On the efficiency of local decoding procedures for error-correcting codes

jkatz s. olumbia.edu. Department of Computer S ien e, Columbia University. Work supported in part by a DoD NDSEG Fellowship. y lu a s. olumbia.edu. Department of Computer S ien e, Columbia University. time (or whose reading devi e is subje t to errors). For example, the data stored in musi CDs and in CD-ROMs is en oded using Reed-Solomon odes. In appli ations to data storage (and also in appli ations to data transmission) a message is typi ally divided into small blo ks, and then ea h blo k is en oded separately. This allows eÆ ient retrieval of

[1]  V. Rich.  Personal communication , 1989, Nature.

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

[3]  Joan Feigenbaum,et al.  Hiding Instances in Multioracle Queries , 1990, STACS.

[4]  Ronitt Rubinfeld,et al.  Self-testing/correcting for polynomials and for approximate functions , 1991, STOC '91.

[5]  Leonid A. Levin,et al.  Checking computations in polylogarithmic time , 1991, STOC '91.

[6]  Noam Nisan,et al.  BPP has subexponential time simulations unlessEXPTIME has publishable proofs , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[7]  Madhu Sudan,et al.  Highly Resilient Correctors for Polynomials , 1992, Inf. Process. Lett..

[8]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[9]  Joan Feigenbaum,et al.  Random-Self-Reducibility of Complete Sets , 1993, SIAM J. Comput..

[10]  Daniel A. Spielman,et al.  Nearly-linear size holographic proofs , 1994, STOC '94.

[11]  Andris Ambainis,et al.  On Lower Bounds for the Communication Complexity of Private Information Retrieval ∗ , 2000 .

[12]  Sanjeev Arora,et al.  Probabilistic checking of proofs: a new characterization of NP , 1998, JACM.

[13]  Eyal Kushilevitz,et al.  Private information retrieval , 1998, JACM.

[14]  Carsten Lund,et al.  Proof verification and the hardness of approximation problems , 1998, JACM.

[15]  Elizabeth D Mann.  Private access to distributed information , 1998 .

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

[17]  Luca Trevisan,et al.  Pseudorandom generators without the XOR Lemma (extended abstract) , 1999, STOC '99.