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By John G. Webster (Editor)

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It is widely used in image, audio, and speech compression applications. The most popular vector quantization is fixed-length vector quantization. In the quantization process, consecutive input samples are grouped into fixed-length vectors first. As an example, we can group L samples of input speech as one L-dimensional vector, which forms the input vector to the vector quantizer. For a typical vector quantizer, both the encoder and the decoder share a common codebook, C ϭ ͕ci; i ϭ 1, . , N͖, which can be predefined, fixed, or changed adaptively.

The variables yi, Xik, i ϭ1, . , n, k ϭ 1, . , d are observed, where yi = θ1 Xi1 + · · · + θd Xid + ei The ei are random disturbances and ␪1, . , ␪d should be estimated. Let us denote Xi ϭ (Xi1, . , Xid)T, ␪ ϭ (␪1, . , ␪d)T. The estimate θˆn = arg min θ X n ( yi − θ T Xi )2 i=1 of ␪ is referred to as the least squares estimate. J. ), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc. 162 ESTIMATION THEORY Example 3. Let f(x) be an unknown signal, observed at the points, Xi ϭ i/n, i ϭ1, .

N. 6–21. 9. R. N. , New York: McGraw-Hill, 1978, pp. 204–215. 10. H. Nyquest, Certain topics in telegraph transmission theory, Trans. AIEE, 47: 617–644, 1928. or equivalently, D(r) = σ 2 e−2R 11. Y. Linde, A. Buzo, and R. M. Gray, An algorithm for vector quantizer design, IEEE Trans. , 28: 84–95, 1980. which provides an optimal trade-off with which real systems can be compared. Shannon and others extended this approach to sources with memory and a variety of coding structures. The Shannon bounds are always useful as lower bounds, but they are often over conservative because they reflect only in the limit of very large dimensions and hence very complicated codes.

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29.Information Theory by John G. Webster (Editor)


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