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In this paper, we propose CodedSketch, as a distributed straggler-resistant scheme to compute an approximation of the multiplication of two massive matrices. The objective is to reduce the recovery threshold, defined as the total number of…
This paper establishes the rate region for a class of source coding function computation setups where sources of information are available at the nodes of a tree and where a function of these sources must be computed at the root. The rate…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
Coded Distributed Matrix Multiplication (CDMM) is a distributed matrix multiplication (DMM) for large-scale matrices through a coding scheme such that any $R$ worker node among all $N$ worker nodes can recover the final product, where $N$…
Large matrix multiplications are central to large-scale machine learning applications. These operations are often carried out on a distributed computing platform with a master server and multiple workers in the cloud operating in parallel.…
Galois field arithmetic circuits find application in a range of domains including error correction codes, communications, signal processing, and security engineering. This paper aims to elucidate the importance of error detection and…
We study Reed--Solomon codes over arbitrary fields, inspired by several recent papers dealing with Gabidulin codes over fields of characteristic zero. Over the field of rational numbers, we derive bounds on the coefficient growth during…
We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which…
Motivated by a concept studied in [1], we consider a property of matrices over finite fields that generalizes triangular totally nonsingular matrices to block matrices. We show that (1) matrices with this property suffice to construct good…
We consider a generalization of the gradient coding framework where a dataset is divided across $n$ workers and each worker transmits to a master node one or more linear combinations of the gradients over its assigned data subsets. Unlike…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
This paper presents a new erasure code called Treeplication designed for distributed recovery of the full information word, while most prior work in coding for distributed storage only supports distributed repair of individual symbols. A…
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…
The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Distributed matrix computations -- matrix-matrix or matrix-vector multiplications -- are well-recognized to suffer from the problem of stragglers (slow or failed worker nodes). Much of prior work in this area is (i) either sub-optimal in…
Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…