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Signal and Coding for Communications (SICOM SIGMA S9) - 5PMSSCC6

  • Number of hours

    • Lectures 16.0
    • Projects 0
    • Tutorials 16.0
    • Internship 0
    • Laboratory works 0


    ECTS 2.0


Understand the main signal processing tools for digital communications.
Modeling of channel imperfections and dealing with them: OFDM, equalization, error correcting codes, MIMO techniques.
These techniques are used in mobile communication, ADSL, WIFI, ...

Contact Benoit GELLER, Jean-Marc BROSSIER



* Carrier recovery, PLL (Costas and Decision Feedback loops)
* Maximum Likelihood for phase estimation versus PLLs.
* Timing recovery.

* Zero Forcing - Wiener filters
* Inversion with basic examples.
* Stability, Causality
* Main equalization structures: FIR equalizers, Decision Feedback Equalizers (DFE).
* Adaptive equalizers - LMS approach

Multicarriers schemes OFDM.

MIMO SYSTEMS Spatial diversity

Convolutional codes and turbo codes
* VITERBI for coding and equalization.

  • Equalization and synchronization
    • Lecture 1 - Notion of adaptive algorithm. Application examples (mean estimation, identification, equalization).
    • Lecture 2 - Baseband carrier recovery - adaptive approach.
    • Lecture 3 - Equalization by inverse filtering. Examples: inversion of a RIF filter with 2 coefficients, inversion of the discrete RC filter, inversion of a rational fraction.
    • Lecture 4 - Equalization by Wiener filtering, LMS algorithm.
    • Lecture 5 - Other structures (linear recursive, DFE, Viterbi).
    • Lecture 6-7 - MIMO systems.
  • Error correcting codes
    • Lecture 8 - Introduction to error correcting codes. Block codes. Generator and control matrices. Syndrome decoding and the notion of complexity. Limits (information theory).
    • Lecture 9 - Introduction to algebraic coding. From linear codes to algebraic codes: necessity of finite fields. Definition of operations in a 16-element field. Implementation of the calculations. Generation of pseudorandom sequences. Application to the GPS system.
    • Lecture 10 - Introduction to Galois fields. General properties. Cyclic structure. Minimal polynomials. Application to symmetric encryption.
    • Lecture 11 - Cyclic codes. Associated registers. Applications to real telecommunications systems: protocols with retransmission.
    • Course 12 BCH codes. Peterson's algorithm. Applications to sensor networks.
    • Course 13 RS codes. Berlekamp-Massey algorithm. Applications to optical fiber networks and mass media: CD, DVD.
    • Course 14 - Convolutional codes. From block codes to convolutional codes. Viterbi (hard and soft). Applications to real systems: cellular mobile networks, Wifi, DVB, NASA codes.
    • TD 15 - Turbo codes. Flexible decoding by erasure. Application to internet. Turbo-codes. Application to the VDSL local loop.


Probability, signal processing


Session 1 :
If in-person courses : 2 hours written examination
If distant learning mandatory : homework report

Session 2 :
Oral examination (by visioconference if distant learning mandatory)

Session 1 :
Si cours en présentiel : examen écrit de 2 heures
Si cours à distance : contrôle continu (rapport à rendre)

Session 2 :
Examen oral (en présentiel ou par visioconférence si le distanciel est imposé)

Additional Information

Course list
Curriculum->Engineering degree->Semester 9
Curriculum->Double-Diploma Engineer/Master->Semester 9


  • J.-M. BROSSIER. Signal et communication numérique. Hermès 1997.
  • Gordon L. Stuber. Principles of Mobile Communication. Kluwer, 2000.