### Abstract

A vector quantizer maps a k-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 An, Dn, and En 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 0.5 bit/pel is presented, which visibly illustrates the performance advantage of vector quantization over scalar quantization.

Original language | English (US) |
---|---|

Pages (from-to) | 805-814 |

Number of pages | 10 |

Journal | IEEE Transactions on Information Theory |

Volume | 30 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1984 |

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### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*30*(6), 805-814. https://doi.org/10.1109/TIT.1984.1056979

**An Algorithm for Uniform Vector Quantizer Design.** / Sayood, Khalid; Gibson, Jerry D.; Rost, Martin C.

Research output: Contribution to journal › Letter

*IEEE Transactions on Information Theory*, vol. 30, no. 6, pp. 805-814. https://doi.org/10.1109/TIT.1984.1056979

}

TY - JOUR

T1 - An Algorithm for Uniform Vector Quantizer Design

AU - Sayood, Khalid

AU - Gibson, Jerry D.

AU - Rost, Martin C.

PY - 1984/1/1

Y1 - 1984/1/1

N2 - A vector quantizer maps a k-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 An, Dn, and En 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 0.5 bit/pel is presented, which visibly illustrates the performance advantage of vector quantization over scalar quantization.

AB - A vector quantizer maps a k-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 An, Dn, and En 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 0.5 bit/pel is presented, which visibly illustrates the performance advantage of vector quantization over scalar quantization.

UR - http://www.scopus.com/inward/record.url?scp=0021517874&partnerID=8YFLogxK

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U2 - 10.1109/TIT.1984.1056979

DO - 10.1109/TIT.1984.1056979

M3 - Letter

VL - 30

SP - 805

EP - 814

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 6

ER -