AbstructWe present several results regarding the properties of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. We find that for the optimal lattice quantizers this noise is wide-sense-stationary and white. Any desirable noise ...

W e present several results regarding the propert ies of a random vector, uniformly distributed over a lattice cell. This random vector is the quantization noise of a lattice quantizer at high resolution, or the noise of a dithered lattice quantizer at all distortion levels. W e find that for the optimal lattice quantizers this noise is wide-sense-stat ionary and white. Any desirable noise spec...

We study the joint transmitter optimization for the flat multiinput multi-output (MIMO) channel under nonlinear distortion from the digital-to-analog converters (DACs). Our design is based on a minimum mean square error (MMSE) approach, taking into account the effects of the transmitter nonlinearities. The derivation does not make use of the assumption of uncorrelated white distortion (quantiza...

We consider the r th power quantization error arising in the optimal approximation of a d-dimensional probability measure P by a discrete measure supported by the realization of n i.i.d. random variables X1, ...,Xn. For all d ≥ 1 and r ∈ (0,∞) we establish mean and variance asymptotics as well as central limit theorems for the r th power quantization error. Limiting means and variances are expr...

We elucidate the asymptotics of the L-quantization error induced by a sequence of Loptimal n-quantizers of a probability distribution P on R when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r + d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for q...

Vector Quantization (VQ) plays important role in codebook generation such that the distortion between the original image and the reconstructed image is the minimum. In this paper we present an effective clustering algorithm to generate codebook for vector quantization. In existing algorithm KEVR while splitting the cluster every time new orientation is introduced using error vector sequence. Th...

Recently, a theory, developed by DeVore, Jawerth, and Popov, of nonlinear approximation by both orthogonal and nonorthogonal wavelets has been applied to problems in surface and image compression by DeVore, Jawerth, and Lucier. This theory relates precisely the norms in which the error is measured, the rate of decay in that error as the compression decreases, and the smoothness of the data. In ...

Error diffusion is an often used method that transforms a continuous tone (multibit) image into an image of lower bit depth, most commonly into a binary output of black and white. The simplicity of the processing and the quality of the output have made error diffusion a frequently used tool. Part of the image quality is attributed to the minimization of quantization errors in the error-diffusio...

In this article, we present a distributed variant of an adaptive stochastic gradient method for training deep neural networks in the parameter-server model. To reduce communication cost among workers and server, incorporate two types quantization schemes, i.e., weight quantization, into proposed Adam. addition, to bias introduced by operations, propose error-feedback technique compensate quanti...

In this paper we present a predictive vector quantizer for distributed speech recognition that makes use of a delayed decision coding scheme, performing the optimal codeword searching by means of the M-algorithm. In single-path predictive vector quantization coders, each frame is coded with the closest codeword to the prediction error. However, prediction errors and quantization errors of futur...