Learning objectives
Instruction aim
1) Knowledge and understanding
The course presents the basic elements for the analysis and design of error control coding schemes, and their use in digital systems and communications.
2) Applying knowledge and understanding
Students learn to analyze and design, also accounting for possible implementation constraints:
- error control schemes
- digital communication systems.
Prerequisites
Prerequisites
Suggested: Signal Theory, Telecommunication Systems, Information Transmission.
Course unit content
Outline
Error control coding. Automatic repeat request (ARQ). Forward error correction (FEC). Block codes. Convolutional codes.
Full programme
Detailed outline
Schemes for error detection and correction - Schemes for automatic repeat request (ARQ). Schemes for forward error correction (FEC). Repetition codes. Parity check codes. Coding gain and cost. Bit interleaving. Code vectors and Hamming distance. Error control properties of a given code. Code rate and redundancy. Performance analysis of FEC systems. ARQ retransmission procedures. Performance analysis of ARQ systems. Outline of hybrid ARQ systems.
Block codes - Linear systematic block codes. Matrix representation of a linear block code. Hamming codes. Maximum likelihood syndrom decoding. Example decoding of a Hamming (7,4) code. Cyclic codes. Cyclic shifts and code polynomials. Generator polynomial of a cyclic code. Systematic codes. Coding and decoding as the remainder of polynomial divisions. Example of a Hamming (7,4) code. Circuit implementation of encoders and decoders for cyclic codes. Outline of BCH and CRC codes. Outline of M-ary and Reed-Solomon codes.
Convolutional codes - Tree, trellis and state diagrams of convolutional codes. Gnerator polynomials. Free distance. Transfer function and weight distribution of a convolutional code. Estimation of error probability. Coding gain. Decoding of convolutional codes. Viterbi decoding. Sequential decoding. Outline of majority logic decoding. Outline of punctured codes. Soft-decision decoding. Examples of convolutional codes and their performance.
Further topics - Punctured codes. Concatenated codes. Convolutional codes with feedback (recursive). Outline of turbo codes.
Bibliography
Reference textbook
A. Bruce Carlson, Paul B. Crilly: Communication systems, 5th edition, McGraw Hill, 2010.
Teaching methods
Instruction methods
The course is organized in lectures and exercise sessions. Homework assignments complement classroom activity.
Assessment methods and criteria
Evaluation methods
Evaluation comprehensively based on:
- level of (active and regular) attendance of lecture and exercise sessions
- written final test
- final oral test including first and second modules, unless exempted for good level of (active and regular) course attendance.
Remedial evaluation based on written examination and oral examination (discouraged option).
Other information
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2030 agenda goals for sustainable development
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