发表机构
KTH Royal Institute of Technology（皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出HiCoMAC，一种基于计算导向调制设计的数字空中计算方法，利用排列不变性降低解码复杂度，并通过优化QAM星座提升计算精度，仿真验证其优于现有基线。
AI 中文摘要
如今，空中计算（AirComp）利用无线多址信道的波形叠加特性，直接从同时传输的信号中计算分布式数据的函数。本文提出了直方图状态编码多址计算（HiCoMAC），一种用于数字AirComp的全新卷积编码方法，它直接从编码和调制的用户信号的叠加中恢复算术和序列。HiCoMAC利用求和函数的排列不变性，通过占据各个编码器状态的用户数量来表示多用户卷积编码器状态。这一核心思想使得对数最大后验（MAP）直方图状态维特比解码能够实现，与联合全状态解码相比，状态复杂度显著降低。我们进一步引入了计算自由距离来区分产生不同算术和序列的直方图路径，并开发了用于其最短路径评估的加权乘积图。然后利用该距离来优化固定标记正交幅度调制（QAM）星座的矩形比，以提高计算精度。仿真结果表明，计算导向的调制设计增加了计算自由距离并降低了归一化均方误差（NMSE），而HiCoMAC在相同的传输和能量预算下优于所考虑的多符号数字AirComp基线。
英文摘要
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.
