This paper studies the performance of code-aided (CA) soft-information based carrier phase recovery, which iteratively exploits the extrinsic information from channel decoder to improve the accuracy of phase synchronization. To tackle the problem of strong coupling between phase recovery and decoding, a semi-analytical model is proposed to express the distribution of extrinsic information as a function of phase offset. Piecewise approximation of the hyperbolic tangent function is employed to linearize the expression of soft symbol decision. Building on this model, open-loop characteristic and closed-loop performance of CA iterative soft decision-directed (ISDD) carrier phase synchronizer are derived in closed-form. Monte Carlo simulation results corroborate that the proposed expressions are able to characterize the performance of CA ISDD carrier phase recovery for systems with different channel codes.