The sumrate bound for a new class of quadratic Gaussian multiterminal source coding problems
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In this paper we show tightness of the BergerTung (BT) sumrate bound for a new class of quadratic Gaussian multiterminal (MT) source coding problems dubbed bieigen equalvariance with equal distortion (BEEVED), where the L X L source covariance matrix has equal diagonal elements with two distinct eigenvalues, and the L target distortions are equal. Let K(K < L) be the number of larger eigenvalues, the BEEV covariance structure allows us to connect K i.i.d virtual Gaussian sources with the L given MT sources via an LXK semiorthogonal transform whose rows have equal Euclidean norm plus additive i.i.d. Gaussian noises, resulting in the two sets of sources being mutually conditional i.i.d. By relating the given MT source coding problem to a generalized Gaussian CEO problem with the K virtual sources as remote sources and the L MT sources as observations, we obtain a lower bound on the MT sumrate, and show its achievability by BT schemes under the equal distortion constraints. Our BEEVED class of quadratic Gaussian MT source coding problems subsumes both the positivesymmetric case considered by Wagner et al. and the negativesymmetric case. Other examples, including a subclass of sources with BE circulant symmetric covariance matrices and equal distortion constraints, are also provided to highlight tightness of the sumrate bound. ©2009 IEEE.
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Yang, YangXiong, Zixiang
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