相关论文: Constrained quantization for the Cantor distributi…
In this paper, for a given family of constraints and the classical Cantor distribution we determine the constrained optimal sets of $n$-points, $n$th constrained quantization errors for all positive integers $n$. We also calculate the…
Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the…
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces $\mathbb{R}^k$ by introducing and analyzing the notions of the $n$th constrained quantization error, constrained…
In this paper, we first consider a family of constraints given by straight lines. For a uniform probability distribution, we determine the constrained optimal sets of $n$-points and the corresponding $n$th constrained quantization errors…
This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…
This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given $k\geq 2$, let $\{S_j : 1\leq…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. Let $P$ be a Borel probability measure on…
Let $\{S_j : 1\leq j\leq 3\}$ be a set of three contractive similarity mappings such that $S_j(x)=rx+\frac {j-1}{2}(1-r)$ for all $x\in \mathbb R$, and $1\leq j\leq 3$, where $0<r<\frac 1 3$. Let $P=\sum_{j=1}^3 \frac 13 P\circ S_j^{-1}$.…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
We consider optimal scalar quantization with $r$th power distortion and constrained R\'enyi entropy of order $\alpha$. For sources with an absolutely continuous distribution the high rate asymptotics of the quantizer distortion has long…
This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
Randomized (dithered) quantization is a method capable of achieving white reconstruction error independent of the source. Dithered quantizers have traditionally been considered within their natural setting of uniform quantization. In this…