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Recently, substantial attention has been paid to increase the achievable rates of wireless networks using different kinds of limited channel state information (CSI) feedback. This paper aims to investigate the effect of limited noisy CSI feedback on the achievable rates of power-limited block fading channels constrained to have limited outage probability. Considering different power allocation strategies and various fading conditions, the results are obtained for different outage probabilities and are compared with the case where there is no outage limitation. Moreover, considering different outage probability constraints, the effect of feedback channel noise on the average rates of the forward channel is studied and compared with the ones obtained under noise-free feedback link assumption. Simulation results show that 1) although the outage probability constraint reduces the channel average rate, its influence diminishes as the channel state information feedback or the input power increases, 2) the effect of the outage probability constraint decreases as the forward channel fading severity or the feedback channel noise is reduced.