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arXiv · 2609.34808

HiCoMAC: Histogram-State Coded Multiple Access Computing via Computation-Oriented Modulation Design

Xiaojing Yan·Carlo Fischione
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Abstract

Nowadays, over-the-air computation (AirComp) exploits the waveform superposition property of the wireless multiple access channel to directly compute a function of distributed data from simultaneously transmitted signals. In this paper, we propose Histogram-State Coded Multiple Access Computing (HiCoMAC), a fundamentally new convolutional-coded method for digital AirComp that directly recovers the arithmetic-sum sequence from the superposition of coded and modulated user signals. HiCoMAC exploits the permutation invariance of the sum function to represent the multi-user convolutional encoder state by the numbers of users occupying the individual encoder states. This central idea enables log-max maximum a posterior (MAP) histogram-state Viterbi decoding with substantially reduced state complexity compared to joint full-state decoding. We further introduce the computational free distance to distinguish histogram paths that produce different arithmetic-sum sequences and develop a weighted product graph for its shortest path evaluation. This distance is then used to optimize the rectangular ratio of a fixed labeled quadrature amplitude modulation (QAM) constellation to improve the computational accuracy. Simulation results show that the computation-oriented modulation design increases the computational free distance and reduces the normalized mean square error (NMSE), while HiCoMAC outperforms the considered multi-symbol digital AirComp baselines under equal transmission and energy budgets.

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BibTeXRIS

Xiaojing Yan, Carlo Fischione. 2026-09-28. HiCoMAC: Histogram-State Coded Multiple Access Computing via Computation-Oriented Modulation Design. https://arxiv.org/abs/2609.34808

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