the capacity-achieving distribution by assigning different probabilities to different constellation points [@forney1984].

The main drawback of probabilistic shaping is its practical implementation. An abundance of probabilistic shaping schemes have been presented, most suffering from high decoding complexity, low flexibility in adapting the spectral efficiency, or error propagation. For a literature review on probabilistic shaping, we refer the reader to [@bocherer2015_bw_efficient_rate_matched_ldpc Section II].

Recently, a new scheme called has been proposed in [@bocherer2015_bw_efficient_rate_matched_ldpc]. Compared to other shaping schemes, yields high flexibility and close-to-capacity performance over a wide range of spectral efficiencies for the channel while still allowing bit-metric decoding. Although originally introduced for the channel, can be applied to other channels with a symmetric capacity-achieving input distribution assuming a sufficiently high spectral efficiency.

In this paper, we consider a similar -based transmission scheme to the one presented in [@shevchenko2018tcom], where data is embedded into the imaginary part of the nonlinear discrete spectrum. As a means to increase the data rate, we demonstrate that the concept of can be adapted to this -based transmission system. In particular, we propose a scheme, enabling similar low complexity and bit-metric decoding as . We take advantage of the dependence of the pulse length on the 