List Decoding in Average-Case Complexity and Pseudorandomness

This is a brief survey into the applications of list decoding in complexity theory, specifically in relating the worst-case and average-case complexity of computational problems, and in construction of pseudorandom generators. Since we do not have space for full proofs, the aim is to give a flavor of the utility of list decoding in these settings together with pointers to where further details can be found.

[1]  Madhu Sudan,et al.  Decoding of Reed Solomon Codes beyond the Error-Correction Bound , 1997, J. Complex..

[2]  Venkatesan Guruswami,et al.  List decoding algorithms for certain concatenated codes , 2000, STOC '00.

[3]  Christopher Umans,et al.  Simple extractors for all min-entropies and a new pseudorandom generator , 2005, JACM.

[4]  Jin-Yi Cai,et al.  On the Hardness of Permanent , 1999, STACS.

[5]  Richard J. Lipton,et al.  New Directions In Testing , 1989, Distributed Computing And Cryptography.

[6]  Luca Trevisan,et al.  Pseudorandom generators without the XOR Lemma , 1999, Electron. Colloquium Comput. Complex..

[7]  Venkatesan Guruswami,et al.  List decoding of error correcting codes , 2001 .

[8]  Madhu Sudan.  List decoding: algorithms and applications , 2000, SIGA.

[9]  Christopher Umans,et al.  Simple extractors for all min-entropies and a new pseudo-random generator , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[10]  Noam Nisan,et al.  Hardness vs. randomness , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[11]  Luca Trevisan,et al.  Some Applications of Coding Theory in Computational Complexity , 2004, Electron. Colloquium Comput. Complex..

[12]  Venkatesan Guruswami,et al.  Improved decoding of Reed-Solomon and algebraic-geometry codes , 1999, IEEE Trans. Inf. Theory.

[13]  Amnon Ta-Shma,et al.  Extractors from Reed-Muller codes , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[14]  Venkatesan Guruswami,et al.  Improved decoding of Reed-Solomon and algebraic-geometric codes , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).