Related papers: Optimal Secure Coded Distributed Computation over …
We consider a coded distributed computing problem in a ring-based communication network, where $N$ computing nodes are arranged in a ring topology and each node can only communicate with its neighbors within a constant distance $d$. To…
We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching…
The classical family of $[n,k]_q$ Reed-Solomon codes over a field $\F_q$ consist of the evaluations of polynomials $f \in \F_q[X]$ of degree $< k$ at $n$ distinct field elements. In this work, we consider a closely related family of codes,…
We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…
Computationally efficient matrix multiplication is a fundamental requirement in various fields, including and particularly in data analytics. To do so, the computation task of a large-scale matrix multiplication is typically outsourced to…
Coded distributed computing has been considered as a promising technique which makes large-scale systems robust to the "straggler" workers. Yet, practical system models for distributed computing have not been available that reflect the…
Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not…
Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage…
We propose a distributed algorithm based on Alternating Direction Method of Multipliers (ADMM) to minimize the sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead…
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…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
The sum-rank metric is a hybrid between the Hamming metric and the rank metric and suitable for error correction in multishot network coding and distributed storage as well as for the design of quantum-resistant cryptosystems. In this work,…
Coded computing has proved to be useful in distributed computing. We have observed that almost all coded computing systems studied so far consider a setup of one master and some workers. However, recently emerging technologies such as…