Prediction-based Lower Triangular Transform Research Articles

Prediction Transform GMM Vector Quantization for Wideband LSFs DOI: 10.14209/jcis.2014.5

Classified vector quantization (VQ) using a Gaussian Mixture Model (GMM) preclassifier is a powerful VQ method. A prediction-based lower-triangular transform (PLT) is proposed for the enhancement of VQ in each cluster. The PLT is defined for generic vector spaces in the context of the covariance method of linear prediction (LP). Optimal quantizer banks are designed in minimum noise structures whose codebooks are used for the proposed Cartesian split VQ (CSVQ), which improves their coding gain. CSVQ is tested forline spectral frequency (LSF) quantization of wideband speech spectra, revealing a comparable average performance to the Karhunen-Loeve transform (KLT) at lower rates with reduced outlier generation and computational complexity.

Prediction Transform GMM Vector Quantization for Wideband LSFs

Classified vector quantization (VQ) using a Gaussian Mixture Model (GMM) preclassifier is a powerful VQ method. A prediction-based lower-triangular transform (PLT) is proposed for the enhancement of VQ in each cluster. The PLT is defined for generic vector spaces in the context of the covariance method of linear prediction (LP). Optimal quantizer banks are designed in minimum noise structures whose codebooks are used for the proposed Cartesian split VQ (CSVQ), which improves their coding gain. CSVQ is tested forline spectral frequency (LSF) quantization of wideband speech spectra, revealing a comparable average performance to the Karhunen-Loeve transform (KLT) at lower rates with reduced outlier generation and computational complexity.

Intra-Predictive Switched Split Vector Quantization of Speech Spectra

Vector quantization (VQ) of speech spectral vectors has been improved by techniques such as split VQ (SVQ), vector transforms and direction switching. This letter proposes Intra-Predictive Switched SVQ (IPSSVQ) with direction switching by a Gaussian Mixture Model (GMM), using at the frame level the prediction-based lower-triangular transform (PLT), which has lower complexity than the Karhunen-Loève transform (KLT). It is shown that equivalent results to GMM KLT SSVQ may be obtained in the quantization of line spectral frequency (LSF) vectors from wideband speech signals, such as transparent coding throughout the range from 46 bit/frame to 41 bit/frame, with about three-fourths as much operational complexity.

Generalized Triangular Decomposition in Transform Coding

A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang This family includes the Karhunen-Loeve transform (KLT) and the generalized version of the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to that of the KLT and the PLT. Even though the original PLT introduced by Phoong is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes, the GTD-based family includes members that are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT, which has the unit noise-gain property. Other special cases of the GTD-TC are the geometric mean decomposition (GMD) and the bidiagonal decomposition (BID) transform coders. The GMD-TC in particular has the property that the optimum bit allocation is a uniform allocation; this is because all its transform domain coefficients have the same variance, implying thereby that the dynamic ranges of the coefficients to be quantized are identical.

Prediction-based lower triangular transform

A new nonunitary transform called the prediction-based lower triangular transform (PLT) is introduced for signal compression. The new transform has the same decorrelation property as the Kahurnen-Loeve transform (KLT), but its implementational cost is less than one half of KLT. Compared with the KLT, the design cost of an M/spl times/M PLT is much lower and is only of the order of O(M/sup 2/). Moreover, the PLT can be factorized into simple building blocks. Using two different factorizations, we introduce two minimum noise structures that have roughly the same complexity as the direct implementation of PLT. These minimum noise structures have the following properties: (1) its noise gain is unity even though the transform is nonunitary; (2) perfect reconstruction is structurally guaranteed; (3) it can be used for both lossy/lossless compression. We show that the coding gain of PLT implemented using the minimum noise structure is the same as that of KLT. Furthermore, universal transform coders using PLT are derived. For AR(1) process, the M/spl times/M PLT has a closed form and needs only (M-1) multiplications and additions.