Essential Coding Theory

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