This letter presents an extended Pawula F-function for computing the error rate of generalized M-ary phase shift keying (MPSK) system in the presence of phase error, quadrature error, and I-Q gain mismatch over additive white Gaussian noise (AWGN) and fading channels. The extended Pawula F-function conditioned on an instantaneous fading carrier-to-noise ratio (CNR) is derived in the form of the Craig representation.

A new stopping criterion of turbo decoding based on the maximum a posteriori (MAP) decoder is proposed and applied to the turbo processing system. The new criterion suggested as the combined parity check (CPC) counts the sign difference between combined parity bits and the re-encode parity bits determined from decoded information bits. The CPC requires decoded parity bits and a turbo encoder but it performs better in terms of the bit error rate and the average number of iterations in the turbo processing system.