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The effects of a noisy feedback channel on a communication system with the decision and information feedback proposed as by Mancianti et al. are described. Expressions for the expected transmitted energy per symbol, expected decision time, and receiver's error probability are derived in terms of the error probability Pef over the noisy information channel. Because of the complexity of exact calculations, we have analyzed in detail only the case of two repetitions per symbol. Then, in order to give a general picture of the system performance, the asymptotic behavior has been examined.