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Distortion bounds for vector quantizers with finite codebook size

1999
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IEEE Transactions on Information Theory
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Upper and lower bounds are presented for the distortion of the optimal N-point vector quantizer applied to k-dimensional signals. Under certain smoothness conditions on the source distribution, the bounds are shown to hold for each and every value of N, the codebook size. These results extend bounds derived in the high-resolution limit, which assumes that the number of code vectors is arbitrarily large. Two approaches to the upper bound are presented. The first, constructive construction,

doi:10.1109/18.771232
fatcat:npvzom5ox5bnhca4bs5algl2iy