This project has been realised during my two-year CPGE class in France and was part of the "Grandes écoles" competitive exam of 2023 where it received a 17/20 grade.
This project is aimed towards studying the main principles of error-correcting codes through the linear algebra spectrum, and coding a simulation of the Hamming code.
- MCOT, it introduces the subject and develops the goals of the presentation, it contains a bibliography.
- Presentation, used as a support during the assessment of the exam.
Made with python, it simulates the emission and reception of a message, while using the Hamming code (7,4) principle to avoid some perturbations.
- The input is an alphanumeric message, converted in binary in ASCII.
- It is then converted in "analogic" (see graphs below), to simulate an over-the-air transmission.
- Perturbations are applied on this signal 1.
- The signal is converted back in binary.
- The Hamming code principle is applied.
- The message is converted in alphanumeric characters.
The input at line 185 can be replaced with any string.
Input : "Hello, World !"
Message initial : Hello, World !
Message converti en binaire : 0100100001100101011011000110110001101111001011000010000001010111011011110111001001101100011001000010000000100001
Message encodé : 0100101100011001101100101010011011011000110110110110001101101101111111001001111000110010011000000001010100111001011011011111110111001001001101101101100011011011001001010010011000000000100110001111
Message perturbé numérique : 0100101000011001101000101010011001011000110111110110001101101101110111001001111001110000011000000001010100101001011011010111110111001000001111101101100011011011001001000010011100000000000110001111
Message corrigé 0100100001100101011011000110110001101111001011000010000001010111011011110111001001101100011001000010000000100001
Message final : Hello, World !The following images are produced :
Footnotes
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The perturbations used are bits inversions and a white noise applied to the "analogic" signal. ↩