  This paper addresses the topic of robust Bayesian compressed sensing over
finite fields. For stationary and ergodic sources, it provides asymptotic (with
the size of the vector to estimate) necessary and sufficient conditions on the
number of required measurements to achieve vanishing reconstruction error, in
presence of sensing and communication noise. In all considered cases, the
necessary and sufficient conditions asymptotically coincide. Conditions on the
sparsity of the sensing matrix are established in presence of communication
noise. Several previously published results are generalized and extended.
