Analog Lagrange Coded Computing
Analog Lagrange Coded Computing
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DOI：
10.1109/jsait.2021.3056377
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
M. Soleymani;Hessam Mahdavifar;A. Avestimehr
中科院分区：
文献类型：
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作者：
M. Soleymani;Hessam Mahdavifar;A. Avestimehr
考虑了分布式计算方案，其中一组工人节点的计算能力用于通过分散在工人中的数据集上执行某些计算任务。众所周知的Lagrange多项式在这种情况下以有效的平行方式对数据集进行多项式评估，同时将数据的隐私保留在可能的工人中。将数据量化为有限的字段，因此，Shamir的秘密共享作为其主要的构建块之一，可以通过数据集的大小适当地扩展到该解决方案这是一个关键的问题，我们提出了将LCC的新型扩展到模拟域，称为模拟LCC（ALCC）。 {\ Mathbb C} $，但对于实际实现，我们使用了ALCC中数据的隐私，而与任何一定数量的工人相比信息安全性（MIS）指标。 ALCC及其隐私水平被观察到数字评估，我们实施了拟议的方案，以在一批材料上执行矩阵 - 矩阵乘法。假设这两个方案都使用相等数量的位来表示数据符号。
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 ${ \mathbb R}/ { \mathbb C}$ 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.