  This work considers the quadratic Gaussian multiterminal (MT) source coding
problem and provides a new sufficient condition for the Berger-Tung sum-rate
bound to be tight. The converse proof utilizes a set of virtual remote sources
given which the MT sources are block independent with a maximum block size of
two. The given MT source coding problem is then related to a set of
two-terminal problems with matrix-distortion constraints, for which a new lower
bound on the sum-rate is given. Finally, a convex optimization problem is
formulated and a sufficient condition derived for the optimal BT scheme to
satisfy the subgradient based Karush-Kuhn-Tucker condition. The set of sum-rate
tightness problems defined by our new sufficient condition subsumes all
previously known tight cases, and opens new direction for a more general
partial solution.
