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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

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

Table $4.6$ presents two examples of uniquely decodable codes. Code $\mathcal{A}$ is a simpler method to construct a uniquely decodable set of sequences because all codewords have the same length and it is a non-singular code.

Code $\mathcal{B}$ is also uniquely decodable. It is also called a comma code because the digit zero is used to separate the codewords (Abramson, 1963).

Consider the code shown in Table 4.7. Code $\mathcal{C}$ differs from $\mathcal{A}$ and $\mathcal{B}$ from Table $4.6$ in an important aspect. If a binary sequence composed of codewords from code $\mathcal{C}$ occurs, it is not possible to decode the sequence.

Example: If the bit stream 100000 is received, for example, it is not possible to decide if it corresponds to symbol $x_5$, unless the next symbol is available. If the next symbol is 1 , then the sequence is 100000 , but if it is 0 , then it is necessary to inspect one more symbol to know if the sequence corresponds to $x_6(1000000)$ or $x_7(10000000)$.

A uniquely decodable code is instantaneous if it is possible to decode each codeword in a sequence with no reference to subsequent symbols (Abramson, 1963). Codes $\mathcal{A}$ and $\mathcal{B}$ are instantaneous, and $\mathcal{C}$ is not.

It is possible to devise a test to indicate when a code is instantaneous. Let $X_i=x_{i 1} x_{i 2} \ldots x_{i m}$ be a word from a certain code. The sequence of symbols $\left(x_{i 1} x_{i 2} \ldots x_{i j}\right)$, with $j \leq m$, is called the prefix of the codeword $X_i$.

## 计算机代写|密码学与网络安全代写cryptography and network security代考|Construction of Instantaneous Codes

In order to construct a binary instantaneous code for a source with five symbols, one can begin by attributing the digit 0 to symbol $s_0$ (Abramson, 1963)
$$x_0 \leftarrow 0 .$$
In this case, the remaining source symbols should correspond to the codewords that begin with the digit 1 . Otherwise, it is not a prefix code. It is not possible to associate $x_1$ with the codeword 1 because no other symbol would remain to begin the other codewords.

This codeword assignment requires that the remaining codewords begin with 11 . If
$$x_2 \leftarrow 110,$$
then, the only unused prefix with 3 bits is 111 , which implies that
$$x_3 \leftarrow 1110$$
and
$$x_4<1111 .$$
In the previously constructed code, note that if one begins the code construction by making $x_0$ to correspond to 0 , this restricts the available number of codewords, because the remaining codewords had to, necessarily, begin with 1 .

On the other hand, if a two-digit word had been chosen to represent $x_0$, there would be more freedom to choose the others, and there would be no need to assign very long codewords to the last ones.

A binary instantaneous code can be constructed to represent the five symbols (Abramson, 1963). The first assignment is
$$x_0 \leftarrow 00$$

# 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cryptography and network security代考|瞬时代码

. crypgraphy and network-security代考-instantane – Codes “>计算机代写|密码学与网络安全代写cryptography and network security代考|瞬时代码

## 计算机代写|密码学与网络安全代写cryptography and network security代考|瞬时代码的构建

. crypgraphy -and-network-security

$$x_0 \leftarrow 0 .$$

$$x_2 \leftarrow 110,$$

$$x_3 \leftarrow 1110$$

$$x_4<1111 .$$

$$x_0 \leftarrow 00$$

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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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