Error-Correcting Codes and Coded Modulations Applied to Optical Communications

Catalogue des cours de Télécom SudParis


CSC 7413



Langue d'enseignement


Crédits ECTS


Heures programmées / Charge de travail



  • LEHMANN Frederic


- Communications, Images et Traitement de l'information


On completion of the course students should be able to:
- Parameterize an error correcting code according to Shannon’s channel coding theorem
- Implement a codec for algebraic or LDPC codes
- Evaluate the performances of error correcting codes in the context of optical communications


Course Objectives:
- Understand the basics of algebraic coding and decoding
- Understand the basics of modern coding theory and the associated probabilistic decoding
- Comprehend the performance evaluation techniques of error correcting codes
Chapter 1: Introduction to algebraic coding and finite fields (3h - lecture)
- Bloc codes: generator and parity matrices
- Syndrome decoding
- Families of algebraic block codes
Chapter 2: Finite fields
- Construction of Galois fields
- Operations in a Galois field (addition, multiplication, division)
- Minimal polynomial
Chapter 3: Algebraic codes and their decoding
- Cyclic codes and their encoding using the generating polynomial
- Classes of cyclic codes: BCH and Reed-Solomon codes
- Decoding algorithms: Peterson, Forney, Euclidian, Berlekamp-Massey
- Performance bounds
Chapter 4: Factor graphs and the sum-product algorithm
- Definition of a factor graph
- Computation of marginal probabilities using the sum-product algorithm
- Correctness of the sum-product algorithm on an acyclic graph
- Performances of the sum-product algorithm for decoding block codes
Chapter 5: LDPC codes: definition, construction and decoding
- Construction of regular LDPC codes
- Tanner graphs and the sum-product algorithm for decoding LDPC codes
- Complexity reduction techniques
Chapter 6: Performance analysis of LDPC codes
- Weight enumerating functions of ensembles of codes
- Upper bounds on the performances of ensembles of codes
- Convergence analysis of sum-product decoding (density evolution, EXIT charts)
- Codes optimization techniques for irregular and generalized LDPC codes




M1 Level course in Information Theory M1 Level course in Digital Communications


Written examination

Approches pédagogiques




Fiche mise à jour : 01/09/2015 10:35:35