lec # | TOPICS | KEY 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 |
6 | Decoding Reed-Solomon Codes - The Welch-Berlekamp Algorithm | |
7 |
Abstracting the RS Decoding Algorithm Beyond Unique Decoding |
|
8 | List Decoding of Reed-Solomon Codes | Problem set 2 out |
9 |
Concatenated Codes and Decoding Justesen Codes |
Problem set 2 due |
10 | Achieving Shannon Capacity in Polytime with Concatenated Codes | |
11 | List Decoding versus Rate versus Distance | |
12 | The Gap between Constructive and Existential Results in Coding Theory | |
13 | Algebraic Geometry Codes | |
14 | Linear-time Decodable Codes | |
15 | Linear-time Encodable and Decodable Codes | |
16 |
Spielman Codes and Decoding Correcting Random Error in Linear Time, Expander Codes (Type II) |
|
17 | Expander Codes - the ABNNR Construction | |
18 | Computation and Randomness: Pseudo-randomness, Limited Independence, Small-bias Spaces | |
19 | Extraction of Randomness, Min-entropy, Statistical Difference, Extractors and Codes | |
20 | Trevisan's Extractor | |
21 | Ta-Shma-Zuckerman-Safra Extractor, Guruswami-codes | |
22 | Ta-Shma-Zuckerman-Safra Extractor (cont.) | |
23 | Expanders, Eigenvalues and the Zig-Zag Product | |
24 | TBA | |
25 | TBA |