If a random variable X with variance rs’ is quantized optimally, being mapped into s discrete levels, the quantization error is roughly proportional to 6 ’ / s 2 . In many applications in speech coding and image digitization, we are given sets of random variables and we have to quantize them in some way so as to represent their realizations with as few discretized levels (bits) as possible. Thi...

This paper studies the optimal bit allocation for shape-gain vector quantization of wireless channels in multiuser (MU) multiple-input multiple-output (MIMO) downlink systems based on linear precoding. Our design minimizes the mean squared-error between the original and quantized channels through optimal bit allocation across shape (direction) and gain (magnitude) for a fixed feedback overhead ...

The JPEG image compression method has been widely implemented in digital camera devices. The quantization process plays a primary role in JPEG image compression. The quantization process is used to determine the visibility threshold of the human visual system. The quantization tables are generated from a series psychovisual experiments from several angle points of experimental views. This paper...

We consider quantization from the perspective of minimizing filtering error when quantized instead of continuous measurements are used as inputs to a nonlinear filter, specializing to discrete-time two-state hidden Markov models (HMMs) with continuous-range output. An explicit expression for the filtering error when continuous measurements are used is presented. We also propose a quantization s...

We approximate the uniform measure on an equilateral triangle by a measure supported on n points. We find the optimal sets of points (n-means) and corresponding approximation (quantization) error for n ≤ 4, give numerical optimization results for n ≤ 21, and a bound on the quantization error for n → ∞. The equilateral triangle has particularly efficient quantizations due to its connection with ...

We present an analysis of the quantization error for generalized (nonuniform and/or nonmonotonic) quantizers. The mean value and mean squared value of the quantization error and the quantized output are derived in terms of the observed signals. The results can be used to identify basic parameters of ADC converters. The results can be utilized in the reference models used in the ADC test methods...