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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…
A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. A family of linear LRC codes that generalize the classic construction of…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
We consider the problem of evaluating arbitrary multivariate polynomials over a massive dataset containing multiple inputs, on a distributed computing system with a master node and multiple worker nodes. Generalized Lagrange Coded Computing…
This paper introduces new constructions of sum-rank metric codes derived from algebraic function fields, as existing results on such codes remain limited. A major challenge lies in the determination of their parameters. We address this…
In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of $A^n$, where $A$ is an arbitrary finite set. Three classes of…
In this paper, we extend the work of Abbondati et al. (2024) on decoding simultaneous rational function codes by addressing two important scenarios: multiplicities and poles (zeros of denominators). First, we generalize previous results to…
Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on…
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms.…
In coding theory, a very interesting problem (but at the same time, a very difficult one) is to determine the weight distribution of a given code. This problem is even more interesting for cyclic codes, and this is so, mainly because they…
We consider the problem of secure distributed matrix multiplication (SDMM). Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against workers and boosting the…
A code is locally recoverable when each symbol in one of its code words can be reconstructed as a function of $r$ other symbols. We use bundles of projective spaces over a line to construct locally recoverable codes with availability; that…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
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…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…
Due to the rapid growth of data and computational resources, distributed optimization has become an active research area in recent years. While first-order methods seem to dominate the field, second-order methods are nevertheless attractive…
Local Reconstruction Codes (LRCs) allow for recovery from a small number of erasures in a local manner based on just a few other codeword symbols. A maximally recoverable (MR) LRC offers the best possible blend of such local and global…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…