## SP513E - Classical Channel Coding

### Objectifs

#### Objectif général :

Two main general objectives are pursued in this course.

First, the students should be familiar with the fundamentals of information theory field and should understand the aim of channel coding and its limits.

Second, the students should know the most important classic channel codes and their decoding methods. Moreover, they should also be able not only to evaluate the performances of a code but also to compare different codes.

#### Objectifs détaillés :

First, the students should perfectly know the scheme of the digital communication chain and should be able to provide a clear definition of the function of each block constituting the chain. Moreover, they should perfectly understand the aim of channel coding.

Second, the students should know the fundamentals of the information theory field. More specifically, the students should be perfectly acquainted with the entropy of a random source, the mutual information between two random variables, channel capacity, reliable communication and noisy channel coding theorem. Moreover, the different types of propagations channels should be known and for which analysis purpose is each one used. Finally, the students should be able to determine the demodulation performance bounds of a communication signal from its implemented channel code, modulation, etc.

Third, the students should be able to classify the two main families’ types of channel codes, block linear channel codes and convolutional codes, and they should be able to define the main characteristics of a channel code, detection capability, correction capability, minimum distance and code rate. Finally, the student should be able to differentiate classic channel codes from modern channel codes from their decoding methods.

Fourth, the students should perfectly master the basis of linear block channel codes. They should be able to define the generator matrix, parity check matrix, syndrome, etc, of any block linear channel code. Moreover, they should be able to apply the standard array and syndrome decoding method and determine its performance.

Fifth, the students should know which the special characteristics of a cyclic channel code are. Moreover, they should master the implementation of two specificl cyclic channel codes: BCH and Reed-Solomon. They should be able to generate these codes from the communication signal needs and they should be able to decode them and provide their decoding performance.

Sixth, the student should perfectly master the basis of convolutional codes. They should be able to determine the tree diagram, state diagram, trellis diagram and the channel encoder block of a convolutional channel code. Moreover, the students should be able to determine the channel code transfer function and determine the channel code performance from the transfer function. Finally, the students must completely master the Viterbi decoding algorithm.

Seventh and last, the student should understand the notion of concatenated channel codes.

Planning:

1. An introduction to channel coding

a. Digital Communication chain

b. Aim of channel coding

2. Information theory

a. Fundamentals

b. Channels models and channel capacity

3. Channel coding

a. Definition

b. Classification

4. General Linear Block Channel Codes

a. Fundamentals

b. Decoding method

5. Cyclic Channel Codes

a. Fundamentals

b. BCH codes

c. Reed-Solomon codes

6. Convolutional Channel Codes

a. Fundamentals

b. Viterbi algorithm

7. Concatenated Codes

### Place dans le cursus

Cours n°1, Cours n°2, Cours n°3, Cours n°4, Cours n°5, TD n°1, Cours n°6, TD n°2

#### Volume horaire (h)

- Travaux Dirigés : 4h
- Cours Magistraux : 12h

### En bref

Crédits ECTS : Cf UE

Nombre d'heures 16

Langue d'enseignement

Anglais