We present the channel capacity, specifically the mutual information, of an additive white Gaussian noise (AWGN) channel in the presence of phase noise, and investigate the effect of phase noise impairment on powerful error-correcting codes (ECCs) that normally operate in low signal-to-noise ratio (SNR) regions. This channel-induced impairment is common in digital coherent transmission systems and is caused by imperfect carrier tracking of the phase error detector for coherent demodulation. It is shown through semi-analytical derivation that decreasing the information rate from its ideal capacity to an information rate lower than its inherent capacity significantly mitigates the impairment caused by phase noise, and that operating systems in the low SNR region also lessen the phase noise impairment by transforming typical phase noise behavior into Gaussian-like behavior. We also demonstrate by computer simulation using turbo-trellis coded modulation (TTCM) with high-order quadrature amplitude modulation (QAM) signals that the use of capacity-approaching codes (CACs) makes transmission systems invulnerable to phase noise. To verify the effect of CACs on phase noise, simulation results of TTCM are also compared to that of trellis-coded modulation (TCM), which is used as an example of a conventional ECC operating at a relatively high SNR.