Geometrically shaped (GS) 8-, 16, and 32-ary modulation formats are investigated for use in coherent passive optical networks. The modulation formats are designed to improve receiver sensitivity when paired with a binary, soft-decision forward error correction code (SD-FEC), such as a low density parity check (LDPC). Herein we consider the LDPC code specified in the draft 50G EPON standard, and show how this type of code can be particularly advantageous in a coherent transmission system. A receiver sensitivity of −26.7 dBm is achieved at a post-FEC bit error rate below 3.8×10 −6 for a polarizationscrambled 32-ary GS modulation format at 25 GBd, received using a single-polarization, phase-diverse coherent receiver. This yielded a bit rate of 100 Gbit/s, net of coding and pilot overhead. This modulation format was shown to perform equally well in transmission, with no observed dispersion penalty after 80 km standard single mode fiber. Finally, this modulation format was received, at a reduced data rate of 50 Gbit/s, using a heterodyne coherent receiver based on a single balanced photodiode. The receiver sensitivity for this simplified receiver configuration was −28.5 dBm, yielding a power budget of 34.2 dB.