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This paper proposes a new method for decoding multicarrier symbols with severe nonlinear distortion. The first part evaluates mutual information expressions for practical nonlinear models and shows the performance bounds for commonly used receiver structures. Then, we derive the optimal maximum likelihood (ML) receiver, which unfortunately has an exponential complexity due to the nonlinear distortion. This extremely large complexity can be reduced with a simple algorithm that iteratively estimates the nonlinear distortion, thereby reducing the exponential-ML to the standard ML without nonlinear distortion. The proposed method can be used to reduce the peak to average power ratio (PAR) of multicarrier signals by clipping the transmit sequence. It can also be used to correct any nonlinear distortion present in transmitter/receiver amplifiers that are operating close to saturation.