On Entropy-Constrained Vector Quantization using

A flexible and low-complexity entropy-constrained vector quantizer (ECVQ) scheme based on Gaussian mixture models (GMMs), lattice quantization, and arithmetic coding is presented. The source is assumed to have a probability density function of a GMM. An input vector is first classified to one of the mixture components, and the Karhunen-Lo` eve transform of the selected mixture component is applied to the vector, followed by quantization using a lattice structured codebook. Finally, the scalar elements of the quantized vector are entropy coded sequentially using a specially designed arithmetic coder. The computational complexity of the proposed scheme is low, and independent of the coding rate in both the encoder and the decoder. Therefore, the proposed scheme serves as a lower complexity alternative to the GMM based ECVQ proposed by Gardner, Subramaniam and Rao (1). The performance of the proposed scheme is analyzed under a high-rate assumption, and quantified for a given GMM. The practical performance of the scheme was evaluated through simulations on both synthetic and speech line spectral frequency (LSF) vectors. For LSF quantiza- tion, the proposed scheme has a comparable performance to (1) at rates relevant for speech coding (20-28 bits per vector) with lower computational complexity.

[1]  Alexander Vardy,et al.  Closest point search in lattices , 2002, IEEE Trans. Inf. Theory.

[2]  Jorma Rissanen,et al.  Generalized Kraft Inequality and Arithmetic Coding , 1976, IBM J. Res. Dev..

[3]  Y. Attikiouzel,et al.  Dimension and structure of the speech space , 1992 .

[4]  Philip A. Chou,et al.  Entropy-constrained vector quantization , 1989, IEEE Trans. Acoust. Speech Signal Process..

[5]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[6]  Kris Popat,et al.  Cluster-based probability model applied to image restoration and compression , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[7]  Robert M. Gray.  Gauss mixture vector quantization , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[8]  W. Klein,et al.  Vowel spectra, vowel spaces, and vowel identification. , 1970, The Journal of the Acoustical Society of America.

[9]  Allen Gersho,et al.  Asymptotically optimal block quantization , 1979, IEEE Trans. Inf. Theory.

[10]  Richard Clark Pasco,et al.  Source coding algorithms for fast data compression , 1976 .

[11]  Jan Skoglund,et al.  Vector quantization based on Gaussian mixture models , 2000, IEEE Trans. Speech Audio Process..

[12]  W. Bastiaan Kleijn,et al.  On the Estimation of Differential Entropy From Data Located on Embedded Manifolds , 2007, IEEE Transactions on Information Theory.

[13]  Tamás Linder,et al.  High-Resolution Source Coding for Non-Difference Distortion Measures: The Rate-Distortion Function , 1997, IEEE Trans. Inf. Theory.

[14]  R. Gray.  Source Coding Theory , 1989 .

[15]  Bhaskar D. Rao,et al.  Low-Complexity Source Coding Using Gaussian Mixture Models, Lattice Vector Quantization, and Recursive Coding with Application to Speech Spectrum Quantization , 2006, IEEE Transactions on Audio, Speech, and Language Processing.

[16]  Bhaskar D. Rao,et al.  PDF optimized parametric vector quantization of speech line spectral frequencies , 2003, IEEE Trans. Speech Audio Process..

[17]  Tamás Linder,et al.  High-Resolution Source Coding for Non-Difference Distortion Measures: Multidimensional Companding , 1999, IEEE Trans. Inf. Theory.

[18]  Tamás Linder,et al.  Asymptotic entropy-constrained performance of tessellating and universal randomized lattice quantization , 1994, IEEE Trans. Inf. Theory.

[19]  Jonas Samuelsson,et al.  Recursive coding of spectrum parameters , 2001, IEEE Trans. Speech Audio Process..

[20]  N. J. A. Sloane,et al.  Fast quantizing and decoding and algorithms for lattice quantizers and codes , 1982, IEEE Trans. Inf. Theory.

[21]  P. Wintz,et al.  Image Coding by Adaptive Block Quantization , 1971 .

[22]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[23]  Thomas Eriksson,et al.  Optimization of Lattices for Quantization , 1998, IEEE Trans. Inf. Theory.