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This course introduces the theory of error-correcting codes to computer scientists.
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English
English [CC]
FREE
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Description
This theory, dating back to the works of Shannon and Hamming from the late 40’s, overflows with theorems, techniques, and notions of interest to theoretical computer scientists. The course will focus on results of asymptotic and algorithmic significance. Principal topics include:
- Construction and existence results for error-correcting codes.
- Limitations on the combinatorial performance of error-correcting codes.
- Decoding algorithms.
- Applications in computer science.
Course content
- Introduction Unlimited
- Shannon’s Theory of Information Unlimited
- Shannon Theory vs. Hamming Theory Unlimited
- Asymptotically Good Codes Unlimited
- Algebraic Codes: Reed-Solomon, Reed-Muller, Hadamard Unlimited
- Decoding Reed-Solomon Codes – The Welch-Berlekamp Algorithm Unlimited
- Abstracting the RS Decoding Algorithm Unlimited
- List Decoding of Reed-Solomon Codes Unlimited
- Concatenated Codes and Decoding Unlimited
- List Decoding versus Rate versus Distance Unlimited
- The Gap between Constructive and Existential Results in Coding Theory Unlimited
- Algebraic Geometry Codes Unlimited
- Linear-time Decodable Codes Unlimited
- Linear-time Encodable and Decodable Codes Unlimited
- Spielman Codes and Decoding Unlimited
- Expander Codes – the ABNNR Construction Unlimited
- Computation and Randomness Unlimited
- Extraction of Randomness Unlimited
- Ta-Shma-Zuckerman-Safra Extractor, Guruswami-codes Unlimited
- Ta-Shma-Zuckerman-Safra Extractor (cont.) Unlimited
- Expanders, Eigenvalues and the Zig-Zag Product Unlimited
Instructor
Massachusetts Institute of Technology
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1916
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