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In this paper, we investigate the sensitivity of the digital coherent receiver both theoretically and experimentally. The receiver sensitivity close to the shot-noise limit is demonstrated in the 10-Gbit/s binary phase-shift keying system with the help of a low-noise optical preamplifier. We also introduce polarization diversity into our receiver. Maximal-ratio polarization combining in the digital domain makes the receiver sensitivity independent of the state of polarization of the incoming signal without power penalty.