Related papers: On Erasure Combinatorial Batch Codes
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…
To achieve reliability in distributed storage systems, data has usually been replicated across different nodes. However the increasing volume of data to be stored has motivated the introduction of erasure codes, a storage efficient…
A \textit{functional $k$-batch} code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. Any multiset request of size $k$ of linear combinations (or requests) of the information…
We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be sequentially…
Erasure coding is a storage-efficient alternative to replication for achieving reliable data backup in distributed storage systems. During the storage process, traditional erasure codes require a unique source node to create and upload all…
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions…
To cluster, classify and represent are three fundamental objectives of learning from high-dimensional data with intrinsic structure. To this end, this paper introduces three interpretable approaches, i.e., segmentation (clustering) via the…
In this work we study two families of codes with availability, namely private information retrieval (PIR) codes and batch codes. While the former requires that every information symbol has $k$ mutually disjoint recovering sets, the latter…
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,…
Erasure codes are increasingly being studied in the context of implementing atomic memory objects in large scale asynchronous distributed storage systems. When compared with the traditional replication based schemes, erasure codes have the…
The amount of digital data is rapidly growing. There is an increasing use of a wide range of computer systems, from mobile devices to large-scale data centers, and important for reliable operation of all computer systems is mitigating the…
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…
In an $(n,k,d)$ rack-aware storage model, the system consists of $n$ nodes uniformly distributed across $\bar{n}$ successive racks, such that each rack contains $u$ nodes of equal capacity and the reconstructive degree satisfies…
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node.…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
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…
Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an…
Centralized coded caching of popular contents is studied for users with heterogeneous distortion requirements, corresponding to diverse processing and display capabilities of mobile devices. Users' distortion requirements are assumed to be…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…
An error-erasure channel is a simple noise model that introduces both errors and erasures. While the two types of errors can be corrected simultaneously with error-correcting codes, it is also known that any linear code allows for first…