It is known that noiseless feedback does not increase the capacity of memoryless point-to-point channels. However, such feedback can considerably increase the reliability or reduce the coding complexity of schemes that approach capacity. This thesis first develops a new class of coding schemes for additive white noise channels with feedback corrupted by additive noise, focusing much of the results and discussions on additive white Gaussian noise channels. These schemes are variants of the well-known Schalkwijk-Kailath coding scheme and are based upon techniques from stochastic approximation. The resulting schemes enable a tradeoff between transmission rate and mean-square error performance in the presence of noisy feedback. By contrast, straightforward application of the classic Schalkwijk-Kailath schemes offer enhanced rate or reliability in the presence of noisy feedback, but do not provide a trade-off between the two.
This thesis also develops cooperative communication strategies based upon distributed stochastic approximation algorithms for the Gaussian relay channel with several configurations of perfect and noisy feedback. In addition to being simple, the strategies can be shown to provide doubly exponential error decay in the case of noiseless feedback and appealing tradeoffs between effective transmission rate and reliability in the case of noisy feedback.