Error Control Coding

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Advanced Image Processing

Course Contents

Basics. Channel capacity. Classical coding and decoding techniques. Multilevel coding, multistage decoding. Concatenated codes. Soft decision decoding algorithms: MAP, log-MAP, SOVA, parallel concatenated (turbo) codes. Iterative decoding. Interleavers. Code design and error performance analysis. EXIT diagrams. Turbo-like codes. Serial cocatenated codes. Hybrid concatenated codes. Applications of serial and paralel concatenated codes. Bandwidth and power efficient concatenated codes. Multilevel concatenated codes. Low density parity check codes. Message transfer algorithms. Serial and parallel concatenated space-time codes. Coding for multi input – multi output channels.

Weekly Schedule

1) Block codes: Introduction to block codes, Hamming codes.
2) Yumuşak kararı kod çözme, Otomatik-tekrar-isteme algoritması.
3) Linear codes: Definition of linear codes, Generator matrices, Parity-check matrices.
4) Error syndromes, Error detection and correction, Shortened and extended linear codes
5) Cyclic codes: Definition of cyclic codes, Polynomials, Generator polynomials, Encoding cyclic codes
6) Decoding cyclic codes, Factors of xn+l, Parity-check polynomials, Dual cyclic codes, Generator and parity-check matrices of cyclic codes
7) Linear-feedback shift registers for encoding and decoding cyclic codes: Linear-feedback shift registers, The polynomial-division register, Registers for encoding.
8) midterm exam
9) Registers for error detection and correction, The Meggitt decoder.
10) Linear algebra: Sets, Groups, Fields, Vector spaces, Matrices, Linear codes as vector spaces, Dual codes.
11) Galois fields: Roots of equations, The Galors field GF(23), The fields GF(24) and GF(25), Primitive field elements.
12) Irreducible and primitive polynomials, Minimal polynomials, Solution of equations in GF(24) and GF(23).
13) Bose-Chaudhuri-Hocquenghem codes: Definition and construction of binary BCH codes, Error syndromes in finite fields, Decoding SEC and DEC binary BCH codes, The error-location polynomial.
14) The Peterson-Gorenstein-Zierler decoder, Reed-Solomon codes, The Berlekamp algorithm, The error-evaluator polynomial.
15) Convolution codes: Convolution, Encoding convolutional codes, Generator matrices for convolutional codes, Generator polynomials for convolutional codes, Graphical representation of convolutional codes, The Viterbi decoder.
16) Final exam

Recommended or Required Reading

1- 1- Modern Digital and Analog Communication Systems, Bhagwandas Pannalal LATHI, Holt, Rinehart and Winston, 1989 2- Fundamentals Of Communication Systems, John G. Proakis, Masoud Salehi, Prentice Hall, 2004 3- Analog and Digital Comminication, Hwei P. Hsu, Schaum's Outline Series, McGraw-Hill, 1993 4- Introduction to Error Control Codes Salvatore Gravano 2001 Oxford University Press ISBN 0-19-856231-4

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer
3) Discussion
4) Group Study
5) Case Study
6) Self Study

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	40%
Number Percentage Semester Studies Midterm Examination 1 70% Quiz 1 30%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required