It is assumed that n real valued samples Z1, Z2,..., Zn from stationary source P are given. For a compression scheme that uses blocks of length k, the minimal distortion induced by a vector quantizer of fixed rate R, designed from the training experience, is explored. For a certain class of dependent sources, conditions are derived ensuring that the empirically designed quantizer performs well as the optimal quantizer, for almost every training sequence emitted by the source. In particular, it is observed that for a code rate R, the optimal way to choose the dimension of the quantizer is kn = [(1-δ)R-1 log n]. The problem of empirical design of vector quantizer of fixed 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 square 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(√log n/n), for almost every training sequence emitted by the source.
|Number of pages
|Proceedings of the Data Compression Conference
|Published - 1998
|Proceedings of the 1998 Data Compression Conference, DCC - Snowbird, UT, USA
Duration: 30 Mar 1998 → 1 Apr 1998