Uniform and piecewise uniform lattice vector quantization for memoryless Gaussian and Laplacian sources

Jeong, Dae Gwon; Gibson, J.D.

doi:10.1109/18.256488

Cited by 76 publications

(56 citation statements)

References 37 publications

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“…Since D is the quadratic function of m i it is obvious that (9) gives its global minimum with respect to m i . Above discussion confirms that (8) and (9) gives the global minimum of D, with respect to r, if an optimal point (r,m) satisfiesr i ≤m i ≤r i+1…”

Section: Optimization Of R I and M Isupporting

confidence: 81%

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An iterative method for optimal resolution‐constrained polar quantizer design

Petković

Perić

Jovanović

2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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This paper addresses the problem of polar quantization optimization. Particularly, the aim of this investigation is to find the method for the optimal resolution-constrained polar quantizer design.The new iterative algorithm for determination of the optimal decision and representation magnitude levels and algorithm for optimization of number of phase cells within each magnitude level, is proposed.At high rates, the new optimal polar quantizer outperforms the optimal polar compander for 0.2dB, while the more significant gain should be expected at lower rates. In this paper, in order to enable practical implementation of quantizer model, algorithm which transforms real values for the optimal numbers of phase cells within magnitude levels into integer ones is also proposed. Moreover, the approximate closed form of signal to quantization ratio (SQNR) is derived.Since circularly symmetric sources and complex presentation of signals arise in numerous applications, it can be concluded that the usage area of the suggested proposal is very wide (audio coding, image coding, spectral phase coding SPC, synthetic aperture radars systems SARs, coding of the discrete Fourier transform).It should be emphasized that in contrast to earlier work, where models have been designed under high-rate assumption, the obtained nonuniform unrestricted polar quantizer is optimal for all rates.

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Section: Optimization Of R I and M Isupporting

confidence: 81%

“…Suppose that r is fixed and m is determined optimally, according to (8). Additionally suppose that r i < m i < r i+1 .…”

Section: Optimization Of M Imentioning

confidence: 99%

An iterative method for optimal resolution‐constrained polar quantizer design

Petković

Perić

Jovanović

2011

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…T consisting of independent and identically distributed Laplacian samples x i with zero mean and variance σ [13,14,17] f…”

Section: Radial Scalar Compression Function Of High Dynamic Range Geomentioning

confidence: 99%

Radial compression function for vector quantizer of Laplacian source with high dynamic variance range

Perić

Jovanović

2010

Trans Emerging Tel Tech

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In this paper, our aim is to define a high dynamic range vector quantization model for an i.i.d. Laplacian source. In order to do this we use a geometric approach and lattice quantization. As a result, we achieve symmetry in distribution of code vectors and introduce the radial scalar compression function for lattice cell side determination. This enables derivation of a sophisticated creation for a condition which the radial compression function should satisfy in order to make the SQNR nondependent on variance. It is interesting that the obtained solution represents the generalisation of solution in the case of high dynamic range scalar quantization. Because of that, in the second part of the paper, the well-known semilogarithmic A-law compression characteristic is utilized as radial scalar compression function of geometric vector quantizer. It is shown that such a model has very good performances over a very wide variance range. The proper choice of compression parameter A and dimension n enables the constant SQNR to sustain over much wider variance range than in case of log-scalar quantization. Particularly, the high dimension makes it possible to broaden the variance range over which SQNR remains constant by increasing the A value simultaneously holding the SQNR level unchanged. In comparison with the widely used log-scalar quantization, the presented solution for dimensions from 10 to 140 gives a quality improvement of 7--9 dB, while comparison of maximal SQNR value to that of optimal scalar quantization shows the SQNR growth of 3--5 dB. Furthermore, for dimension 40 the SQNR maximum is only for 0.5 dB lower than that of optimal vector quantization, while dynamic range characteristic broadening is considerable. The cited benefits of high dynamic range vector quantization make it possible to realize a high quality signal compression. Besides, in comparison with the adaptive quantization, our proposal has a smaller implementation complexity.

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“…Some related methods used to obtain a lattice quantizer for a non-uniform source have already been presented in the literature as the multidimensional companding [9] and the embedded algebraic VQ [15] or piecewise uniform lattice VQ [5]. We have tested the companding by transforming the distribution of the input vectors into a uniform one using spherical companding.…”

Section: Predictive Multiple-scale Lattice Vqmentioning

confidence: 99%

Predictive multiple-scale lattice VQ for LSF quantization

Vasilache

Vasilache²,

Tăbuş³

1999

1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)

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This paper introduces a new lattice quantization scheme, the multiple-scale lattice vector quantization (MSLVQ), based on the truncation of the D + 10 lattice. The codebook is composed of several copies of the truncated lattice scaled with different scaling factors. A fast nearest neighbor search is introduced. We compare the performance of predictive MSLVQ for quantization of LSF coefficients with the quantization technique used in the codec G.729 and show the better performance of our method in terms of spectral distortion. The MSLVQ scheme achieves the transparent quality at 21 bits/frame.

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Uniform and piecewise uniform lattice vector quantization for memoryless Gaussian and Laplacian sources

Cited by 76 publications

References 37 publications

An iterative method for optimal resolution‐constrained polar quantizer design

An iterative method for optimal resolution‐constrained polar quantizer design

Radial compression function for vector quantizer of Laplacian source with high dynamic variance range

Predictive multiple-scale lattice VQ for LSF quantization

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