In this paper, we show how the Gaussian mixture modeling framework used to develop efficient source encoding schemes can be further exploited to model source statistics during channel decoding in an iterative framework to develop an effective joint source-channel decoding scheme. The joint probability density function (PDF) of successive source frames is modeled as a Gaussian mixture model (GMM). Based on previous work, the marginal source statistics provided by the GMM is used at the encoder to design a low-complexity memoryless source encoding scheme. The source encoding scheme has the specific advantage of providing good estimates to the probability of occurrence of a given source code-point based on the GMM. The proposed iterative decoding procedure works with any channel code whose decoder can implement the soft-output Viterbi algorithm that uses a priori information (APRI-SOVA) or the BCJR algorithm to provide extrinsic information on each source encoded bit. The source decoder uses the GMM model and the channel decoder output to provide a priori information back to the channel decoder. Decoding is done in an iterative manner by trading extrinsic information between the source and channel decoders. Experimental results showing improved decoding performance are provided in the application of speech spectrum parameter compression and communication.

In this paper, we use the Gaussian mixture model (GMM) based multidimensional companding quantization framework to develop two important quantization schemes. In the first scheme, the scalar quantization in the companding framework is replaced by more efficient lattice vector quantization. Low-complexity lattice pruning and quantization schemes are provided for the$E_8$Gossett lattice. At moderate to high bit rates, the proposed scheme recovers much of the space-filling loss due to the product vector quantizers (PVQ) employed in earlier work, and thereby, provides improved performance with a marginal increase in complexity. In the second scheme, we generalize the compression framework to accommodate recursive coding. In this approach, the joint probability density function (PDF) of the parameter vectors of successive source frames is modeled using a GMM. The conditional density of the parameter vector of the current source frame based on the quantized values of the parameter vector of the previous source frames is used to generate a new codebook for every current source frame. We demonstrate the efficacy of the proposed schemes in the application of speech spectrum quantization. The proposed scheme is shown to provide superior performance with moderate increase in complexity when compared with conventional one-step linear prediction based compression schemes for both narrow-band and wide-band speech.

We show how the Gaussian mixture modelling framework used to develop efficient source encoding schemes can be further exploited to model source statistics during channel decoding in an iterative framework to develop an effective joint source-channel decoding scheme. The joint probability density function (PDF) of successive source frames is modelled as a Gaussian mixture model (GMM). Based on previous work, the marginal source statistics provided by the GMM is used at the encoder to design a low-complexity memoryless source encoding scheme. The source encoding scheme has the specific advantage of providing good estimates to the probability of occurrence of a given source code-point based on the GMM. The proposed iterative decoding procedure works with any channel code whose decoder can implement the soft-output Viterbi algorithm that uses a priori information (APRI-SOVA) to provide extrinsic information on each source encoded bit. The source decoder uses the GMM model and the channel decoder output to provide a priori information back to the channel decoder. Decoding is done in an iterative manner by trading extrinsic information between the source and channel decoders. Experimental results showing improved decoding performance are provided in the application of speech spectrum parameter compression and communication.

A joint source-channel decoding scheme that improves the performance of conventional channel decoders over erasure channels by exploiting the cross-correlation between successive speech frames is presented. Speech spectrum parameters are quantized using the scheme presented in Subramaniam and Rao (2001). The joint probability density function (PDF) of the spectrum parameters of successive speech frames is modelled using a Gaussian mixture model (GMM). This model is then used to process the channel decoder output over erasure channels. The performance of two decoding strategies, namely, maximum likelihood decoding (ML) and minimum mean squared error decoding (MMSE) is shown to provide significantly better performance than prediction based schemes.

A low complexity vector quantization scheme for the recursive coding of speech spectrum parameters is proposed. In this scheme, the joint probability density function (pdf) of the spectrum parameters of successive speech frames is modelled using a Gaussian mixture model whose parameters are estimated using the Expectation Maximization (EM) algorithm. The conditional density of the spectrum parameters of the current speech frame based on the quantized values of the spectrum parameters of previous speech frames is used to generate a new codebook for every current speech frame. An efficient quantization scheme using transform coding and bit allocation techniques which allows easy and computationally efficient mapping from observation to quantized value is developed. Transparent quality speech for the first order fixed rate recursive coding case is achieved at 20 bits per frame.

This paper introduces noncausal all-pole models that are capable of efficiently capturing both the magnitude and phase information of voiced speech. It is shown that noncausal all-pole filter models are better able to match both magnitude and phase information and are particularly appropriate for voiced speech due to the nature of the glottal excitation. By modeling speech in the frequency domain, the standard difficulties that occur when using noncausal all-pole filters are avoided. Several algorithms for determining the model parameters based on frequency-domain information and the masking effects of the ear are described. Our work suggests that high-quality voiced speech can be produced using a 14th-order noncausal all-pole model.

This paper presents a class of quadratically weighted distortion measures which provide optimal performance for the high rate vector quantization (VQ) of linear predictive coding (LPC) parameters. It is shown that the quantization distortion of a high rate VQ converges to a quadratically weighted measure, where the quadratic weighting matrix is a "sensitivity" matrix, which is a generalization of the scalar sensitivity concept to the vector case. The sensitivity matrix is the second order term of the Taylor series expansion of the original distortion measure. Closed form expressions and computationally efficient methods for computing the sensitivity matrices of the different LPC parameterizations are given, which involve no numerical integration and can be implemented in real-time on modern DSP chips. In the general case, the "sum of sensitivity weighted scalar errors" is not equivalent to the original distortion measure. However the sensitivity matrix of the line spectral pair (LSP) frequencies is exactly diagonal, demonstrating that for LSPs only a "sum of sensitivity weighted scalar errors" will result in optimal performance.

The paper presents a theoretical analysis of high-rate vector quantization (VQ) systems that use suboptimal, mismatched distortion measures, and describes the application of the analysis to the problem of quantizing the linear predictive coding (LPC) parameters in speech coding systems. First, it is shown that in many high-rate VQ systems the quantization distortion approaches a simple quadratically weighted error measure, where the weighting matrix is a "sensitivity matrix" that is an extension of the concept of the scalar sensitivity. The approximate performance of VQ systems that train and quantize using mismatched distortion measures is derived, and is used to construct better distortion measures. Second, these results are used to determine the performance of LPC vector quantizers, as measured by the log spectral distortion (LSD) measure, which have been trained using other error measures, such as mean-squared (MSE) or weighted mean-squared error (WMSE) measures of LEPC parameters, reflection coefficients and transforms thereof, and line spectral pair (LSP) frequencies. Computationally efficient algorithms for computing the sensitivity matrices of these parameters are described. In particular, it is shown that the sensitivity matrix for the LSP frequencies is diagonal, implying that a WMSE measured LSP frequencies converges to the LSD measure in high-rate VQ systems. Experimental results to support the theoretical performance estimates are provided.>

Mixed-phase AR models are introduced for encoding the magnitudes and phases of the harmonics of voiced speech. Motivation for the use of the mixed-phase AR models is given and several cost functions are introduced, forming the basis for algorithms which estimate the model parameters. An efficient algorithm based on a quasi-linear least squares approach is presented, and a more sophisticated algorithm based on the perceptual masking properties of the ear is described. When the algorithms are used to model voiced speech signals using a 14th order mixed-phase model, high quality speech can be produced.>