  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 R/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.
