  We consider probabilistic amplitude shaping (PAS) as a means of increasing
the spectral efficiency of fiber-optic communication systems. In contrast to
previous works in the literature, we consider probabilistic shaping with hard
decision decoding (HDD). In particular, we apply the PAS recently introduced by
B\"ocherer \emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD
that uses a staircase code as the forward error correction code. We show that
the CM scheme with PAS and staircase codes yields significant gains in spectral
efficiency with respect to the baseline scheme using a staircase code and a
standard constellation with uniformly distributed signal points. Using a single
staircase code, the proposed scheme achieves performance within $0.57$--$1.44$
dB of the corresponding achievable information rate for a wide range of
spectral efficiencies.
