  Certain binary asymmetric channels, such as Z-channels in which one of the
two crossover probabilities is zero, demand optimal ones densities different
from 50%. Some broadcast channels, such as broadcast binary symmetric channels
(BBSC) where each component channel is a binary symmetric channel, also require
a non-uniform input distribution due to the superposition coding scheme, which
is known to achieve the boundary of capacity region. This paper presents a
systematic technique for designing nonlinear turbo codes that are able to
support ones densities different from 50%. To demonstrate the effectiveness of
our design technique, we design and simulate nonlinear turbo codes for the
Z-channel and the BBSC. The best nonlinear turbo code is less than 0.02 bits
from capacity.
