Related papers: Fractional repetition codes with flexible repair f…
The problem of string reconstruction from substring information has found many applications due to its relevance in DNA- and polymer-based data storage. One practically important and challenging paradigm requires reconstructing mixtures of…
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…
Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…
We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a…
We derive the spectral domain properties of two-dimensional (2-D) $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_q$ using the 2-D finite field Fourier transform (FFFT). Based on the spectral nulls of 2-D $(\lambda_1,…
Locality enables storage systems to recover failed nodes from small subsets of surviving nodes. The setting where nodes are partitioned into subsets, each allowing for local recovery, is well understood. In this work we consider a…
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the…
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code.…
A method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…
Regeneration codes with exact-repair property for distributed storage systems is studied in this paper. For exact- repair problem, the achievable points of ({\alpha},{\beta}) tradeoff match with the outer bound only for minimum storage…
We show how to construct a large class of quantum error correcting codes, known as CSS codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger…
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node.…
Regenerating codes are a class of distributed storage codes that optimally trade the bandwidth needed for repair of a failed node with the amount of data stored per node of the network. Minimum Storage Regenerating (MSR) codes minimize…
A locally recoverable code is an error-correcting code such that any erasure in a coordinate of a codeword can be recovered from a set of other few coordinates. In this article we introduce a model of local recoverable codes that also…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
There exist many scenarios where pixel information is available only on a non-regular subset of pixel positions. For further processing, however, it is required to reconstruct such images on a regular grid. Besides many other algorithms,…
Interference management techniques are critical to the performance of heterogeneous cellular networks, which will have dense and overlapping coverage areas, and experience high levels of interference. Fractional frequency reuse (FFR) is an…
In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…