  We consider a diffusive Coupled Map Lattice (CML) for which the local map is
piece-wise affine and has two stable fixed points. By introducing a
spatio-temporal coding, we prove the one-to-one correspondence between the set
of global orbits and the set of admissible codes. This relationship is applied
to the study of the (uniform) fronts' dynamics. It is shown that, for any given
velocity in $[-1,1]$, there is a parameter set for which the fronts with that
velocity exist and their shape is unique. The dependence of the velocity of the
fronts on the local map's discontinuity is proved to be a Devil's staircase.
Moreover, the linear stability of the global orbits which do not reach the
discontinuity follows directly from our simple map. For the fronts, this
statement is improved and as a consequence, the velocity of all the propagating
interfaces is computed for any parameter. The fronts are shown to be also
nonlinearly stable under some restrictions on the parameters. Actually, these
restrictions follow from the co-existence of uniform fronts and non-uniformly
travelling fronts for strong coupling. Finally, these results are extended to
some $C^{\infty}$ local maps.
