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On the performance of vector quantizers empirically designed from dependent sources
 in Proceedings of Data Compression Conference, DCC'98
, 1998
"... Suppose we are given n real valued samples Z1�Z2�:::�Zn from a stationary source P. We consider the following question. For a compression scheme that uses blocks of length k, what is the minimal distortion (for encoding the true source P) induced by a vector quantizer of xed rate R, designed from th ..."
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Suppose we are given n real valued samples Z1�Z2�:::�Zn from a stationary source P. We consider the following question. For a compression scheme that uses blocks of length k, what is the minimal distortion (for encoding the true source P) induced by a vector quantizer of xed rate R, designed from the training sequence. For a certain class of dependent sources, we derive conditions ensuring that the empirically designed quantizer performs as well (on the average) as the optimal quantizer, for almost every training sequence emitted by the source. In particular, we observe that for a code rate R, the optimal way to choose the dimension of the quantizer is kn = b(1;)R;1 log nc. The problem of empirical design of vector quantizer of xed dimension k based on a vector valued training sequence X1 � X2�:::�Xn is also considered. For a class of dependent sources, it is shown that the mean squared error (MSE) of the empirically designed quantizer w.r.t the true source distribution converges to the minimum possible MSE at a rate of O ( p log n=n), for almost every training sequence emitted by the source. In addition, the expected value of the distortion redundancy { the di erence between the MSE's of the quantizers { converges to zero for a sequence of increasing block lengthsk, ifwehave at our disposal corresponding training sequences whose length grows as n =2 (R+)k. Some of the derivations extend recent results in empirical quantizer design using an i.i.d. training sequence, obtained by Linder et al. [7] and Merhav and Ziv [8]. Proof techniques rely on recent results in the theory of empirical processes, indexed by VC function classes.