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Traditional information-theoretic approaches to study channel feedback assume that the information is sent from the receiver to the transmitter via an ideal (instantaneous high-rate and error-free) feedback link. This paper investigates the problem of reliable communication over non-ergodic memoryless (stationary) channels using non-errorfree feedback links. We first provide a coding theorem showing that the estimation-induced outage (EIO) capacity is achieved by using rate splitting and hierarchical encoding, where the codes of different layers are jointly designed to exploit the feedback information. The feedback encoder uses hierarchical quantization to compress the state information, allowing the forward encoder to obtain successive refinement of the feedback information during the transmission. The capacity is evaluated for a fading MIMO channel assuming a single-antenna fading feedback link and imperfect channel estimation at the receiver. Simulation results show the joint impact of: (i) successive refinement of quantized feedback, (ii) noisy feedback and (iii) imperfect channel estimation, on the EIO capacity.