Michael Viderman

Michael Viderman
Technion – Israel Institute of Technology | technion · Faculty of Computer Science

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23
Publications
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269
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Introduction
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Publications

Publications (23)
Article
The study of locally testable codes (LTCs) has benefited from a number of nontrivial constructions discovered in recent years. Yet, we still lack a good understanding of what makes a linear error correcting code locally testable and as a result we do not know what is the rate-limit of LTCs and whether asymptotically good linear LTCs with constant q...
Article
Ben-Sasson and Sudan (RSA 2006) showed that repeated tensor products of linear codes with a very large distance are locally testable. Due to the requirement of a very large distance the associated tensor products could be applied only over sufficiently large fields. Then Meir (SICOMP 2009) used this result (as a black box) to present a combinatoria...
Conference Paper
An error-correcting code C is called (q, ϵ)-strong locally testable code (LTC) if there exists a tester that makes at most q queries to the input word. This tester accepts all code words with probability 1 and rejects all non-code words x with probability at least ϵ · δ(x, C), where δ(x, C) denotes the relative Hamming distance between the word x a...
Conference Paper
An error-correcting code C ⊆ Fn is called (q, ε)-strong locally testable code (LTC) if there exists a randomized algorithm (tester) that makes at most q queries to the input word. This algorithm accepts all codewords with probability 1 and rejects all non-codewords x ∉ C with probability at least ε · δ(x, C), where δ(x, C) denotes the relative Hamm...
Article
A code C subset of F-n(2) is a (c, delta, epsilon)-expander code if it has a Tanner graph, where every variable node has degree c, and every subset of variable nodes L-0 such that vertical bar L-0 vertical bar <= delta n has at least epsilon c vertical bar L-0 vertical bar neighbors. Feldman et al. (2007) [3] proved that LP decoding corrects 3 epsi...
Article
Alon et al. (SICOMP 2001) showed that all regular languages are testable with a constant number of queries. On the other hand, they also showed that some context free languages require \(\Omega(\sqrt{n})\) queries to test. Following this, Alon et al. suggested the problem of classifying the context free languages that are testable with a constant n...
Article
Locally testable codes (LTCs) are error-correcting codes for which membership in the code can be tested by probing few symbols of a purported codeword. Motivated by applications in cryptography, we initiate the study of zero knowledge locally testable codes (ZK-LTCs). ZK-LTCs are LTCs which admit a randomized encoding function, such that even a mal...
Article
Full-text available
A code $C \subseteq \F_2^n$ is a $(c,\epsilon,\delta)$-expander code if it has a Tanner graph, where every variable node has degree $c$, and every subset of variable nodes $L_0$ such that $|L_0|\leq \delta n$ has at least $\epsilon c |L_0|$ neighbors. Feldman et al. (IEEE IT, 2007) proved that LP decoding corrects $\frac{3\epsilon-2}{2\epsilon-1} \...
Conference Paper
Full-text available
The main open problem in the area of locally testable codes (LTCs) is whether there exists an asymptotically good family of LTCs, and to resolve this question, it suffices to consider the case of query complexity 3. We argue that to refute the existence of such an asymptotically good family, it is sufficient to prove that the number of dual codewor...
Article
Full-text available
Sipser and Spielman (IEEE IT, [1996]) showed that any c,d)-regular expander code with expansion parameter >¾ is decodable in linear time from a constant fraction of errors. Feldman et al. (IEEE IT, [2007]) proved that expansion parameter >&frac23; &plus; 1/3c is sufficient to correct a constant fraction of errors in polynomial time using LP decodin...
Article
In this paper, we obtain a composition theorem that allows us to construct locally testable codes (LTCs) by repeated two-wise tensor products. This is the first composition theorem showing that repeating the two-wise tensor operation any constant number of times still results in a locally testable code, improving upon previous results which only wo...
Article
Full-text available
We study the relation between locally testable and locally decodable codes. Locally testable codes (LTCs) are error-correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. Locally decodable codes (LDCs) allow to recover each message entry with high probability by readi...
Article
Full-text available
Three results are shown regarding locally testable and locally decodable linear codes. All three results rely on the observation that repetition codes have the same local testability and local decodability parameters as the unrepeated base code used to create them. The first two results deal with families of sparse linear codes, i.e., codes with di...
Article
Full-text available
Inspired by recent construction of high-rate locally correctable codes with sublinear query complexity due to Kopparty, Saraf and Yekhanin (2010) we address the similar question for locally testable codes (LTCs). In this note we show a construction of high-rate LTCs with sublinear query complexity. More formally , we show that for every , ρ > 0 the...
Chapter
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We continue the study of the local testability of error correcting codes constructed by taking the two-wise tensor product of a “base-code” with itself. We show that if the base-code is any locally testable code (LTC) or any expander code, then the code obtained by taking the repeated two-wise tensor product of the base-code with itself is locally...
Article
Full-text available
Locally testable codes (LTCs) are error- correcting codes for which membership, in the code, of a given word can be tested by examining it in very few locations. Most known constructions of locally testable codes are linear codes, and give error-correcting codes whose duals have (superlinearly) many small weight codewords. Examining this feature ap...
Chapter
Full-text available
We continue the study of robust tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robust two-wise tensor products. In particular, we show that all unique-neighbor expander codes and all locally correctable codes, when tensored with any other good-distance code, ar...

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