An algorithm for uniform vector quantizer design

A vector quantizer maps a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> -dimensional vector into one of a finite set of output vectors or "points". Although certain lattices have been shown to have desirable properties for vector quantization applications, there are as yet no algorithms available in the quantization literature for building quantizers based on these lattices. An algorithm for designing vector quantizers based on the root lattices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Aₙ, Dₙ</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Eₙ</tex> and their duals is presented. Also, a coding scheme that has general applicability to all vector quantizers is presented. A four-dimensional uniform vector quantizer is used to encode Laplacian and gamma-distributed sources at entropy rates of one and two bits/sample and is demonstrated to achieve performance that compares favorably with the rate distortion bound and other scalar and vector quantizers. Finally, an application using uniform four- and eight-dimensional vector quantizers for encoding the discrete cosine transform coefficients of an image at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</tex> bit/pel is presented, which visibly illustrates the performance advantage of vector quantization over scalar quantization.