Information Theory
TeachersMORI, Takuo
Grade, SemesterYear 3 1st semest [Department of Information and Electronic Engineering, Faculty of Science and Engineering]
CategorySpecial Subjects
Elective, CreditsElective 2credit
 Syllabus Number3C224

Course Description

In this course, students learn the information theory that is a theory of digital communications and storage which supports the information society of nowadays.

Information theory is a theory that deals with the theoretical bounds of encoding and concrete encoding algorithms. In this theory, encodings are classified into source coding to increase the efficiency of communications, and into channel coding to increase the reliability of communications.

In this course, students aim at being possible to discuss theoretically the infimum of the average code length of source coding, and the supremum of the code rate of channel coding without errors, giving the probabilistic model of a source or a channel. In addition, students aim at being able to decide which encoding algorithm is effective for a given purpose concretely.

Moreover, this course deals with analog source/channel, analog-to-digital or digital-to-analog conversion, the sampling theory, character encoding, the relation between information theory and cryptology.

Students acquire skills related to the diplomatic policy, DP4C.

Course Objectives

The goal of this course is that students master the following abilities;

Students can explain the relation of system model of communication, noise source, source coding and channel coding.
Students can explain the purpose of source/channel coding, the meanings of Shannon's source coding theorem and Shannon's noisy-channel coding theorem.
Students can explain the model of the memoryless source, source with memory, the memoryless channel, the burst channel.
Students can explain features which source coding algorithms should have by using code tree.
Students can process basic source coding/encoding algorithm as for basic source coding algorithms.
Students can explain the amount of information, entropy, mutual information, and can compute those values
as for some basic sources.
Students can explain the meanings of channel capacity, and compute that as for some basic channels.
Students can process basic binary channel coding algorithms as for some basic channel coding algorithms.
Students understand the sampling theorem and can obtain appropriate sampling frequency given maximum frequency of a signal.
Students can explain the necessity of character codes and the features of representative character codes.

Grading Policy

Grading policy:
Midterm report(50%), Examination(50%).

The way of feedback;
Answers for questions or feedback for the contents of class, worksheets, and examination will be given in a class, through LMS or during office hours.

Textbook and Reference

KindTitleAuthorPublisher
Textbook情報理論 改訂2版今井秀樹著オーム社、ISBN-13: 978-4274223259
References

Requirements(Assignments)

Before each class, materials related to the class will be published through LMS. Students should download them to their own devices or print them to make it possible to refer to or to take notes.
Students should read these materials and grasp what they do not understand and they understand in an hour.
After each class, student should review the class through tests on the LMS in half an hour.

Note

Students can hardly earn credits not submitting the mid-term report. Thus, it is expected students to observe the deadline.
As for the self-learning support students are expected to utilize materials, such as slides, handouts and quizzes on the LMS.

Before taking this course, students should take the following courses;
Mathematical Logic, Linear Algebra, Discrete Mathematics, Applied Mathematics, Mathematical Statics, Digital Image Processing.

At the same semester with this course, students should take Multimedia Information Processing.
After taking this course, students should take the following courses;
Introduction to Stochastic Processes, Information Security, Communication, Communication Systems.

If a student has a question on quizzes or mid-term report or examinations, ask the question in the class or in office hours or through LMS.
This course is a required course, and relates to the mid term 4-1 of the attaining targets for learning and educating, in the JABEE program.

Schedule

1Introduction
Problems in the Information Theory
2Review of Probability Theory
Modeling digital information sources
3Modeling digital channels
4Analog information sources, channels
Fourier series expansion, Sampling Theory, Analog to Digital Conversion, Character codes
5Source coding and its bound
Basic concepts in source coding, the bound of average code length
6Source coding and its bound
Huffman coding, extended information source, block coding, Shannon's source coding theorem
7Entropy of basic information source/Source coding1
Entropy of independently, identically distributed(i.i.d.) information source, Entropy of Markov information source, Huffman Block Coding, Run-length Huffman Coding
8Source coding 2/Entropy and Mutual Information, Arithmetic coding
9Entropy, distortion
10Channel coding and its bound
Channel Capacity, Basic concepts in channel coding, noisy channel coding theorem
11Channel Coding 1
Single error detection/correction
12Channel Coding 2
Cyclic codes

13Channel Coding 3
Decoding of cyclic codes, Cyclic Redundancy Code(CRC), Cyclic Hamming Codes
14Analog information source and analog channel, Information Theory and Cryptology
15Summary and examination