Calendar

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

Course Info

Learning Resource Types

notes Lecture Notes