  Let (e_i) be a dictionary for a separable Banach space X. We consider the
problem of approximation by linear combinations of dictionary elements with
quantized coefficients drawn usually from a `finite alphabet'. We investigate
several approximation properties of this type and connect them to the Banach
space geometry of X. The existence of a total minimal system with one of these
properties, namely the coefficient quantization property, is shown to be
equivalent to X containing c_0.
