Achievability Over Gaussian Cascade and Relay Channels With Feedback
Inspired by the Robbins-Munro stochastic approximation scheme, Schalkwijk and Kailath developed a coding scheme for Gaussian point-to-point channels with feedback. However, it is not obvious how to extend this scheme to networks with intermediate nodes. This paper develops coding strategies based upon distributed stochastic approximation algorithms for communication across a three-node Gaussian network with feedback. Specifically, the authors consider two scenarios with a relay: a cascade of two Gaussian point-to-point channels, and a Gaussian relay channel. In addition to being simple, the strategies can be shown to provide a doubly exponential error decay. The analysis also gives insights on power allocation and relay placement under a total power constraint.