相关论文: Correcting an ordered deletion-erasure
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The…
Recent work by Smagloy et al. (ISIT 2020) shows that the redundancy of a single-deletion $s$-substitution correcting code is asymptotically at least $(s+1)\log n+o(\log n)$, where $n$ is the length of the codes. They also provide a…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
This paper considers insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available…
Erasure correcting codes are widely used to ensure data persistence in distributed storage systems. This paper addresses the simultaneous repair of multiple failures in such codes. We go beyond existing work (i.e., regenerating codes by…
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, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. We study the decoding problem using the state space description and this…
The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as…
Linear codes correcting one deletions have rate at most $1/2$. In this paper, we construct linear list decodable codes correcting edits with rate approaching $1$ and reasonable list size. Our encoder and decoder run in polynomial time.
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements,…
We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine…
A simple algorithm for decoding both errors and erasures of Reed-Solomon codes is described.
We present the first known efficient decoding algorithm for correcting multiple insertion-deletion errors in Helberg codes and their non-binary generalizations, extending a known algorithm for correcting multiple deletion errors.