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Related papers: A Group Theoretic Construction of Batch Codes

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Coding theoretic approached have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade…

Information Theory · Computer Science 2020-08-04 Nicholas Woolsey , Rong-Rong Chen , Mingyue Ji

Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…

Quantum Physics · Physics 2017-04-11 Shota Nagayama

Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…

Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…

Machine Learning · Computer Science 2018-06-05 Jack Kosaian , K. V. Rashmi , Shivaram Venkataraman

Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…

Rings and Algebras · Mathematics 2018-04-04 Ted Hurley

Coded distributed batch computation distributes a computation task, such as matrix multiplication, $N$-linear computation, or multivariate polynomial evaluation, across $S$ servers through a coding scheme, such that the response from any…

Information Theory · Computer Science 2019-11-18 Zhuqing Jia , Syed A. Jafar

We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…

Combinatorics · Mathematics 2013-11-28 Hye Jung Kim , J. B. Nation , Anne V. Shepler

The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…

Group Theory · Mathematics 2023-08-29 María Isabel González Vasco , Delaram Kahrobaei , Eilidh McKemmie

Coded distributed computing (CDC) introduced by Li \emph{et al.} can greatly reduce the communication load for MapReduce computing systems. In the general cascaded CDC with $K$ workers, $N$ input files and $Q$ Reduce functions, each input…

Information Theory · Computer Science 2023-11-22 Minquan Cheng , Youlong Wu , Xianxian Li , Dianhua Wu

Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…

Information Theory · Computer Science 2025-11-26 Niccolò Brembilla , Yinbin Ma , Pietro Belotti , Federico Malucelli , Daniela Tuninetti

The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…

Information Theory · Computer Science 2019-01-15 Zitan Chen , Alexander Barg

In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes Hybrid LDPC codes. Although efficient optimization techniques…

Information Theory · Computer Science 2007-07-16 Lucile Sassatelli , David Declercq

Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family…

Information Theory · Computer Science 2014-10-21 Natalia Silberstein

We investigate block designs, under the A- and MV-criteria, when each treatment can have only one or two replications due to resource constraints, as can happen, for example, in early generation varietal trials. While these are commonly…

Statistics Theory · Mathematics 2026-03-25 R. A. Bailey , Rahul Mukerjee

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…

Information Theory · Computer Science 2021-01-01 Xiangliang Kong , Xin Wang , Gennnian Ge

We present new upper bounds on the parameters of batch codes with restricted query size. These bounds are an improvement on the Singleton bound. The techniques for derivations of these bounds are based on the ideas in the literature for…

Information Theory · Computer Science 2016-02-10 Hui Zhang , Vitaly Skachek

Error-correcting codes are essential for ensuring fault tolerance in modern distributed data storage systems. However, in practice, factors such as the failure rates of storage devices can vary significantly over time, resulting in changes…

Information Theory · Computer Science 2025-04-22 Haoming Shi , Weijun Fang , Yuan Gao

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…

Information Theory · Computer Science 2015-12-23 Can Xiang

This paper studies the caching system of multiple cache-enabled users with random demands. Under nonuniform file popularity, we thoroughly characterize the optimal uncoded cache placement structure for the coded caching scheme (CCS).…

Information Theory · Computer Science 2022-07-28 Yong Deng , Min Dong

We consider the recently proposed Coded Distributed Computing (CDC) framework that leverages carefully designed redundant computations to enable coding opportunities that substantially reduce the communication load of distributed computing.…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-04 Mehrdad Kiamari , Chenwei Wang , A. Salman Avestimehr