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Many images and videos are primarily processed by computer vision algorithms, involving only occasional human inspection. When this content requires compression before processing, e.g., in distributed applications, coding methods must…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and error-correction radius. Specifically, for every $0 < R < 1$ and $\eps> 0$, we present an explicit construction of…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…
We study quantum networks with tree structures, in which information propagates from a root to leaves. At each node in the network, the received qubit unitarily interacts with fresh ancilla qubits, after which each qubit is sent through a…
In the current thesis we first talk about the six-qubit quantum error-correcting code and show its connections to entanglement-assisted error-correcting coding theory and then to subsystem codes. This code bridges the gap between the…
Fountain codes like LT or Raptor codes, also known as rateless erasure codes, allow to encode a message as some number of packets, such that any large enough subset of these packets is sufficient to fully reconstruct the message. It…
Three-dimensional (3D) printing's accessibility enables rapid manufacturing but also poses security risks, such as the unauthorized production of untraceable firearms and prohibited items. To ensure traceability and accountability,…
A key problem in random network coding (NC) lies in the complexity and energy consumption associated with the packet decoding processes, which hinder its application in mobile environments. Controlling and hence limiting such factors has…
We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we…
In various wireless systems, such as sensor RFID networks and body area networks with implantable devices, the transmitted signals are simultaneously used both for information transmission and for energy transfer. In order to satisfy the…
The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting)…
This paper addresses the problem of collaborative navigation in an unknown environment, where two robots, referred to in the sequel as the Seeker and the Supporter, traverse the space simultaneously. The Supporter assists the Seeker by…
We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla…
This paper investigates the problem of secure lossy source coding in the presence of an eavesdropper with arbitrary correlated side informations at the legitimate decoder (referred to as Bob) and the eavesdropper (referred to as Eve). This…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum…