  In Compressed Sensing, a real-valued sparse vector has to be estimated from
an underdetermined system of linear equations. In many applications, however,
the elements of the sparse vector are drawn from a finite set. For the
estimation of these discrete-valued vectors, matched algorithms are required
which take the additional knowledge of the discrete nature into account. In
this paper, the estimation problem is treated from a communications engineering
point of view. A powerful new algorithm incorporating techniques known from
digital communications and information theory is derived. For comparison, Turbo
Compressed Sensing is adapted to the discrete setup and a simplified and
generalized notation is presented. The performance of the algorithms is covered
by numerical simulations.
