Analog Lagrange Coded Computing

A distributed computing scenario is considered, where the computational power of a set of worker nodes is used to perform a certain computation task over a dataset that is dispersed among the workers. Lagrange coded computing (LCC), proposed by Yu et al. , leverages the well-known Lagrange polynomia...

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Vydáno v:IEEE journal on selected areas in information theory Ročník 2; číslo 1; s. 283 - 295
Hlavní autoři: Soleymani, Mahdi, Mahdavifar, Hessam, Avestimehr, A. Salman
Médium: Journal Article
Jazyk:angličtina
Vydáno: Piscataway IEEE 01.03.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Accuracy
analog coding
Coded computing
Computer networks
Cryptography
Data privacy
Datasets
Distributed processing
Fields (mathematics)
Floating point arithmetic
Machine learning
Measurement
Multiplication
Polynomials
Privacy
privacy-preserving computing
Protocols
Security
Task analysis
Workers
ISSN:2641-8770, 2641-8770
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Popis
Shrnutí:A distributed computing scenario is considered, where the computational power of a set of worker nodes is used to perform a certain computation task over a dataset that is dispersed among the workers. Lagrange coded computing (LCC), proposed by Yu et al. , leverages the well-known Lagrange polynomial to perform polynomial evaluation of the dataset in such a scenario in an efficient parallel fashion while keeping the privacy of data amidst possible collusion of workers. This solution relies on quantizing the data into a finite field, so that Shamir's secret sharing, as one of its main building blocks, can be employed. Such a solution, however, is not properly scalable with the size of dataset, mainly due to computation overflows. To address such a critical issue, we propose a novel extension of LCC to the analog domain, referred to as analog LCC (ALCC). All the operations in the proposed ALCC protocol are done over the infinite fields of <inline-formula> <tex-math notation="LaTeX">{ \mathbb R}/ { \mathbb C} </tex-math></inline-formula> but for practical implementations floating-point numbers are used. We characterize the privacy of data in ALCC, against any subset of colluding workers up to a certain size, in terms of the distinguishing security (DS) and the mutual information security (MIS) metrics. Also, the accuracy of outcome is characterized in a practical setting assuming operations are performed using floating-point numbers. Consequently, a fundamental trade-off between the accuracy of the outcome of ALCC and its privacy level is observed and is numerically evaluated. Moreover, we implement the proposed scheme to perform matrix-matrix multiplication over a batch of matrices. It is observed that ALCC is superior compared to the state-of-the-art LCC, implemented using fixed-point numbers, assuming both schemes use an equal number of bits to represent data symbols.
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ISSN:2641-8770
2641-8770
DOI:10.1109/JSAIT.2021.3056377