Fading observation alignment via feedback

In some remote sensing applications, the functional relationship between the source being observed and the sensor readings may not be known. Because of communication constraints, this uncertainty may result in poor end-to-end distortion. If the sensors have some knowledge of their joint statistics, they may be able to communicate collaboratively to combat the channel noise. A model is proposed for capturing some of the uncertainty in the observation process, called a fading observation model. An example with fading observations is analysed. For M sensors with no fading there exists a scheme for which the achievable distortion scales with M as M^-1, but with fading the distortion does not scale with M. In this paper, a one-bit feedback scheme is presented that provides enough information about the joint statistics to achieve scaling rates like M^-13/. Additional feedback improves the achievable scaling rate. For comparison, a scheme based on separate source and channel coding at best gives a distortion scaling behaviour of (log M)^-1. Some extensions to multiple sources and observation models with unknown delay are discussed.