  In this paper, we analyze the operational information rate distortion
function (RDF) ${R}_{S;Z|Y}(\Delta_X)$, introduced by Draper and Wornell, for a
triple of jointly independent and identically distributed, multivariate
Gaussian random variables (RVs), $(X^n, S^n, Y^n)= \{(X_{t}, S_t, Y_{t}):
t=1,2, \ldots,n\}$, where $X^n$ is the source, $S^n$ is a measurement of $X^n$,
available to the encoder, $Y^n$ is side information available to the decoder
only, $Z^n$ is the auxiliary RV available to the decoder, with respect to the
square-error fidelity, between the source $X^n$ and its reconstruction
$\widehat{X}^n$. We also analyze the RDF ${R}_{S;\widehat{X}|Y}(\Delta_X)$ that
corresponds to the above set up, when side information $Y^n$ is available to
the encoder and decoder. The main results include,
  (1) Structural properties of test channel realizations that induce
distributions, which achieve the two RDFs,
  (2) Water-filling solutions of the two RDFs, based on parallel channel
realizations of test channels,
  (3) A proof of equality ${R}_{S;Z|Y}(\Delta_X) =
{R}_{S;\widehat{X}|Y}(\Delta_X)$, i.e., side information $Y^n$ at both the
encoder and decoder does not incur smaller compression, and
  (4) Relations to other RDFs, as degenerate cases, which show past literature,
contain oversights related to the optimal test channel realizations and value
of the RDF ${R}_{S;Z|Y}(\Delta_X)$.
