Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
List decoding: algorithms and applications
ACM SIGACT News
List Decoding of Error-Correcting Codes: Winning Thesis of the 2002 ACM Doctoral Dissertation Competition (Lecture Notes in Computer Science)
Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Explicit capacity-achieving list-decodable codes
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Correlated Algebraic-Geometric Codes: Improved List Decoding over Bounded Alphabets
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Concatenated codes can achieve list-decoding capacity
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
List decoding and property testing of error-correcting codes
List decoding and property testing of error-correcting codes
List decoding and pseudorandom constructions
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Linear-time encodable/decodable codes with near-optimal rate
IEEE Transactions on Information Theory
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Under the notion of list decoding, the decoder is allowed to output a small list of codeword such that the transmitted codeword is present in the list. Even though combinatorial limitations on list decoding had been known since the 1970's, there was essentially no algorithmic progress till the breakthrough works of Sudan [14] and Guruswami-Sudan [11] in the mid to late 1990's. There was again a lull in algorithmic progress till a couple of recent papers [12, 8] closed the gap in our knowledge about combinatorial and algorithmic limitations of list decoding (for codes over large alphabets). This article surveys these latter algorithmic progress.