Asymptotically-Good RLCCs with (log n)^(2+ o (1)) Queries
G Cohen, T Yankovitz - 39th Computational Complexity …, 2024 - drops.dagstuhl.de
Abstract Recently, Kumar and Mon reached a significant milestone by constructing
asymptotically good relaxed locally correctable codes (RLCCs) with poly-logarithmic query …
asymptotically good relaxed locally correctable codes (RLCCs) with poly-logarithmic query …
Relaxed locally correctable codes
T Gur, G Ramnarayan, R Rothblum - Theory of Computing, 2020 - theoryofcomputing.org
Locally decodable codes (LDCs) and locally correctable codes (LCCs) are errorcorrecting
codes in which individual bits of the message and codeword, respectively, can be recovered …
codes in which individual bits of the message and codeword, respectively, can be recovered …
A hierarchy theorem for interactive proofs of proximity
T Gur, RD Rothblum - 2017 - repository.cam.ac.uk
The number of rounds, or round complexity, used in an interactive protocol is a fundamental
resource. In this work we consider the significance of round complexity in the context of …
resource. In this work we consider the significance of round complexity in the context of …
Relaxed locally correctable codes with nearly-linear block length and constant query complexity
Locally correctable codes (LCCs) are error correcting codes which admit local algorithms
that correct any individual symbol of a corrupted codeword via a minuscule number of …
that correct any individual symbol of a corrupted codeword via a minuscule number of …
Relaxed locally decodable and correctable codes: Beyond tensoring
G Cohen, T Yankovitz - 2022 IEEE 63rd Annual Symposium on …, 2022 - ieeexplore.ieee.org
In their highly influential paper, Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (STOC
2004) introduced the notion of a relaxed locally decodable code (RLDC). Similarly to a …
2004) introduced the notion of a relaxed locally decodable code (RLDC). Similarly to a …
A Structural Theorem for Local Algorithms with Applications to Coding, Testing, and Verification
We prove a general structural theorem for a wide family of local algorithms, which includes
property testers, local decoders, and probabilistically checkable proofs of proximity. Namely …
property testers, local decoders, and probabilistically checkable proofs of proximity. Namely …
On the power of relaxed local decoding algorithms
A locally decodable code (LDC) C:{0,1\}^k→{0,1\}^n is an error correcting code wherein
individual bits of the message can be recovered by only querying a few bits of a noisy …
individual bits of the message can be recovered by only querying a few bits of a noisy …
Proofs of proximity for distribution testing
Distribution testing is an area of property testing that studies algorithms that receive few
samples from a probability distribution D and decide whether D has a certain property or is …
samples from a probability distribution D and decide whether D has a certain property or is …
Strong locally testable codes with relaxed local decoders
Locally testable codes (LTCs) are error-correcting codes that admit very efficient codeword
tests. An LTC is said to be strong if it has a proximity-oblivious tester, that is, a tester that …
tests. An LTC is said to be strong if it has a proximity-oblivious tester, that is, a tester that …
Distribution-Free Proofs of Proximity
H Aaronson, T Gur, N Rajgopal… - arXiv preprint arXiv …, 2023 - arxiv.org
Motivated by the fact that input distributions are often unknown in advance, distribution-free
property testing considers a setting in which the algorithmic task is to accept functions …
property testing considers a setting in which the algorithmic task is to accept functions …