In this paper, we present an algorithm for joint carrier phase estimation and turbo decoding for the case of rapidly varying carrier phase during the transmitted block. The proposed algorithm shows improved performance over previously proposed communication schemes, both coherent and noncoherent, for channels with additive white Gaussian noise and high carrier phase noise. The novel algorithm utilizes a modified "two dimensional" bit carrier phase a posteriori probability (BCAPP) decoder containing additional states representing the received carrier phase. The BCAPP decoder calculates two extrinsic metrics: one representing the bit soft value and the other representing the received carrier phase probability density function approximation. A modified structure of the turbo code iterations is suggested, implementing separate propagation of the two metrics between the BCAPP decoders. One additional attractive property of the suggested algorithm is its robustness against phase noise model mismatch.