Exponential lower bound for 2-query locally decodable codes via a quantum argument

Exponential lower bound for 2-query locally decodable codes via a quantum argument (2003)

Cached

Download Links

[homepages.cwi.nl]
[arxiv.org]
[www.cs.umd.edu]
[www.cwi.nl]

Other Repositories/Bibliography

DBLP

by Iordanis Kerenidis , Ronald De Wolf

Venue:	Journal of Computer and System Sciences
Citations:	123 - 18 self

BibTeX

@INPROCEEDINGS{Kerenidis03exponentiallower,
    author = {Iordanis Kerenidis and Ronald De Wolf},
    title = {Exponential lower bound for 2-query locally decodable codes via a quantum argument},
    booktitle = {Journal of Computer and System Sciences},
    year = {2003},
    pages = {106--115}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

Abstract A locally decodable code encodes n-bit strings x in m-bit codewords C(x) in such a way that one can recover any bit xi from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2 classical queries require exponential length: m = 2 \Omega (n). Previously this was known only for linear codes (Goldreich et al. 02). The

Citations

1352	Quantum Computation and Quantum Information - Nielsen, Chuang - 2000
476	Quantum complexity theory - Bernstein, Vazirani - 1997
415	Private information retrieval - Chor, Goldreich, et al. - 1995
277	circuit complexity - Yao
274	Expander codes - Sipser, Spielman - 1996
269	Quantum lower bounds by polynomials - Beals, Buhrman, et al. - 1998
260	Checking computations in polylogarithmic time - Babai, Fortnow, et al. - 1991
158	Hiding instances in multi-oracle queries - Beaver, Feigenbaum - 1990
126	Pseudorandom generators without the XOR lemma - Sudan, Trevisan, et al.
118	On the efficiency of local decoding procedures for error-correcting codes - Katz, Trevisan - 2000
112	BPP has subexponential time simulations unless EXPTIME has publishable proofs - Babai, Fortnow, et al. - 1993
107	New directions in testing - Lipton - 1991
90	Quantum entanglement and the communication complexity of the inner product function - Cleve, Dam, et al. - 1998
87	Upper bound on the communication complexity of private information retrieval - Ambainis - 1997
85	Optimal lower bounds for quantum automata and random access codes - Nayak - 1999
81	Self-testing/correcting for polynomials and for approxiamte functions - Gemmell, Lipton, et al. - 1991
80	Salil Vadhan. Robust PCPs of proximity, shorter PCPs, and applications to coding - Ben-Sasson, Goldreich, et al. - 2006
79	Nearly-linear size holographic proofs - Polishchuk, Spielman - 1994
70	On the random self-reducibility of complete sets - Feigenbaum, Fortnow - 1991
69	The polynomial method in circuit complexity - Beigel - 1993
62	Quantum communication - Kremer - 1995
57	Are bitvectors optimal - Buhrman, Miltersen, et al. - 2000
51	Lower bounds for linear locally decodable codes and private information retrieval - Goldreich, Karloff, et al.
51	Extractors: Optimal up to constant factors - Lu, Reingold, et al. - 2003
48	A limit on the speed of quantum computation in determining parity. Quantum Physics e-Print archive - Farhi, Goldstone, et al.
46	Highly resilient correctors for polynomials - Gemmell, Sudan - 1986
44	Private access to distributed information - Mann - 1998
44	Breaking the O(n 1/(2k−1) ) barrier for information-theoretic Private Information Retrieval - Beimel, Ishai, et al. - 2002
42	Robust Information-Theoretic Private Information Retrieval - Beimel, Stahl - 2002
33	Interaction in quantum communication and the complexity of set disjointness - Klauck, Nayak, et al. - 2001
26	Quantum oracle interrogation: Getting all information for almost half the price - Dam - 1998
26	Privacy and interaction in quantum communication complexity and a theorem about the relative entropy of quantum states - JAIN, RADHAKRISHNAN, et al. - 2002
23	Optimal lower bounds for 2-query locally decodable linear codes - Obata - 2002
21	Better lower bounds for locally decodable codes - Deshpande, Jain, et al. - 2002
16	New bounds in secret-key agreement: the gap between formation and secrecy extraction - Renner, Wolf - 2003
15	Linking classical and quantum key agreement: Is there a classical analog to bound entanglement - GISIN, RENNER, et al. - 2002
15	Insecurity of quantum secure computations - Lo - 1997
10	Lower bounds in the quantum cell probe model - Sen, Venkatesh - 2001
8	The quantum complexity of set membership - Radhakrishnan, Sen, et al.
8	On the e#ciency of local decoding procedures for error correcting codes - Katz, Trevisan - 2000
3	Breaking the O(n 1 2k\Gamma 1 ) barrier for informationtheoretic private information retrieval - Beimel, Ishai, et al. - 2002
2	Nearly tight bounds for private information retrieval systems.Technical Report 2002-L001N - Beigel, Fortnow, et al. - 2001
2	Exact bounds on any 1-round private information retrieval with 1-bit answers. Unpublished manuscript - Beigel, Fortnow, et al. - 2002
1	A Optimal 1-Query Quantum Algorithms for 2-Bit Functions In this appendix we show that every 2-bit Boolean function f can be computed with success probability 9=10 using only one quantum query, and that this is optimal for functions like AND and OR. If f - Trevisan - 2002