  We prove achievability of the recently characterized quadratic Gaussian
rate-distortion function (RDF) subject to the constraint that the distortion is
uncorrelated to the source. This result is based on shaped dithered lattice
quantization in the limit as the lattice dimension tends to infinity and holds
for all positive distortions. It turns out that this uncorrelated distortion
RDF can be realized causally. This feature, which stands in contrast to
Shannon's RDF, is illustrated by causal transform coding. Moreover, we prove
that by using feedback noise shaping the uncorrelated distortion RDF can be
achieved causally and with memoryless entropy coding. Whilst achievability
relies upon infinite dimensional quantizers, we prove that the rate loss
incurred in the finite dimensional case can be upper-bounded by the space
filling loss of the quantizer and, thus, is at most 0.254 bit/dimension.
