Related papers: Monotone Erasure Codes
This paper studies the fundamental problem of data persistency for a general family of redundancy schemes in distributed storage systems, called replicated erasure codes. Namely, we analyze two strategies of replicated erasure codes…
In this paper, we introduce both monotone and nonmonotone variants of LiBCoD, a \textbf{Li}nearized \textbf{B}lock \textbf{Co}ordinate \textbf{D}escent method for solving composite optimization problems. At each iteration, a random block is…
LT (Luby transform) codes are a celebrated family of rateless erasure codes (RECs). Most of existing LT codes were designed for applications in which a centralized encoder possesses all message blocks and is solely responsible for encoding…
We consider the problem of designing codes for distributed storage that protect user data against eavesdroppers that can gain access to network links as well as individual nodes. Our goal is to achieve weak security (also known as block…
Although blockchain, the supporting technology of various cryptocurrencies, has offered a potentially effective framework for numerous decentralized trust management systems, its performance is still sub-optimal in real-world networks. With…
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…
Monomial codes were recently equipped with partial order relations, fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar codes. Here, we refine the existing order relations in the…
People have used cloud computing approach to store their data remotely. As auspicious as this approach is, it brings forth many challenges: from data security to time latency issues with data computation as well as delivery to end users.…
Founsure is an open-source software library that implements a multi-dimensional graph-based erasure coding entirely based on fast exclusive OR (XOR) logic. Its implementation utilizes compiler optimizations and multi-threading to generate…
A blockchain is a distributed ledger for recording transactions, maintained by many nodes without central authority through a distributed cryptographic protocol. All nodes validate the information to be appended to the blockchain, and a…
The exponential growth of data necessitates distributed storage models, such as peer-to-peer systems and data federations. While distributed storage can reduce costs and increase reliability, the heterogeneity in storage capacity, I/O…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in…
Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted…
We construct deletion error-correcting codes in the oblivious model, where errors are adversarial but oblivious to the encoder's randomness. Oblivious errors bridge the gap between the adversarial and random error models, and are motivated…
Motivated by applications in blockchains and sensor networks, we consider a model of $n$ nodes trying to reach consensus on their majority bit. Each node $i$ is assigned a bit at time zero, and is a finite automaton with $m$ bits of memory…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
Starting from a practical use of Reed-Solomon codes in a cryptographic scheme published in Indocrypt'09, this paper deals with the threshold of linear $q$-ary error-correcting codes. The security of this scheme is based on the…
Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this…
We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…