Matrix analysis
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Dense quantum coding and a lower bound for 1-way quantum automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Breaking the O(n1/(2k-1)) Barrier for Information-Theoretic Private Information Retrieval
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Information-Theoretic Private Information Retrieval: A Unified Construction
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Upper Bound on Communication Complexity of Private Information Retrieval
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
An optimal lower bound for 2-query locally decodable linear codes
Information Processing Letters
A tight lower bound for restricted PIR protocols
Computational Complexity
Towards 3-query locally decodable codes of subexponential length
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Towards 3-query locally decodable codes of subexponential length
Journal of the ACM (JACM)
The Complexity of Local List Decoding
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
On Locally Decodable Codes, Self-correctable Codes, and t-Private PIR
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Quantum multiparty communication complexity and circuit lower bounds
Mathematical Structures in Computer Science
3-query locally decodable codes of subexponential length
Proceedings of the forty-first annual ACM symposium on Theory of computing
Communications of the ACM
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Quantum multiparty communication complexity and circuit lower bounds
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
SIAM Journal on Computing
Lower bounds on matrix rigidity via a quantum argument
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Private locally decodable codes
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We prove new lower bounds for locally decodable codes and private information retrieval. We show that a 2-query LDC encoding n-bit strings over an ℓ-bit alphabet, where the decoder only uses b bits of each queried position, needs code length $m=exp\left(\Omega\left(\frac{n}{2^{b}{\sum_{i=0}^{b}}(^{l}_{i})}\right)\right)$ Similarly, a 2-server PIR scheme with an n-bit database and t-bit queries, where the user only needs b bits from each of the two ℓ-bit answers, unknown to the servers, satisfies $t=\Omega \left(\frac{n}{2^{b}\sum_{i=0}^{b}(^{l}_{i})}\right)$ This implies that several known PIR schemes are close to optimal. Our results generalize those of Goldreich et al. [8], who proved roughly the same bounds for linear LDCs and PIRs. Like earlier work by Kerenidis and de Wolf [12], our classical bounds are proved using quantum computational techniques. In particular, we give a tight analysis of how well a 2-input function can be computed from a quantum superposition of both inputs.