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The feedback coding problem for additive noise systems, in which the noise may be colored, nonstationary, and correlated between channels, is formulated in terms of arbitrary linear operations at the transmitting and receiving points. This rather general linear formulation provides a unified approach for deriving new results, as well as previous results obtained under more restrictive assumptions, in a straightforward manner. Thus the sequential form of the optimum linear feedback code with an average power constraint on the transmitter is derived for noiseless feedback but forward noise of arbitrary covariance. It is shown explicitly that noiseless feedback increases the capacity of a channel with colored noise. The noisy feedback problem is considered and upper and lower bounds on the performance presented.