  In this paper, we investigate the use of the learned digital back-propagation
(LDBP) for equalizing dual-polarization fiber-optic transmission in
dispersion-managed (DM) links. LDBP is a deep neural network that optimizes the
parameters of DBP using the stochastic gradient descent. We evaluate DBP and
LDBP in a simulated WDM dual-polarization fiber transmission system operating
at the bitrate of 256 Gbit/s per channel, with a dispersion map designed for a
2016 km link with 15% residual dispersion. Our results show that in
single-channel transmission, LDBP achieves an effective signal-to-noise ratio
improvement of 6.3 dB and 2.5 dB, respectively, over linear equalization and
DBP. In WDM transmission, the corresponding $Q$-factor gains are 1.1 dB and 0.4
dB, respectively. Additionally, we conduct a complexity analysis, which reveals
that a frequency-domain implementation of LDBP and DBP is more favorable in
terms of complexity than the time-domain implementation. These findings
demonstrate the effectiveness of LDBP in mitigating the nonlinear effects in DM
fiber-optic transmission systems.
