In the first half, this course reviews the fundamentals of information theory learned in undergraduate course, and teaches some information measures and their properties. Then, picking up general information source and channel as the most general source and channel without assuming stationarity nor ergodicity, source and channel coding theorems are demonstrated. As applications of these theorems, topics include the relation between source coding and random number generation, rate-distortion theory, and multi-terminal information theory.
In the second half, after reviewing the fundamentals of coding theory, compare the computation complexity required for encoding and decoding, to understand the importance of efficient error correction. Students learn the definition and analysis of sum-product algorithm and low-density parity-check codes and how the algorithm is derived. As applications, students will learn the design method of capacity achieving codes, coding for memory channels, compression, and packet loss correction.
By the end of this course, students will be able to
1) Understand various information measures and their properties, and use mathematical models for information communication networks.
2) Understand the information for the general source and channel, and acquire the basic methods to use them.
3) Understand the theory of error-correcting code which can be implemented with low computational complexity, and acquire its design method.
information theory, general source, general channel, source coding theorem, channel coding theorem, random number generation, rate-distortion theory, multi-terminal information theory, sum-product algorithm, low-density parity-check code, performance analysis method, coding for channel with memory, data compression, correction of packet loss
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
The instructor explains certain topics in every class.
|Course schedule||Required learning|
|Class 1||Introduction of information theory||Review information theory.|
|Class 2||Various information measures||Explain various information measures and its properties.|
|Class 3||Coding problem for general information sources||Explain the general source and the source coding theorem.|
|Class 4||Random number generation||Explain the random number generation problem and its fundamental theorem.|
|Class 5||Coding problem for general channle||Explain the general channel and the channel coding theorem.|
|Class 6||Rate-distortion theory||Explain the definition of rate-distortion function and its representation.|
|Class 7||Multi-terminal information theory||Explain correlated sources and multiple-access channel, and their coding theorems.|
|Class 8||Introduction of coding theory|
|Class 9||Decoding and computational complexity, sum-product algorithm|
|Class 10||Decoding linear codes|
|Class 11||Definition of low-density parity-check codes|
|Class 12||Properties of low-density parity-check codes|
|Class 13||Design method of capacity achieving codes|
|Class 14||Coding memory channels and compression|
|Class 15||Correction of packet loss and rate-less codes|
Course materials are provided.
T. S. Han, Information Spectrum Method in Information Theory, Springer, 2003.
T. Richardson and R. Urbanke, Modern Coding Theory, Cambridge University Press, 2008.
Final exam : 70%
Homework assignments : 30%