  There has been much interest in the non-linear frequency-division
multiplexing (NFDM) transmission scheme in the optical fibre communication
system. Up to date, most of the demonstrated NFDM schemes have employed only
single polarisation for data transmission. Employing both polarisations can
potentially double the data rate of NFDM systems. We investigate in simulation
a dual-polarisation NFDM transmission with data modulation on the
$b$-coefficient. First, a transformation that facilitates the dual-polarisation
$b$-modulation was built upon an existing transformation. Second, the $q_c$-
and $b$-modulation for dual-polarisation were compared in terms of Q-factor,
spectral efficiency (SE), and correlation of sub-carriers. The correlation is
quantified via information theoretic metrics, joint and individual entropy. The
polarisation-multiplexed $b$-modulation system shows 1 dB Q-factor improvement
over $q_c$-modulation system due to a weaker correlation of sub-carriers and
less effective noise. Finally, the $b$-modulation system was optimised for high
data rate, achieving a record net data rate of 400 Gbps (SE of 7.2 bit/s/Hz)
over $12\times 80$ km of standard single-mode fibre (SSMF) with erbium-doped
fibre amplifiers (EDFAs). Based on the above simulation results, we further
point out the drawbacks of our current system and quantify the error introduced
by the transceiver algorithms and non-integrability of the channel.
