Locally Testable Codes Require Redundant Testers

Proceedings of the Annual IEEE Conference on Computational Complexity

Volumn , Issue , 2009, Pages 52-61

  Ben Sasson, Eli ^c   Guruswami, Venkatesan ^a   Kaufman, Tali ^b   Sudan, Madhu ^b   Viderman, Michael ^c  

^a UNIVERSITY OF WASHINGTON   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Dual codes; Ldpc codes; Linear codes; Lower bounds; Property testing

Indexed keywords

DUAL CODES; LDPC CODES; LINEAR CODES; LOWER BOUNDS; PROPERTY TESTING;

ARTIFICIAL INTELLIGENCE; COMPUTATIONAL COMPLEXITY; CONTROL THEORY; RATE CONSTANTS;

CODES (SYMBOLS);

EID: 70350624763     PISSN: 10930159     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CCC.2009.6     Document Type: Conference Paper

References (26)

1. N. Alon, J. Bruck, J. Naor, M. Naor, and R. M. Roth, "Construction of asymptotically good low-rate errorcorrecting codes through pseudo-random graphs, " IEEE Transactions on Information Theory, vol. 38, no. 2, p. 509, 1992.
2. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, "Proof verification and the hardness of approximation problems, " Journal of the ACM, vol. 45, no. 3, pp. 501-555, May 1998.
3. S. Arora and S. Safra, "Probabilistic checking of proofs: A new characterization of NP, " Journal of the ACM, vol. 45, no. 1, pp. 70-122, Jan. 1998.
4. L. Babai, A. Shpilka, and D. Stefankovic, "Locally testable cyclic codes, " in Proceedings: 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2003, 11-14 October 2003, Cambridge, Massachusetts, IEEE, Ed. IEEE Computer Society Press, 2003, pp. 116-125.
5. M. Bellare, O. Goldreich, and M. Sudan, "Free bits, PCPs, and nonapproximability-towards tight results, " SIAM Journal on Computing, vol. 27, no. 3, pp. 804- 915, Jun. 1998.
6. Y. Ben-Haim and S. Litsyn, "Upper bounds on the rate of LDPC codes as a function of minimum distance, " IEEE Transactions on Information Theory, vol. 52, no. 5, pp. 2092-2100, 2006. [Online]. Available: http://doi.ieeecomputersociety.org/10.1109/TIT.2006.872972.
7. E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. P. Vadhan, "Robust PCPs of proximity, shorter PCPs, and applications to coding, " SIAM Journal on Computing, vol. 36, no. 4, pp. 889-974, 2006.
8. E. Ben-Sasson, O. Goldreich, and M. Sudan, "Bounds on 2-query codeword testing, " in RANDOM-APPROX, ser. Lecture Notes in Computer Science, vol. 2764. Springer, 2003, pp. 216-227. [Online]. Available: http://springerlink.metapress.com/openurl.asp?genre=article&issn= 0302-9743&volume=2764&spage=216.
9. E. Ben-Sasson, P. Harsha, O. Lachish, and A. Matsliah, "Sound 3-query PCPPs are long, " in ICALP (1), ser. Lecture Notes in Computer Science, vol. 5125. Springer, 2008, pp. 686-697. [Online]. Available: http://dx.doi.org/10.1007/978-3-540-70575-856.
10. E. Ben-Sasson, P. Harsha, and S. Raskhodnikova, "Some 3CNF properties are hard to test, " SIAM Journal on Computing, vol. 35, no. 1, pp. 1- 21, 2005. [Online]. Available: http://epubs.siam.org/SICOMP/volume-35/ art44544.html.
11. E. Ben-Sasson and M. Sudan, "Simple PCPs with poly-log rate and query complexity, " in STOC. ACM, 2005, pp. 266-275. [Online]. Available: http://doi.acm.org/10.1145/1060590.1060631.
12. E. Ben-Sasson and M. Sudan, "Robust locally testable codes and products of codes, " Random Struct. Algorithms, vol. 28, no. 4, pp. 387-402, 2006. [Online]. Available: http://dx.doi.org/10.1002/rsa.20120. (Pubitemid 43998384)
13. I. Dinur, "The PCP theorem by gap amplification, " Journal of the ACM, vol. 54, no. 3, pp. 12: 1-12: 44, Jun. 2007.
14. I. Dinur and O. Reingold, "Assignment testers: Towards a combinatorial proof of the PCP theorem, " SIAM Journal on Computing, vol. 36, no. 4, pp. 975- 1024, 2006. [Online]. Available: http://dx.doi.org/10.1137/ S0097539705446962.
15. I. Dinur, M. Sudan, and A. Wigderson, "Robust local testability of tensor products of LDPC codes, " in APPROX-RANDOM, ser. Lecture Notes in Computer Science, vol. 4110. Springer, 2006, pp. 304-315. [Online]. Available: http://dx.doi.org/10.1007/1183092429.
16. O. Goldreich, "Short locally testable codes and proofs (survey), " Electronic Colloquium on Computational Complexity (ECCC), no. 014, 2005. [Online]. Available: http://eccc.hpi-web.de/eccc-reports/2005/TR05-014/index. html.
17. O. Goldreich and M. Sudan, "Locally testable codes and PCPs of almost-linear length, " Journal of the ACM, vol. 53, no. 4, pp. 558-655, Jul. 2006. (Pubitemid 44435052)
18. E. Grigorescu, T. Kaufman, and M. Sudan, "2-transitivity is insufficient for local testability, " in IEEE Conference on Computational Complexity. IEEE Computer Society, 2008, pp. 259-267. [Online]. Available: http://doi.ieeecomputersociety.org/10.1109/CCC.2008.31.
19. V. Guruswami, "On 2-query codeword testing with near-perfect completeness, " in ISAAC, ser. Lecture Notes in Computer Science, vol. 4288. Springer, 2006, pp. 267-276. [Online]. Available: http://dx.doi.org/10. 1007/1194012828.
20. T. Kaufman and M. Sudan, "Sparse random linear codes are locally decodable and testable, " in FOCS. IEEE Computer Society, 2007, pp. 590- 600. [Online]. Available: http://doi.ieeecomputersociety.org/10.1109/FOCS.2007. 65.
21. T. Kaufman and M. Sudan, "Algebraic property testing: the role of invariance, " in STOC. ACM, 2008, pp. 403-412. [Online]. Available: http://doi.acm.org/10.1145/1374376.1374434.
22. O. Meir, "Combinatorial construction of locally testable codes, " in STOC. ACM, 2008, pp. 285-294. [Online]. Available: http://doi.acm.org/10.1145/1374376.1374419.
23. R. M. Roth, Introduction to coding theory. pub- CAMBRIDGE: adr: Cambridge University Press, 2006.
24. D. A. Spielman, "Linear-time encodable and decodable error-correcting codes, " IEEE Transactions on Information Theory, vol. 42, no. 6, pp. 1723-1731, 1996. [Online]. Available: ,
25. http://theory.csail.mit.edu/∼madhu/FT01/
26. P. Valiant, "The tensor product of two codes is not necessarily robustly testable, " in APPROX-RANDOM, ser. Lecture Notes in Computer Science, vol. 3624. Springer, 2005, pp. 472-481. [Online]. Available: http://dx.doi.org/10.1007/1153846240.