  Constellation shaping is an energy-efficient strategy involving the
transmission of lower-energy signals more frequently than higher-energy
signals. Previous work has shown that shaping is particularly effective when
used with coded amplitude phase-shift keying (APSK), a modulation that has been
popularized recently due to its inclusion in the DVB-S2 standard. While shaped
APSK can provide significant gains when used with standard off-the-shelf LDPC
codes, such as the codes in the DVB-S2 standard, additional non-negligible
gains can be achieved by optimizing the LDPC code with respect to the shaped
APSK modulation. In this paper, we optimize the degree distributions of the
LDPC code used in conjunction with shaped APSK. The optimization process is an
extension of the EXIT-chart technique of ten Brink, et al., which has been
adapted to account for the shaped APSK modulation. We begin by constraining the
code to have the same number of distinct variable-node degrees as the codes in
the DVB-S2 standard, and show that the optimization provides 32-APSK systems
with an additional coding gain of 0.34 dB at a system rate of R=3 bits per
symbol, compared to shaped systems that use the long LDPC code from the DVB-S2
standard. We then increase the number of allowed variable node degrees by one,
and find that an additional 0.1 dB gain is achievable.
