Posted on Categories:信息论, 数学代写

# 数学代写|信息论代写Information Theory代考|ECE6063 Rate of convergence between the values of Shannon’s and Hartley’s information

avatest™

avatest信息论information theory代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。https://avatest.org/， 最高质量的信息论information theory作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此信息论information theory作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest™ 为您的留学生涯保驾护航 在澳洲代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的澳洲代写服务。我们的专家在信息论information theory代写方面经验极为丰富，各种信息论information theory相关的作业也就用不着 说。

## 数学代写|信息论代写Information Theory代考|Rate of convergence between the values of Shannon’s and Hartley’s information

The aforementioned Theorem $11.1$ establishes the fact about asymptotic equivalence of the values of Shannon’s and Hartley’s information amounts. It is of interest how quickly does the difference between these values vanish. We remind the reader that in Chapter 7, right after Theorems $7.1$ and 7.2, which established the fact of asymptotic vanishing of probability of decoding error, contains theorems, in which the rate of vanishing of that probability was studied.

Undoubtedly, we can obtain a large number of results of various complexity and importance, which are concerned with the rate of vanishing of the difference $V(I)-$ $\widetilde{V}(I)$ (as in the problem of asymptotic zero probability of error). Various methods can also be used in solving this problem. Here we give some comparatively simple results concerning this problem. We shall calculate the first terms of the asymptotic expansion of the difference $V(I)-\tilde{V}(I)$ in powers of the small parameter $n^{-1}$. In so doing, we shall determine that the boundedness condition (11.2.14) of the cost function, stipulated in the proof of Theorem 11.1, is inessential for the asymptotic equivalence of the values of different kinds of information and is dictated only by the adopted proof method.

Consider formula (11.2.13), which can be rewritten using the notation $S=$ $\int \lambda d F_2(\lambda)$ as follows:
$$\tilde{R}_n\left(n I_1\right) \leqslant \int S P(d \xi)$$

## 数学代写|信息论代写Information Theory代考|Alternative forms of the main result. Generalizations and special cases

In the previous section we introduced the function $\mu_1(t)=(1 / n) \mu_{\xi}(t)$ instead of function (11.3.8). It was done essentially for convenience and illustration reasons in order to emphasize the relative magnitude of terms. Almost nothing will change if the rate quantities $\mu_1, v_1, R_1, I_1$ and others are used only as factors of $n$, that is if we do not introduce the rate quantities at all. Thus, instead of the main result formula (11.3.40), after multiplication by $n$ we obtain
\begin{aligned} 0 & \leqslant \widetilde{R}(I)-R(I)=V(I)-\widetilde{V}(I) \ & \leqslant \frac{1}{2 \beta} \ln \left[\frac{2 \pi}{\gamma^2} v^{\prime \prime}(\beta) \beta^2\right]+\frac{\mathbb{E}\left[\left(\beta \delta \mu^{\prime}+\delta \mu\right)^2\right]}{2 \beta^3 v^{\prime \prime}(\beta)}+o(1), \end{aligned}
where according to $(11.3 .34),(11.3 .8)$, we have

$$\begin{gathered} v(-t)=\mathbb{E}\left[\mu_{\xi}(t)\right]=\int P(d \xi) \ln \int e^{t c(\xi, \zeta)} P_I(d \zeta), \ \delta \mu=\delta \mu(-\beta) ; \quad \delta \mu^{\prime}=\delta \mu^{\prime}(-\beta) ; \quad \delta \mu(t)=\mu_{\xi}(t)-v(-t) \end{gathered}$$
(index $n$ is omitted, the term $C / \beta$ is moved under the logarithm; $\gamma=e^C=1.781$ ). With these substitutions, just as in paragraph $\mathbf{3}$ in Section 11.2, it becomes unnecessary for the Bayesian system to be the $n$-th degree of some elementary Bayesian system.

Differentiating twice function (11.4.2) at point $t=-\beta$ and taking into account (11.1.16) we obtain that
\begin{aligned} & v^{\prime \prime}(\beta)=\int P(d \xi)\left{\int c^2(\xi, \zeta) e^{-\gamma(\xi)-\beta c(\xi, \zeta)} P_I(d \zeta)-\right. \ &\left.-\left[\int c(\xi, \zeta) e^{-\gamma(\xi)-\beta c(\xi, \zeta)} P_I(d \zeta)\right]^2\right} . \end{aligned}

## 数学代写|信息论代写Information Theory代考|Rate of convergence between the values of Shannon’s and Hartley’s information

$$\bar{R}_n\left(n I_1\right) \leqslant \int S P(d \xi)$$

## 数学代写|信息论代写Information Theory代考|Alternative forms of the main result. Generalizations and special cases

$$0 \leqslant \widetilde{R}(I)-R(I)=V(I)-\widetilde{V}(I) \quad \leqslant \frac{1}{2 \beta} \ln \left[\frac{2 \pi}{\gamma^2} v^{\prime \prime}(\beta) \beta^2\right]+\frac{\mathbb{E}\left[\left(\beta \delta \mu^{\prime}+\delta \mu\right)^2\right]}{2 \beta^3 v^{\prime \prime}(\beta)}+o(1),$$

$$v(-t)=\mathbb{E}\left[\mu_{\xi}(t)\right]=\int P(d \xi) \ln \int e^{t c(\xi, \zeta)} P_I(d \zeta), \delta \mu=\delta \mu(-\beta) ; \quad \delta \mu^{\prime}=\delta \mu^{\prime}(-\beta) ; \quad \delta \mu(t)=\mu_{\xi}(t)-v(-t)$$
(指数 $n$ 被省略，术语 $C / \beta$ 在对数下移动; $\gamma=e^C=1.781$ ). 有了这些指换，就像在段落中一样 3 在 $11.2$ 节中，贝叶斯系统不再 是 $n$-一些初等贝叶斯系统的次级。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。