  Probabilistic shaping based on constant composition distribution matching
(CCDM) has received considerable attention as a way to increase the capacity of
fiber optical communication systems. CCDM suffers from significant rate loss at
short blocklengths and requires long blocklengths to achieve high shaping gain,
which makes its implementation very challenging. In this paper, we propose to
use enumerative sphere shaping (ESS) and investigate its performance for the
nonlinear fiber optical channel. ESS has lower rate loss than CCDM at the same
shaping rate, which makes it a suitable candidate to be implemented in
real-time high-speed optical systems. In this paper, we first show that finite
blocklength ESS and CCDM exhibit higher effective signal-to-noise ratio than
their infinite blocklength counterparts. These results show that for the
nonlinear fiber optical channel, large blocklengths should be avoided. We then
show that for a 400 Gb/s dual-polarization 64-QAM WDM transmission system, ESS
with short blocklengths outperforms both uniform signaling and CCDM. Gains in
terms of both bit-metric decoding rate and bit-error rate are presented. ESS
with a blocklength of 200 is shown to provide an extension reach of about 200
km in comparison with CCDM with the same blocklength. The obtained reach
increase of ESS with a blocklength of 200 over uniform signaling is
approximately 450 km (approximately 19%)
