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In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it communication} required to exactly rebuild a storage node after a failure arises. This repair bandwidth depends on the structure of the…
We consider the problem of evaluating arbitrary multivariate polynomials over a massive dataset containing multiple inputs, on a distributed computing system with a master node and multiple worker nodes. Generalized Lagrange Coded Computing…
The distributed data storage systems are constructed by large number of nodes which are interconnected over a network. Each node in such peer-to-peer network is vulnerable and at a potential risk for attack. The attackers can eavesdrop the…
It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We…
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…
Two widely studied models of multiple-node repair in distributed storage systems are centralized repair and cooperative repair. The centralized model assumes that all the failed nodes are recreated in one location, while the cooperative one…
Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
This paper is concerned with the design of capacity approaching ensembles of Low-Densiy Parity-Check (LDPC) codes for correlated sources. We consider correlated binary sources where the data is encoded independently at each source through a…
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 erroneous data from a single corrupted node to the rest of the…
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
Computing systems have become increasingly complex with the emergence of heterogeneous hardware combining multicore CPUs and GPUs. These parallel systems exhibit tremendous computational power at the cost of increased programming effort.…
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,…
$\epsilon$-Minimum Storage Regenerating ($\epsilon$-MSR) codes form a special class of Maximum Distance Separable (MDS) codes, providing mechanisms for exact regeneration of a single code block in their codewords by downloading slighly…
The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer…
Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of d=n-1.…