Distributed Compression of Linear Functions: Partial SumRate Tightness and Gap to Optimal SumRate
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We consider the problem of distributed compression of the difference Z=Y{1}cY{2} of two jointly Gaussian sources Y{1} and Y{2} under an MSE distortion constraint D on Z. The rate region for this problem is unknown if the correlation coefficient
ho and the weighting factor c satisfy c
ho >0. Inspired by Ahlswede and Han's scheme for the problem of distributed compression of the modulo2 sum of two binary sources, we first propose a hybrid randomstructured coding scheme that is capable of saving the sumrate over both the random quantizeandbin (QB) coding scheme and Krithivasan and Pradhan's structured lattice coding scheme. The main idea is to use a random coding component in the first layer to adjust the source correlation so that the structured coding component in the second layer can be more efficient with the outputs from the first layer as decoder side information. We then provide a new sumrate lower bound for the problem in hand by connecting it to the Gaussian twoterminal source coding problem with covariance matrix distortion constraint. Our lower bound not only improves existing bounds in many cases, but also allows us to prove sumrate tightness of the QB scheme when c is either relatively small or large and D is larger than some threshold. Furthermore, our lower bound enables us to show that our new hybrid scheme performs within two b/s from the optimal sumrate for all values of
ho , c , and D. © 19632012 IEEE.
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