Simultaneous Computation and Communication over MAC
CoRR(2024)
Abstract
We study communication over a Gaussian multiple-access channel (MAC) with two
types of transmitters: Digital transmitters hold a message from a discrete set
that needs to be communicated to the receiver. Analog transmitters hold
sequences of analog values, and some function of these distributed values (but
not the values themselves) need to be conveyed to the receiver. For the digital
messages, it is required that they can be decoded error free at the receiver
with high probability while the recovered analog function values have to
satisfy a fidelity criterion such as an upper bound on mean squared error (MSE)
or a certain maximum error with a given confidence. For the case in which the
computed function for the analog transmitters is a sum of values in [-1,1], we
derive inner and outer bounds for the tradeoff of digital and analog rates of
communication under peak and average power constraints for digital transmitters
and a peak power constraint for analog transmitters. We then extend the
achievability part of our result to a larger class of functions that includes
all linear, but also some non-linear functions.
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