  We propose a new shaping scheme for the Gaussian channel whose complexity is
approximately half the one of a binary distribution matcher (DM). The result is
obtained as follows: We first show that most of the shaping gain can be
obtained via a simplified version of sign-bit shaping, which uses only two
non-uniform binary sources. This is achieved by considering a stepwise
Maxwell-Boltzmann-like distribution of the symbols. One of the two binary
sources has a parameter $p$ close to 0. Hence, we then describe a binary DM
which explicitly takes advantage of this aspect and has a negligible
complexity. Since the two binary sources are used alternately with equal
probability, the complexity of the proposed shaping scheme is half the one of
the second binary DM.
