  We have recently established a strong connection between the Tent map (also
known as Generalized Luroth Series or GLS which is a chaotic, ergodic and
lebesgue measure preserving non-linear dynamical system) and Arithmetic coding
which is a popular source compression algorithm used in international
compression standards such as JPEG2000 and H.264. This was for independent and
identically distributed binary sources. In this paper, we address the problem
of compression of ergodic Markov binary sources with certain words forbidden
from the message space. We shall show that GLS can be modified suitably to
achieve Shannon's entropy rate for these sources.
