JDF) concept. We assume a projection to given subspace at the input of the relay receiver to reduce the dimensionality of the signal. Impact of the choice of the subspace is analyzed in this paper. Various subspaces with different level of the knowledge of a Channel State Estimation (CSE) are considered. For different particular channel realizations, according to the chosen channel model, we numerically evaluate the MAC channel capacity. For comparison we also evaluate the classical MAC region as well as the true information theoretic channel capacity.