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.