  The performance of bit-interleaved coded modulation (BICM) with bit shaping
(i.e., non-equiprobable bit probabilities in the underlying binary code) is
studied. For the Gaussian channel, the rates achievable with BICM and bit
shaping are practically identical to those of coded modulation or multilevel
coding. This identity holds for the whole range of values of signal-to-noise
ratio. Moreover, the random coding error exponent of BICM significantly exceeds
that of multilevel coding and is very close to that of coded modulation.
