Related papers: Shortened regenerating codes
Locally repairable codes (LRCs) have received significant recent attention as a method of designing data storage systems robust to server failure. Optimal LRCs offer the ideal trade-off between minimum distance and locality, a measure of…
A locally repairable code (LRC) with locality $r$ allows for the recovery of any erased codeword symbol using only $r$ other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of…
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…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
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…
We consider the rack-aware storage system where $n=\bar{n}u$ nodes are organized in $\bar{n}$ racks each containing $u$ nodes, and any $k=\bar{k}u+u_0~(0\leq u_0<u)$ nodes can retrieve the original data file. More importantly, the…
We study a generalization of the setting of regenerating codes, motivated by applications to storage systems consisting of clusters of storage nodes. There are $n$ clusters in total, with $m$ nodes per cluster. A data file is coded and…
Regenerating codes (RCs) can significantly reduce the repair-bandwidth of distributed storage networks. Initially, the analysis of RCs was based on the assumption that during the repair process, the newcomer does not distinguish (among all…
The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…
A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery…
Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small…
The repair problem in distributed storage addresses recovery of the data encoded using an erasure code, for instance, a Reed-Solomon (RS) code. We consider the problem of repairing a single node or multiple nodes in RS-coded storage systems…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…
We discuss the similarities and differences between training an auto-encoder to minimize the reconstruction error, and training the same auto-encoder to compress the data via a generative model. Minimizing a codelength for the data using an…
We consider the repair scheme of Guruswami-Wootters for the Reed-Solomon code and ask: can we correctly repair a failed node in the presence of erroneous nodes? Equivalently, we consider the collection of downloaded traces as a code and…
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more…
Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly…