List Decoding of Error-Correcting Codes (Winning Thesis of the 2002 ACM Doctoral Dissertation Competition)

1 Introduction.- 1 Introduction.- 2 Preliminaries and Monograph Structure.- I Combinatorial Bounds.- 3 Johnson-Type Bounds and Applications to List Decoding.- 4 Limits to List Decodability.- 5 List Decodability Vs. Rate.- II Code Constructions and Algorithms.- 6 Reed-Solomon and Algebraic-Geometric Codes.- 7 A Unified Framework for List Decoding of Algebraic Codes.- 8 List Decoding of Concatenated Codes.- 9 New, Expander-Based List Decodable Codes.- 10 List Decoding from Erasures.- III Applications.- Interlude.- III Applications.- 11 Linear-Time Codes for Unique Decoding.- 12 Sample Applications Outside Coding Theory.- 13 Concluding Remarks.- A GMD Decoding of Concatenated Codes.