Unit 8: Error-Correcting Codes

This is an archived version of this module from Fall 2022.
Click here for the current iteration.

This unit covers techniques to detect and correct errors in a communication channel:

• code-distance lower bounds
• parity bits
• Hamming codes

Learning outcomes

1. Understand the context of error-prone communication.
2. Understand concepts of error-detecting codes and error-correcting codes.
3. Know and understand the terminology of block codes.
4. Know and understand Hamming codes, in particular 4+3 Hamming code.
5. Reason about the suitability of a code for an application.

Material

• slides

• lecture notes

• Video 8-1 (2022-12-07): §8.1 Error correcting codes introduction
  This is an archive video covering the same material; audio in recording was broken.

• Video 8-2 (2022-12-07): §8.2 Lower bounds for error correcting codes
  This is an archive video covering the same material; audio in recording was broken.

• Video 8-3 (2022-12-07): §8.3 Hamming codes introduction
  This is an archive video covering the same material; audio in recording was broken.

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Further reading and sources

The exposition is based on Leszek Gąsieniec’s material from previous iterations of COMP526 and the following great book on codes (and much more):

• MacKay: Information Theory, Inference, and Learning Algorithms (2003), Cambridge University Press

Hamming codes a very nicely explained by 3Blue1Brown:

• Hamming codes and error correction

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Unit 7  ⋅  Syllabus  ⋅  Unit 9