201 citations · 365 across the 23 of their papers we have counts for
25 papers · 1 filter
Sequential Random Sampling PIR with Multiple Colluding Servers in DNA-Based Data Storage
Chen Wang, Natalia Silberstein, Eitan Yaakobi
As DNA-based data storage evolves, protecting user privacy during data retrieval has become increasingly important. We study sequential random sampling DNA private information retr…
Locality and Availability of Array Codes Constructed from Subspaces
Natalia Silberstein, Tuvi Etzion, Moshe Schwartz
Ever-increasing amounts of data are created and processed in internet-scale companies such as Google, Facebook, and Amazon. The efficient storage of such copious amounts of data ha…
Constructions of High-Rate MSR Codes over Small Fields
Netanel Raviv, Natalia Silberstein, Tuvi Etzion
A novel technique for construction of minimum storage regenerating (MSR) codes is presented. Based on this technique, three explicit constructions of MSR codes are given. The first…
Optimal Binary Locally Repairable Codes via Anticodes
Natalia Silberstein, Alexander Zeh
This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various antic…
Optimal Fractional Repetition Codes and Fractional Repetition Batch Codes
Natalia Silberstein, Tuvi Etzion
Fractional repetition (FR) codes is a family of codes for distributed storage systems (DSS) that allow uncoded exact repairs with minimum repair bandwidth. In this work, we conside…
Fractional Repetition and Erasure Batch Codes
Natalia Silberstein
Batch codes are a family of codes that represent a distributed storage system (DSS) of nodes so that any batch of data symbols can be retrieved by reading at most one symbo…
Subspace Codes based on Graph Matchings, Ferrers Diagrams and Pending Blocks
Natalia Silberstein, Anna-Lena Trautmann
This paper provides new constructions and lower bounds for subspace codes, using Ferrers diagram rank-metric codes from matchings of the complete graph and pending blocks. We prese…
Optimal Fractional Repetition Codes based on Graphs and Designs
Natalia Silberstein, Tuvi Etzion
Fractional repetition (FR) codes is a family of codes for distributed storage systems that allow for uncoded exact repairs having the minimum repair bandwidth. However, in contrast…
Error-Correcting Regenerating and Locally Repairable Codes via Rank-Metric Codes
Natalia Silberstein, Ankit Singh Rawat, Sriram Vishwanath
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating…
On the Geometry of Balls in the Grassmannian and List Decoding of Lifted Gabidulin Codes
Joachim Rosenthal, Natalia Silberstein, Anna-Lena Trautmann
The finite Grassmannian is defined as the set of all -dimensional subspaces of the ambient space . Subsets of the finite Grassmannian…
Explicit MBR All-Symbol Locality Codes
Govinda M. Kamath, Natalia Silberstein, N. Prakash +5
Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e.…
Optimal Locally Repairable Codes via Rank-Metric Codes
Natalia Silberstein, Ankit Singh Rawat, O. Ozan Koyluoglu +1
This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum…
New Lower Bounds for Constant Dimension Codes
Natalia Silberstein, Anna-Lena Trautmann
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructio…
List Decoding of Lifted Gabidulin Codes via the Plücker Embedding
Anna-Lena Trautmann, Natalia Silberstein, Joachim Rosenthal
Codes in the Grassmannian have recently found an application in random network coding. All the codewords in such codes are subspaces of $\F_q^n$ with a given dimension. In this pap…
Optimal Locally Repairable and Secure Codes for Distributed Storage Systems
Ankit Singh Rawat, O. Ozan Koyluoglu, Natalia Silberstein +1
This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both importan…
Error Resilience in Distributed Storage via Rank-Metric Codes
Natalia Silberstein, Ankit Singh Rawat, Sriram Vishwanath
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneou…
Codes and Designs Related to Lifted MRD Codes
Tuvi Etzion, Natalia Silberstein
Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a bl…
On Perfect Codes in the Johnson Graph
Natalia Silberstein, Tuvi Etzion
In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n,w). We present combinatorial and number theory techniques to provide necessary conditio…
Properties of Codes in the Johnson Scheme
Natalia Silberstein
Codes which attain the sphere packing bound are called perfect codes. The most important metrics in coding theory on which perfect codes are defined are the Hamming metric and the…
Large Constant Dimension Codes and Lexicodes
Natalia Silberstein, Tuvi Etzion
Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with…
Enumerative Coding for Grassmannian Space
Natalia Silberstein, Tuvi Etzion
The Grassmannian space $\Gr$ is the set of all dimensional subspaces of the vector space~\smash{$\F_q^n$}. Recently, codes in the Grassmannian have found an application in netw…
Enumerative Encoding in the Grassmannian Space
Natalia Silberstein, Tuvi Etzion
Codes in the Grassmannian space have found recently application in network coding. Representation of -dimensional subspaces of $\F_q^n$ has generally an essential role in solvin…
Construction of Error-Correcting Codes for Random Network Coding
Tuvi Etzion, Natalia Silberstein
In this work we present error-correcting codes for random network coding based on rank- metric codes, Ferrers diagrams, and puncturing. For most parameters, the constructed codes a…
Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams
Tuvi Etzion, Natalia Silberstein
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagr…