Related papers: An Explicit Construction of Optimal Streaming Code…
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…
In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent…
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors…
In a single hop broadcast packet erasure network, we demonstrate that it is possible to provide multirate packet delivery outside of what is given by the network min-cut. This is achieved by using a deterministic non-block-based network…
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
Classical erasure codes, e.g. Reed-Solomon codes, have been acknowledged as an efficient alternative to plain replication to reduce the storage overhead in reliable distributed storage systems. Yet, such codes experience high overhead…
In a distributed storage system based on erasure coding, an important problem is the \emph{repair problem}: If a node storing a coded piece fails, in order to maintain the same level of reliability, we need to create a new encoded piece and…
The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of K\"otter and Kschischang. A large class of constant-dimension subspace codes is…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
Coding for distributed storage gives rise to a new set of problems in coding theory related to the need of reducing inter-node communication in the system. A large number of recent papers addressed the problem of optimizing the total amount…
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
This paper investigates the use of redundancy and self repairing against node failures in distributed storage systems, using various strategies. In replication method, access to one replication node is sufficient to reconstruct a lost node,…
Consider a binary maximum distance separable (MDS) array code composed of an $m\times (k+r)$ array of bits with $k$ information columns and $r$ parity columns, such that any $k$ out of $k+r$ columns suffice to reconstruct the $k$…
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…
Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed…