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Essential Coding Theory >> Content Detail



Calendar / Schedule



Calendar

lec #TOPICSKEY DATES
1
  • Introduction
  • Hamming Space, Distance, Code
  • Applications
Problem set 1 out
2
  • Shannon's Theory of Information
  • The Coding Theorem
  • Its Converse
3
  • Shannon Theory vs. Hamming Theory
  • Our Goals
  • Tools
  • Linear Codes
Problem set 1, part I due
4
  • Asymptotically Good Codes
  • Projection and Volume Bound
  • Random Codes
5
  • Algebraic Codes: Reed-Solomon, Reed-Muller, Hadamard
  • Plotkin Bound
Problem set 1, part II due
6Decoding Reed-Solomon Codes - The Welch-Berlekamp Algorithm
7
  • Abstracting the RS Decoding Algorithm
  • Beyond Unique Decoding
8List Decoding of Reed-Solomon CodesProblem set 2 out
9
  • Concatenated Codes and Decoding
  • Justesen Codes
Problem set 2 due
10Achieving Shannon Capacity in Polytime with Concatenated Codes
11List Decoding versus Rate versus Distance
12The Gap between Constructive and Existential Results in Coding Theory
13Algebraic Geometry Codes
14Linear-time Decodable Codes
15Linear-time Encodable and Decodable Codes
16
  • Spielman Codes and Decoding
  • Correcting Random Error in Linear Time, Expander Codes (Type II)
17Expander Codes - the ABNNR Construction
18Computation and Randomness: Pseudo-randomness, Limited Independence, Small-bias Spaces
19Extraction of Randomness, Min-entropy, Statistical Difference, Extractors and Codes
20Trevisan's Extractor
21Ta-Shma-Zuckerman-Safra Extractor, Guruswami-codes
22Ta-Shma-Zuckerman-Safra Extractor (cont.)
23Expanders, Eigenvalues and the Zig-Zag Product
24TBA
25TBA

 








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