We consider the problem of designing systems for the transmission of high-quality video signals over certain high-speed segments of the public IP network. Our most important contribution is the definition of a network/coder interface for IP networks which gathers channel state information, and then sets parameters of the video coder to maximize the quality of the signal delivered to the receiver, while remaining fair to other data or video connections. This interface plays a role analogous to that of a Leaky Bucket controller, in that it specifies traffic shaping parameters which result in simultaneous good Quality of Service (QoS) for the source and good network performance. Since the network is not assumed to provide any form of QoS guarantee, fundamental to our construction is a hidden Markov model for the channel, based on which the interface solves a problem of optimal stochastic control, to decide how to configure the encoder. Other contributions are (a) modifications to the standard Internet transport protocol, to make it suitable for the transport of delay-constrained traffic and to gather channel state information, and (b) the design of an error-resilient video coder. Experimental studies reveal that the proposed system is able to stream video signals of the quality of current TV-broadcasts, among hosts in wide-area networks connected to the experimental vBNS backbone.