Channel Coding
| Lecturer (assistant) | |
|---|---|
| Number | 0000004503 |
| Type | lecture with integrated exercises |
| Duration | 5 SWS |
| Term | Summer semester 2026 |
| Language of instruction | English |
| Position within curricula | See TUMonline |
| Dates | See TUMonline |
Admission information
Description
This course deals with modern coding approaches for coding and storage. No previous knowledge of channel coding is required.
- Applications of Channel Coding
- Channel Coding Principles:
Channel Models, Decoding Principles, Hamming Metric
- Finite Fields:
Groups, Fields, Prime Fields, Extension Fields, Vector Spaces
- Linear Block Codes:
Definition, Encoding, Coset Decoding, Bounds (Hamming Bound, Singleton Bound, Gilbert- Varshamov Bound), Hamming Codes, Perfect Codes
- Reed-Solomon Codes:
MDS Codes, Definition, Key Equation, Unique Decoding, List Decoding
- BCH Codes:
Minimal Polynomials, Generator and Parity-Check Polynomial, BCH Bound, Efficient Decoding
- Convolutional Codes:
State Diagram, Shift Register, Viterbi Decoding
- Reed-Muller Codes:
Definition, Simplex Code, Plotkin Construction
- Concatenated Codes:
Basic Concepts
- Applications of Channel Coding
- Channel Coding Principles:
Channel Models, Decoding Principles, Hamming Metric
- Finite Fields:
Groups, Fields, Prime Fields, Extension Fields, Vector Spaces
- Linear Block Codes:
Definition, Encoding, Coset Decoding, Bounds (Hamming Bound, Singleton Bound, Gilbert- Varshamov Bound), Hamming Codes, Perfect Codes
- Reed-Solomon Codes:
MDS Codes, Definition, Key Equation, Unique Decoding, List Decoding
- BCH Codes:
Minimal Polynomials, Generator and Parity-Check Polynomial, BCH Bound, Efficient Decoding
- Convolutional Codes:
State Diagram, Shift Register, Viterbi Decoding
- Reed-Muller Codes:
Definition, Simplex Code, Plotkin Construction
- Concatenated Codes:
Basic Concepts
Prerequisites
- Mathematical basics (linear algebra)
Teaching and learning methods
Lecture: The fundamental theoretical contents are presented in the lecture (by a slide presentation and on the black board) and illustrated with examples. Students are encouraged to ask questions and discuss the topics of the lecture.
Tutorial: In an accompanying tutorial, the contents of the lecture are applied to examples.
Tutorial: In an accompanying tutorial, the contents of the lecture are applied to examples.