  The separability in parallel Gaussian interference channels (PGICs) is
studied in this paper. We generalize the separability results in one-sided
PGICs (OPGICs) by Sung \emph{et al.} to two-sided PGICs (TPGICs). Specifically,
for strong and mixed TPGICs, we show necessary and sufficient conditions for
the separability. For this, we show diagonal covariance matrices are sum-rate
optimal for strong and mixed TPGICs.
