数字通信与网络入门：MIT 6.02电子工程II

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本资源是一份来自麻省理工学院（MIT）电气工程与计算机科学（EECS）系的课程讲义，名为"EECS II Digital Communication Systems"（6.02）。课程由Hari Balakrishnan、Christopher J. Terman和George C. Verghese三位教授共同编撰，最新更新日期为2012年。本课程旨在介绍数字通信与网络的基础，关注的是20世纪对社会产生重大影响的通信技术，特别是互联网及其背后的科学技术。课程第一章的主题是“Introduction”，它强调了在21世纪，信息传递和交换能力通过全球通信网络所带来的革命性变化。在列举的20世纪最具影响力的科技中，通信技术占据了显著位置，包括无线电、电视、电话、互联网和计算机。尽管互联网排名不高，但因其对社会的影响深远，该课程特别关注其技术基础。重点内容可能涉及以下几个知识点： 1. **Bits, Signals, and Packets**: 课程开始会讲解数字化信息的基本单位——比特（bits），以及信号如何在物理世界中编码和传输。数字信号通常由一系列离散的比特组成，而数据包（packets）则是在网络中分段传输，以提高效率和可靠性。 2. **Digital Communications**: 课程深入研究数字信号处理、调制解调技术，以及如何在噪声环境中实现无失真或低失真的通信。这包括编码理论、信道编码、解码算法等，这些都是确保数据准确传输的关键。 3. **Network Fundamentals**: 学习网络架构（如局域网、广域网、互联网协议等）、数据传输模型（如TCP/IP）、路由和拥塞控制，以及网络安全概念，如加密和身份验证。 4. **Internet History and Evolution**: 对互联网的发展历程进行回顾，包括早期的ARPANET，TCP/IP协议栈，以及Web浏览器和其他关键组件的诞生。讨论互联网如何从一个军事研究项目发展成为全球信息基础设施。 5. **Technology Impact**: 探讨互联网对社会、经济和文化的重大影响，以及它如何改变人们的生活方式、工作模式和娱乐方式。通过学习这些内容，学生将获得理解现代通信系统所需的核心理论和技术知识，这对于未来的工程师、科学家和IT专业人员来说是非常重要的。

SECTION 2.4. WHY COMPRESSION?

• Over error-prone links with non-negligible bit error rates, compressing messages be-

fore they are channel-coded using error-correcting codes can help improve through-

put because all the redundancy in the message can be designed in to improve error

resilience, after removing any other redundancies in the original message. It is better

to design in redundancy with the explicit goal of correcting bit errors, rather than

rely on whatever sub-optimal redundancies happen to exist in the original message.

Compression is traditionally thought of as

an end-to-end function, applied as part of the

application-layer protocol. For instance, one might use lossless compression between a

web server and browser to reduce the number of bits sent when transferring a collection of

web pages. As another example, one might use a compressed image format such as JPEG

to transmit images, or a format like MPEG to transmit video. However, one may also ap-

ply compression at the link layer to reduce the number of transmitted bits and eliminate

redundant bits (before possibly applying an error-correcting code over the link). When

applied at the link layer, compression only makes sense if the data is inherently compress-

ible, which means it cannot already be compressed and must have enough redundancy to

extract compression gains.

The next chapter describes two compr

ession (source coding) schemes: Huffman Codes

and Lempel-Ziv-Welch (LZW) compression.

⌅ Acknowledgments

Thanks to Yury Polyanskiy for several useful comments and suggestions.

⌅ Exercises

1. Several people at a party are trying to guess a 3-bit binary number. Alice is told that

the number is odd; Bob is told that it is not a multiple of 3 (i.e., not 0, 3, or 6); Charlie

is told that the number contains exactly two 1’s; and Deb is given all three of these

clues. How much information (in bits) did each player get about the number?

2. After careful data collection, Alyssa P

. Hacker observes that the probability of

“HIGH” or “LOW” trafﬁc on Storrow Drive is given by the following table:

HIGH trafﬁc

level LOW trafﬁc level

If the Red Sox are playing

If the Red

Sox are not playing

P (HIGH trafﬁc) = 0.999 P (LOW trafﬁc) = 0.001

P (HIGH trafﬁc)

= 0.25 P (LOW trafﬁc) = 0.75

(a) If it is known that the

Red Sox are playing, then how much information in bits

is conveyed by the statement that the trafﬁc level is LOW. Give your answer as

a mathematical expression.

(b) Suppose it is known that the

Red Sox are not playing. What is the entropy

of the corresponding probability distribution of trafﬁc? Give your answer as a

mathematical expression.

3. X is an unknown 4-bit binary

number picked uniformly at random from the set of

all possible 4-bit numbers. You are given another 4-bit binary number, Y , and told

CHAPTER 2. INFORMATION, ENTROPY, AND THE MOTIVATIO N FOR SOURCE CODES

that X (the unknown number) and Y (the number you know) differ in precisely two

positions. How many bits of information about X have you been given?

4. In Blackjack the dealer starts by

dealing 2 cards each to himself and his opponent:

one face down, one face up. After you look at your face-down card, you know a total

of three cards. Assuming this was the ﬁrst hand played from a new deck, how many

bits of information do you have about the dealer’s face down card after having seen

three cards?

5. The following table shows the under

graduate and MEng enrollments for the School

of Engineering:

Course (Department) # of students % of total

I (Civil & Env.)

(Mech. Eng.)

III

(Mat. Sci.)

VI (EECS)

X (Chem. Eng.)

XVI (Aero & Astro)

Total

121

389

127

645

237

198

1717

23%

38%

13%

12%

100%

(a) When you learn a randomly

chosen engineering student’s department you get

some number of bits of information. For which student department do you get

the least amount of information?

(b) After studying Huffman codes in

the next chapter, design a Huffman code to

encode the departments of randomly chosen groups of students. Show your

Huffman tree and give the code for each course.

send messages containing only the encodings of the de-

partments for each student in groups of 100 randomly chosen students, what is

the average length of such messages?

6. You’re playing an online card

game that uses a deck of 100 cards containing 3 Aces,

7 Kings, 25 Queens, 31 Jacks and 34 Tens. In each round of the game the cards are

shufﬂed, you make a bet about what type of card will be drawn, then a single card

is drawn and the winners are paid off. The drawn card is reinserted into the deck

before the next round begins.

(a) How much information do you r

eceive when told that a Queen has been drawn

during the current round?

(b) Give a numeric expression for

the information content received when learning

about the outcome of a round.

codes in the next chapter, construct a variable-

length Huffman encoding that minimizes the length of messages that report the

outcome of a sequence of rounds. The outcome of a single round is encoded as

A (ace), K (king), Q (queen), J (jack) or X (ten). Specify your encoding for each

of A, K, Q, J and X.

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