# Error Control Coding

## Om kursen

The emphasis will be on classical channel coding theory (Galois field algebra, block codes, convolutional codes), plus an introduction to iterative decoding (with applications to turbo and LDPC codes).

Aim
Error-control coding is the science of adding redundancy to a digital signal, with the purpose of detecting if any bits have been corrupted after transmission on a communication link, and possibly to correct those bits. This course provides students with the theoretical and practical tools to understand, analyse and apply error-control codes. The course is mathematically advanced and is studied jointly by Master's and Ph.D. students.

Learning outcomes
After completing the course, the students should be able to:
• define common families of block codes (Hamming, BCH, Reed-Solomon, LDPC) and analyse their properties
• explain the relations between minimum distance, error-correcting and error-detecting capability, bit-error rate and coding gain
• apply linear algebra and finite fields to design codes, encoders and decoders
• calculate the minimum free distance of an arbitrary convolutional code
• apply the Viterbi algorithm to decode convolutional codes
• describe the principles of iterative decoding and EXIT charts
• choose a code family, code parameters and a decoding method to fulfill given requirements on error-correcting capability and complexity
• implement an encoder/decoder pair and evaluate its performance by simulations
• independently identify relevant research articles and use these to learn a selected research topic
• prepare and give a presentation matched to the audience's pre-knowledge, while keeping time limits, crediting and referencing other researchers and answering questions in a professional manner
Contents
Channel coding principles
• Finite field algebra
• Block codes
• Convolutional codes
• Concatenated codes
• Hard and soft decoding
• Iterative decoding and iteratively decodable codes
Organisation
The course comprises homework, about 8 group meetings and one research seminar per student, all of them mandatory. The homework assignments consist of reading (and understanding!) a certain section of the book and solving problems. The purpose of the group meetings is to discuss parts of the text that might need clarification and to compare problem solutions. There are no lectures or exercises.

The course is concluded by a seminar series, in which each student gives a presentation in a format similar to a conference session. The course is given every second year, in year 2008, 2010,...

Prerequisites
Courses in linear algebra and mathematical statistics are mandatory. Basic knowledge of digital communications is an advantage but not required.

Examination
The examination is a continuous process throughout the course. The assessment is based on activity at group meetings, solutions of homework and the seminar presentation. There is no written examination. Grades are pass/fail only.

## Mer information

Alexandre Graell
Telephone: 031-772 1753
E-mail: alexandre.graell@chalmers.se

## Kurslitteratur

Shu Lin and Daniel J. Costello, Jr., *Error Control Coding, 2nd edition, Pearson Education/Prentice Hall, 2004, ISBN 013-017973-6 or 013-042672-5.

## Föreläsare

Alexandre Graell i Amat E-mail: alexandre.graell@chalmers.se