  Lower bounds on mutual information (MI) of long-haul optical fiber systems
for hard-decision and soft-decision decoding are studied. Ready-to-use
expressions to calculate the MI are presented. Extensive numerical simulations
are used to quantify how changes in the optical transmitter, receiver, and
channel affect the achievable transmission rates of the system. Special
emphasis is put to the use of different quadrature amplitude modulation
formats, channel spacings, digital back-propagation schemes and probabilistic
shaping. The advantages of using MI over the prevailing $Q$-factor as a figure
of merit of coded optical systems are also highlighted.
