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227-0418-00L 6 Credits BSC , DR , MSC D-ERDW , D-MATH , D-MAVT , D-PHYS , D-ITET

Algebra and Error Correcting Codes

Lecturers & Examiners: Prof. Dr. Hans-Andrea Loeliger
VVZ CR 4.2

Last Updated: 2026-06-03 00:14:16

Abstract

The course is an introduction to error correcting codes covering both classical algebraic codes and modern iterative decoding. The course includes a self-contained introduction of the pertinent basics of "abstract" algebra.

Objective

The course is an introduction to error correcting codes covering both classical algebraic codes and modern iterative decoding. The course includes a self-contained introduction of the pertinent basics of "abstract" algebra.

Content

Error correcting codes: coding and modulation, linear codes, Hamming space codes, Euclidean space codes, trellises and Viterbi decoding, convolutional codes, factor graphs and message passing algorithms, low-density parity check codes, turbo codes, polar codes, Reed-Solomon codes. Algebra: groups, rings, homomorphisms, quotient groups, ideals, finite fields, vector spaces, polynomials.

Resources

Lecture Notes

Lecture Notes (english)

Learning Materials (Links)

General Information

Language
English
Levels
BSC , DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture with exercise Algebra and Error Correcting Codes
  • Tue 14:15-18:00 (ETZ E 9)
4 h weekly

Offered In

  • Computational Science and Engineering Bachelor
    • Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
  • Computational Science and Engineering Master
    • Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed. All courses listed as core courses (not electives) for one of the following ETH MSc programmes, MSc Statistics, MSc Physics, MSc Computer Science, MSc (Applied) Mathematics, MSc Neural Systems and Computation, MSc Robotics, Systems, and Control, MSc Data Science, MSc Electrical Engineering and Information Technology, can be taken as an elective course in the MSc CSE without prior permission.)
  • Mathematics Master
    • Application Area (Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area. Credits from other application areas cannot be recognised for further application areas.)
  • Electrical Engineering and Information Technology Master
    • 01 - Courses of specializations
      • Track: Communication (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Communication", see . The individual study plan is subject to the tutor's approval.)
        • Core Courses (These core courses are particularly recommended for the field of "Communication". You may choose core courses form other fields in agreement with your tutor. A minimum of 24 credits must be obtained from core courses during the MSc EEIT.)
      • Track: Signal Processing and Machine Learning (The core courses and specialization courses below are a selection for students who wish to specialize in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
        • Specialization Courses (These specialization courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. Semester / Research Projects are not allowed in this category. A minimum of 40 credits must be obtained from specialization courses during the MSc EEIT.)
  • Doctorate Information Technology and Electrical Engineering (A minimum of 12 ECTS credit points must be obtained during doctoral studies (also see sub-categories for details) More Information at )
    • Subject Specialisation (The courses on offer below are but a small selection out of a much larger available number of courses. Please discuss your course selection with your PhD supervisor.)
  • Quantum Engineering Master
    • Core Courses (A minimum of 24 credits must be obtained from core courses during the MSc QE, course selection is subject to the tutor's agreement.)
      • Engineering Core Courses (These core courses target students with a physics background and all those who need additional engineering foundations.)
  • Space Systems Master