Introduction to Coding Theory (lecture 9): generalized Reed-Solomon codes; GRS codes as cyclic codes.

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Klipi teostus: Mirjam Paales 22.04.2014 2512 vaatamist Arvutiteadus


Lecture 9: generalized Reed-Solomon codes; GRS codes as cyclic codes.

Seotud videod

Introduction to Coding Theory (tutorial 1): introduction into the finite fields
14.02.14
Introduction to Coding Theory (lecture 3): Shannon's theorems; correction and detection of errors; correction of erasures.
25.02.14
Introduction to Coding Theory (lecture 4): linear codes; generator matrix; parity-check matrix.
04.03.14
Introduction to Coding Theory (tutorial 3): Euclid's algorithm.

07.03.14
Introduction to Coding Theory (lecture 5): parity-check matrix; dual code; Hamming code.
11.03.14
Introduction to Coding Theory (tutorial 4): construction of extension fields.

14.03.14
Introduction to Coding Theory (tutorial 5): properties of linear codes.
21.03.14
Introduction to Coding Theory (lecture 6): extended Hamming code; concatenated code.
25.03.14
Introduction to Coding Theory (tutorial 6): decoding of linear codes; Reed-Muller codes.
28.03.14
Introduction to Coding Theory (lecture 7:) Singleton bound; sphere-packing bound.
01.04.14
Introduction to Coding Theory (tutorial 7): sphere-packing bound; Plotkin bound. 
04.04.14
Introduction to Coding Theory (lecture 8): asymptotic bounds; Gilbert-Varshamov bound, Reed-Solomon codes; Vandermonde matrix.
08.04.14
Introduction to Coding Theory (tutorial 9): information-theoretic security via coset coding. 

25.04.14
Introduction to Coding Theory (lecture 10): Shamir's secret sharing scheme: coding theory point of view.
29.04.14
Introduction to Coding Theory (lecture 11): decoding of GRS codes; key equation. 
06.05.14
Introduction to Coding Theory (tutorial 10): Peterson-Gorenstein-Zierler decoding algorithm

09.05.14
Introduction to Coding Theory (tutorial 11): decoding of Reed-Solomon codes using Euclid's algorithm.

16.05.14
Introduction to Coding Theory (lecture 13): Chien's search; finding error values by using Forney's algorithm; summary of decoding of generalzied Reed-Solomon codes.
20.05.14
Introduction to Coding Theory (tutorial 12): example of decoding of generalized Reed-Solomon codes.

23.05.14
Introduction to Coding Theory (lecture 14): LDPC codes and codes built using expander graphs.
27.05.14
Introduction to Coding Theory (tutorial 13): introduction into network coding.

30.05.14
Introduction to Coding Theory (lecture 2): ML and nearest-neighbor decoding; examples of simple codes
16.02.15