Related papers: Recovery Sets of Subspaces from a Simplex Code
In this short paper, Kuratowski problem will be investigated in vector space. The highest number of distinct sets that can be generated from one convex set in linear space by repeatedly applying algebraic closure and complement in any order…
In this paper, we introduce a model of a single-failure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the well-studied index coding problem. The relation between the…
We investigate the task of retrieving information from compositional distributed representations formed by Hyperdimensional Computing/Vector Symbolic Architectures and present novel techniques which achieve new information rate bounds.…
Much of the existing literature in sparse recovery is concerned with the following question: given a sparsity pattern and a corresponding regularizer, derive conditions on the dictionary under which exact recovery is possible. In this…
Consider a connected network of n nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and exchanges coded packets with its neighbors. This paper provides necessary and sufficient…
Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…
The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…
We investigate in this work the problem of Erasure Combinatorial Batch Codes, in which $n$ files are stored on $m$ servers so that every set of $n-r$ servers allows a client to retrieve at most $k$ distinct files by downloading at most $t$…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…
The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures.The maximum file size that can be stored…
In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However,…
The paper presents techniques for analyzing the expected download time in distributed storage systems that employ systematic availability codes. These codes provide access to hot data through the systematic server containing the object and…
Distributed storage systems support failures of individual devices by the use of replication or erasure correcting codes. While erasure correcting codes offer a better storage efficiency than replication for similar fault tolerance, they…
The joint sparse recovery problem is a generalization of the single measurement vector problem which is widely studied in Compressed Sensing and it aims to recovery a set of jointly sparse vectors. i.e. have nonzero entries concentrated at…
Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (MDS for short) codes. Thus, the number of nodes is upper bounded by $2^{\fb}$, where $\fb$ is the bits of data stored…
In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known.…
Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and…
We derive theoretical guarantees for the exact recovery of piecewise constant two-dimensional images from a minimal number of non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities of the image…
A classical vector retrieval problem typically considers a \emph{single} query embedding vector as input and retrieves the most similar embedding vectors from a vector database. However, complex reasoning and retrieval tasks frequently…