  It is well known that reconstruction problems, as the interdisciplinary
subject, have been studied in numerous contexts including statistical physics,
information theory and computational biology, to name a few. We consider a
$2q$-state symmetric model, with two categories of $q$ states in each category,
and 3 transition probabilities: the probability to remain in the same state,
the probability to change states but remain in the same category, and the
probability to change categories. We construct a nonlinear second order
dynamical system based on this model and show that the Kesten-Stigum
reconstruction bound is not tight when $q \geq 4$.
