相关论文: Nearly Optimal Constructions of PIR and Batch Code…

The classic exact pattern matching problem, given two strings -- a pattern $P$ of length $m$ and a text $T$ of length $n$ -- asks whether $P$ occurs as a substring of $T$. A property tester for the problem needs to distinguish (with high…

We investigate the problem of determining a set S of k indistinguishable integers in the range [1,n]. The algorithm is allowed to query an integer $q\in [1,n]$, and receive a response comparing this integer to an integer randomly chosen…

Diversity coding is a network restoration technique which offers near-hitless restoration, while other state-of-the art techniques are significantly slower. Furthermore, the extra spare capacity requirement of diversity coding is…

For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this…

Combinatorial batch codes were defined by Paterson, Stinson, and Wei as purely combinatorial versions of the batch codes introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai. There are $n$ items and $m$ servers, each of which stores a…

In symmetric private information retrieval (SPIR), a user communicates with multiple servers to retrieve from them a message in a database, while not revealing the message index to any individual server (user privacy), and learning no…

A private information retrieval (PIR) scheme is a protocol that allows a user to retrieve a file from a database without revealing the identity of the desired file to a curious database. Given a distributed data storage system, efficient…

Dictionaries have been one of the central questions in data structures. A dictionary data structure maintains a set of key-value pairs under insertions and deletions such that given a query key, the data structure efficiently returns its…

Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…

The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate…

Private information retrieval (PIR) protocols ensure that a user can download a file from a database without revealing any information on the identity of the requested file to the servers storing the database. While existing protocols…

A private information retrieval (PIR) scheme allows a client to retrieve a data item $x_i$ among $n$ items $x_1,x_2,\ldots,x_n$ from $k$ servers, without revealing what $i$ is even when $t < k$ servers collude and try to learn $i$. Such a…

In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…

Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and…

We consider the problem of single-round private information retrieval (PIR) from $N$ replicated databases. We consider the case when $B$ databases are outdated (unsynchronized), or even worse, adversarial (Byzantine), and therefore, can…

A Batch Private Information Retrieval (batch-PIR) scheme allows a client to retrieve multiple data items from a database without revealing them to the storage server(s). Most existing approaches for batch-PIR are based on batch codes, in…

In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $n$ items among which $k$ are defective, the…

We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…

We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…

The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…