Related papers: Correcting an ordered deletion-erasure
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…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
The deletion channel is known to be a notoriously diffcult channel to design error-correction codes for. In spite of this difficulty, there are some beautiful code constructions which give some intuition about the channel and about what…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the…
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by…
Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…
In this paper, we investigate binary reconstruction codes capable of correcting one deletion and one substitution. We define the \emph{single-deletion single-substitution ball} function $ \mathcal{B} $ as a mapping from a sequence to the…
Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to…
Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
Determining the largest size, or equivalently finding the lowest redundancy, of q-ary codes for given length and minimum distance is one of the central and fundamental problems in coding theory. Inspired by the construction of…
As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article…
In this work, we introduce maximally recoverable codes with locality and availability. We consider locally repairable codes (LRCs) where certain subsets of $ t $ symbols belong each to $ N $ local repair sets, which are pairwise disjoint…
Erasure codes play an important role in storage systems to prevent data loss. In this work, we study a class of erasure codes called Multi-Erasure Locally Recoverable Codes (ME-LRCs) for storage arrays. Compared to previous related works,…
Recently, codes for correcting a burst of errors have attracted significant attention. One of the most important reasons is that bursts of errors occur in certain emerging techniques, such as DNA storage. In this paper, we investigate a…
In this paper, we prove the equivalence of inserting separable quantum states and deletions. Hence any quantum code that corrects deletions automatically corrects separable insertions. First, we describe the quantum insertion/deletion error…
Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes…
An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into…