# 计算机代写|密码学与网络安全代写cryptography and network security代考|COMP431

#### Doug I. Jones

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 计算机代写|密码学与网络安全代写cryptography and network security代考|Model for a Communication Channel

A communication channel can be modeled based on the previous developments. Consider a source that has the given alphabet $X$. The source transmits the information to the destiny using a certain channel. The system may be described by a joint probability matrix, which gives the joint probability of occurrence of a transmitted symbol and a received one,
$$[P(X, Y)]=\left[\begin{array}{cccc} p\left(x_1, y_1\right) & p\left(x_1, y_2\right) & \cdots & p\left(x_1, y_N\right) \ p\left(x_2, y_1\right) & p\left(x_2, y_2\right) & \cdots & p\left(x_2, y_N\right) \ \cdots & \cdots & \cdots & \cdots \ p\left(x_M, y_1\right) & p\left(x_M, y_2\right) & \cdots & p\left(x_M, y_N\right) \end{array}\right]$$
There are five probability schemes to analyze:

1. $[P(X, Y)]$, joint probability matrix;
2. $[P(X)]$, marginal probability matrix of $X$;
3. $[P(Y)]$, marginal probability matrix of $Y$;
4. $[P(X \mid Y)]$, probability matrix conditioned on $Y$;
5. $[P(Y \mid X)]$, probability matrix conditioned on $X$;
Those probability schemes produce five entropy functions, associated with the communication channel, whose interpretations are given as follows:
6. $H(X)$ – Average information per source symbol, or source entropy;
7. $H(Y)$ – Average information per received symbol, or receiver entropy;
8. $H(X, Y)$ – Average information associated with pairs of transmitted and received symbols, or average uncertainty of the communication system;
9. $H(X \mid Y)$ – Average information measurement of the received symbol, given that $X$ was transmitted, or conditional entropy;$H(Y \mid X)$ – Average information measurement of the source, given that $Y$ was received, or equivocation.

## 计算机代写|密码学与网络安全代写cryptography and network security代考|Noiseless Channel

For the noiseless discrete channel, each symbol from the input alphabet has a one-to-one correspondence with the output. The joint probability matrix as well as the transition probability matrix have the same diagonal format
$$\begin{gathered} {[P(X, Y)]=\left[\begin{array}{cccc} p\left(x_1, y_1\right) & 0 & \cdots & 0 \ 0 & p\left(x_2, y_2\right) & \cdots & 0 \ \cdots & \cdots & \cdots & \cdots \ 0 & 0 & \cdots & p\left(x_N, y_N\right) \end{array}\right]} \ {[P(X \mid Y)]=[P(Y \mid X)]=\left[\begin{array}{cccc} 1 & 0 & \cdots & 0 \ 0 & 1 & \cdots & 0 \ \cdots & \cdots & \cdots & \cdots \ 0 & 0 & \cdots & 1 \end{array}\right]} \end{gathered}$$
The joint entropy equals the marginal entropies
$$H(X, Y)=H(X)=H(Y)=-\sum_{i=1}^N p\left(x_i, y_i\right) \log p\left(x_i, y_i\right)$$
and the conditional entropies are null
$$H(Y \mid X)=H(X \mid Y)=0 .$$
As a consequence, the receiver uncertainty is equal to the source entropy, and there is no ambiguity at the reception, which indicates that the conditional entropies are all zero.

# 密码学与网络安全代考

## 计算机代写|密码学与网络安全代写密码与网络安全代考|通信通道模型

.通信通道模型 .通信通道模型 .通信通道模型

$$[P(X, Y)]=\left[\begin{array}{cccc} p\left(x_1, y_1\right) & p\left(x_1, y_2\right) & \cdots & p\left(x_1, y_N\right) \ p\left(x_2, y_1\right) & p\left(x_2, y_2\right) & \cdots & p\left(x_2, y_N\right) \ \cdots & \cdots & \cdots & \cdots \ p\left(x_M, y_1\right) & p\left(x_M, y_2\right) & \cdots & p\left(x_M, y_N\right) \end{array}\right]$$

1. $[P(X, Y)]$，联合概率矩阵，
2. $[P(X)]$的边际概率矩阵 $X$
3. .$[P(Y)]$的边际概率矩阵 $Y$
4. .$[P(X \mid Y)]$条件下的概率矩阵 $Y$
5. .$[P(Y \mid X)]$条件下的概率矩阵 $X$
这些概率格式产生了与通信信道相关的五个熵函数，其解释如下:
6. $H(X)$ -每个源符号的平均信息，或源熵;
7. $H(Y)$ -每个接收到的符号的平均信息，或接收熵;
8. $H(X, Y)$ -与发送和接收的符号对相关的平均信息，或通信系统的平均不确定度;
9. $H(X \mid Y)$ -给定所接收符号的平均信息测量 $X$ 即条件熵;$H(Y \mid X)$ -给定，源的平均信息测量 $Y$

## 计算机代写|密码学与网络安全代写cryptography and network security代考|Noiseless Channel

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$$\begin{gathered} {[P(X, Y)]=\left[\begin{array}{cccc} p\left(x_1, y_1\right) & 0 & \cdots & 0 \ 0 & p\left(x_2, y_2\right) & \cdots & 0 \ \cdots & \cdots & \cdots & \cdots \ 0 & 0 & \cdots & p\left(x_N, y_N\right) \end{array}\right]} \ {[P(X \mid Y)]=[P(Y \mid X)]=\left[\begin{array}{cccc} 1 & 0 & \cdots & 0 \ 0 & 1 & \cdots & 0 \ \cdots & \cdots & \cdots & \cdots \ 0 & 0 & \cdots & 1 \end{array}\right]} \end{gathered}$$

$$H(X, Y)=H(X)=H(Y)=-\sum_{i=1}^N p\left(x_i, y_i\right) \log p\left(x_i, y_i\right)$$
，条件熵为null
$$H(Y \mid X)=H(X \mid Y)=0 .$$

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## 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。

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