Simultaneous Computation and Communication Over MAC

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 with vanishing error probability. Analog transmitters hold sequences of analog values. Some funct...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 71; no. 5; pp. 3644 - 3665
Main Authors Frey, Matthias, Bjelakovic, Igor, Gastpar, Michael C., Zhu, Jingge
Format Journal Article
LanguageEnglish
Published IEEE 01.05.2025
Subjects
Digital communication
Encoding
Fading channels
Gaussian channels
multiple-access channels
over-the-air computation
Parity check codes
Receivers
semantic communication
Sensors
Signal to noise ratio
Transmitters
Wireless communications
Wireless networks
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Summary: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 with vanishing error probability. Analog transmitters hold sequences of analog values. Some functions of these distributed values (but not the values themselves) need to be conveyed to the receiver, subject to a fidelity criterion such as mean squared error (MSE) or a certain maximum error with given confidence. For the case in which the computed function for the analog transmitters is a sum of values in <inline-formula> <tex-math notation="LaTeX">[-1,1] </tex-math></inline-formula>, 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 result to a class of functions that includes all linear and some non-linear functions. This extended scheme works over fading channels as long as full channel state information is available at the transmitter. The practicality of our proposed communication scheme is shown in channel simulations that use a version of the scheme based on low density parity check (LDPC) coding. We evaluate the system performance for different block lengths and Gaussian as well as non-Gaussian noise distributions.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2025.3542673