  We introduce novel diffusion based adaptive estimation strategies for
distributed networks that have significantly less communication load and
achieve comparable performance to the full information exchange configurations.
After local estimates of the desired data is produced in each node, a single
bit of information (or a reduced dimensional data vector) is generated using
certain random projections of the local estimates. This newly generated data is
diffused and then used in neighboring nodes to recover the original full
information. We provide the complete state-space description and the mean
stability analysis of our algorithms.
