Related papers: On the Optimal Recovery Threshold of Coded Matrix …
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…
A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the…
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…
Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…
Coded computation is an emerging research area that leverages concepts from erasure coding to mitigate the effect of stragglers (slow nodes) in distributed computation clusters, especially for matrix computation problems. In this work, we…
We construct optimal secure coded distributed schemes that extend the known optimal constructions over fields of characteristic 0 to all fields. A serendipitous result is that we can encode \emph{all} functions over finite fields with a…
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst…
Distributed computing systems are well-known to suffer from the problem of slow or failed nodes; these are referred to as stragglers. Straggler mitigation (for distributed matrix computations) has recently been investigated from the…
We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a…
Multi-party computation (MPC) is promising for designing privacy-preserving machine learning algorithms at edge networks. An emerging approach is coded-MPC (CMPC), which advocates the use of coded computation to improve the performance of…
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…
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 $N$…
We present Modular Polynomial (MP) Codes for Secure Distributed Matrix Multiplication (SDMM). The construction is based on the observation that one can decode certain proper subsets of the coefficients of a polynomial with fewer evaluations…
We consider the problem of designing secure and private codes for distributed matrix-matrix multiplication. A master server owns two private matrices and hires worker nodes to help compute their product. The matrices should remain…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
In this paper, we present a novel variation of the coded matrix multiplication problem which we refer to as fully private grouped matrix multiplication (FPGMM). In FPGMM, a master wants to compute a group of matrix products between two…