This work considers the quadratic Gaussian multiterminal (MT) source codingproblem and provides a new sufficient condition for the Berger-Tung sum-ratebound to be tight. The converse proof utilizes a set of virtual remote sourcesgiven which the MT sources are block independent with a maximum block size oftwo. The given MT source coding problem is then related to a set oftwo-terminal problems with matrix-distortion constraints, for which a new lowerbound on the sum-rate is given. Finally, a convex optimization problem isformulated and a sufficient condition derived for the optimal BT scheme tosatisfy the subgradient based Karush-Kuhn-Tucker condition. The set of sum-ratetightness problems defined by our new sufficient condition subsumes allpreviously known tight cases, and opens new direction for a more generalpartial solution.
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