%0 Journal Article %T Achievable Rates for Four-Dimensional Coded Modulation with a Bit-Wise Receiver %A Alex Alvarado %A Erik Agrell %J Computer Science %D 2013 %I arXiv %X We study achievable rates for four-dimensional (4D) constellations for spectrally efficient optical systems based on a (suboptimal) bit-wise receiver. We show that PM-QPSK outperforms the best 4D constellation designed for uncoded transmission by approximately 1 dB. Numerical results using LDPC codes validate the analysis. %U http://arxiv.org/abs/1310.4149v1