In this letter the fiber-optic communication channel with Quadrature Amplitude Modulation (QAM) input constella- tion is treated. Using probabilistic shaping, we show that high order QAM constellations can achieve and slightly exceed the lower bound on the channel capacity, set by ring constellations in . We then propose a mapping function for turbo coded bit interleaved coded modulation based on optimization of the mu- tual information between the channel input and output. Using this mapping, spectral efficiency as high as 6.5 bits/s/Hz/polarization is achieved on a simulated single channel long-haul fiber-optical link excluding the pilot overhead, used for synchronization, and taking into account frequency and phase mismatch impairments, as well as laser phase noise and analog-to-digital conversion quantization impairments. The simulations suggest that major improvements can be expected in the achievable rates of optical networks with high order QAM.