Andres Buzo

An Algorithm for Vector Quantizer Design

An efficient and intuitive algorithm is presented for the design of vector quantizers based either on a known probabilistic model or on a long training sequence of data. The basic properties of the algorithm are discussed and demonstrated by examples. Quite general distortion measures and long blocklengths are allowed, as exemplified by the design of parameter vector quantizers of ten-dimensional vectors arising in Linear Predictive Coded (LPC) speech compression with a complicated distortion measure arising in LPC analysis that does not depend only on the error vector.

Speech coding based upon vector quantization

With rare exception, all presently available narrow-band speech coding systems implement scalar quantization (independent quantization) of the transmission parameters (such as reflection coefficients or transformed reflection coefficients in LPC systems). This paper presents a new approach called vector quantization. For very low data rates, realistic experiments have shown that vector quantization can achieve a given level of average distortion with 15 to 20 fewer bits/frame than that required for the optimized scalar quantizing approaches presently in use. The vector quantizing approach is shown to be a mathematically and computationally tractable method which builds upon knowledge obtained in linear prediction analysis studies. This paper introduces the theory in a nonrigorous form, along with practical results to date and an extensive list of research topics for this new area of speech coding.

Distortion measures for speech processing

Several properties, interrelations, and interpretations are developed for various speech spectral distortion measures. The principle results are 1) the development of notions of relative strength and equivalence of the various distortion measures both in a mathematical sense corresponding to subjective equivalence and in a coding sense when used in minimum distortion or nearest neighbor speech processing systems; 2) the demonstration that the Itakura-Saito and related distortion measures possess a property similar to the triangle inequality when used in nearest neighbor systems such as quantization and cluster analysis; and 3) that the Itakura-Saito and normalized model distortion measures yield efficient computation algorithms for generalized centroids or minimum distortion points of groups or clusters of speech frames, an important computation in both classical cluster analysis techniques and in algorithms for optimal quantizer design. We also argue that the Itakura-Saito and related distortions are well-suited computationally, mathematically, and intuitively for such applications.

Double-loop sigma-delta modulation with DC input

A discrete-time model having a two-bit (2-b) quantizer is analyzed exactly, and an analytical expression for the quantizer noise sequence is found. Rigorous answers are then provided to two fundamental questions for a double-loop sigma-delta modulation system with DC input: (1) What is the long-term statistical behavior of the internal quantizer noise? (2) How does the asymptotic mean square sigma-delta quantization error vary as a function of the oversampling ratio?. >

Achievability proof of some multiuser channel coding theorems using backward decoding

New and simpler achievability proofs that are based on the backward decoding technique are presented for the well-known coding theorems for the multiple-access channel (MAC) with perfect feedback and the degraded relay channel. A class of MACs with different generalized feedback signals is also considered, and achievable-rate regions that are larger than those previously presented in the literature are established. >

Multiloop sigma-delta quantization

It is shown that, for a multiloop sigma-delta modulator driven by a DC input, the statistical behavior (described by long-term time averages) of the error process from an inner (multibit) quantizer is consistent with that of a signal-independent. white. uniform noise. The same result also holds for sinusoidal inputs, provided that the modulator has three or more loops. This behavior is exploited to obtain trade-offs between asymptotic system performances and oversampling ratios, for several sigma-delta modulator/decoding filter pairs. For an L-loop modulator with a simple sinc/sup L+1/ decoding filter, it is shown that doubling the oversampling ratio can result in an improvement of 3.01(2L+1) dB in the signal-to-quantization-noise ratio. >

Multi-loop sigma-delta quantization: spectral analysis

An exact spectral analysis of oversampled discrete-time L-loop (L>or=2) sigma-delta modulator ( Sigma Delta M) with DC (constant) input is presented. It is shown by a novel application of ergodic theory that the embedded quantizer error sequence is asymptotically uniformly distributed, white and uncorrelated with the input, a fact usually assumed a priori in the linearized models. It was found that for the following linear demodulators: (1) optimum FIR (finite-impulse response) filter, (2) sinc/sup k/ filters (k>or=L+1), and (3) the ideal low-pass filter, the overall system ( Sigma Delta M plus demodulator) can provide a normalized average quantization noise power inversely proportional to the (2L+1)-st power of the oversampling ratio, confirming the performance superiority of multiloop Sigma Delta M over single-loop Sigma Delta M.<<ETX>>

Rate-distortion bounds for quotient-based distortions with application to Itakura- Saito distortion measures

In many linear predictive coding (LPC) speech compression systems the encoding of the LPC parameters is performed using a product code book scheme. One possible approach consists in organizing the set of LPC reproduction models as the Cartesian product of a vector code book describing the shape of each reproduction LPC model and a scalar codebook describing the gain or energy. We first present a formal development of rate-distortion theoretic results for distortion functions based on quotients of input and reproduction symbols. We also obtain theoretical bounds for the rate-distortion function of the gain term of LPC systems (which, depending on the quantization scheme, can use about 10-25 percent of the transmission rate), as well as asymptotic (small distortions) approximations to the performance of the optimal scalar quantizer for these gain terms, when the overall fidelity criterion is the Itakura-Saito distortion measure, which is a member of the class of quotient distortion measures. The approximations and bounds are compared finally with experimental results.

Optimal quantizations of coefficient vectors in LPC speech

Recently developed algorithms for determining locally optimum vector quantizers for a given bit rate, distortion measure, and data training sequence are applied to vectors of reflection coefficients from LPC coded speech files with Itakura‐Saito and spectral deviation distortion measures. The resulting quantizers with 7 or 8 bits per frame for 10 dimensional reflection coefficient vectors, yield comparable average spectral distortion to nonvector quantizers using far more bits. Tapes of the low bit rate synthetic speech will be played to illustrate the usefulness of the algorithms, the distortion measures, and the vector quantizers. [Work of first two authors supported by AFOSR.]