In this paper, we introduce the Age of Incorrect Information (AoII) as an
enabler for semantics-empowered communication, a newly advocated communication
paradigm centered around data's role and its usefulness to the communication's
goal. First, we shed light on how the traditional communication paradigm, with
its role-blind approach to data, is vulnerable to performance bottlenecks.
Next, we highlight the shortcomings of several proposed performance measures
destined to deal with the traditional communication paradigm's limitations,
namely the Age of Information (AoI) and the error-based metrics. We also show
how the AoII addresses these shortcomings and captures more meaningfully the
purpose of data. Afterward, we consider the problem of minimizing the average
AoII in a transmitter-receiver pair scenario. We prove that the optimal
transmission strategy is a randomized threshold policy, and we propose an
algorithm that finds the optimal parameters. Furthermore, we provide a
theoretical comparison between the AoII framework and the standard error-based
metrics counterpart. Interestingly, we show that the AoII-optimal policy is
also error-optimal for the adopted information source model. Concurrently, the
converse is not necessarily true. Finally, we implement our policy in various
applications, and we showcase its performance advantages compared to both the
error-optimal and the AoI-optimal policies.

介绍了错误信息时代（Age of Incorrect Information，AoII）的概念，提出该概念作为一种基于数据角色和数据所扮演角色重要性的通讯范式。研究了传统通讯模式的局限性、AoI 和基于错误的度量方式的不足之处，探讨了 AoII 的性能优势，收敛于基于阈值的随机策略，并将其应用于各种场景验证了其性能优势。

错误信息的时代：语义强化通信的推动者

The Age of Incorrect Information: an Enabler of Semantics-Empowered  Communication

Federated learning is a privacy-preserving approach to train a global model
at a central server by collaborating with wireless devices, each with its own
local training data set. In this paper, we present a compressive sensing
approach for federated learning over massive multiple-input multiple-output
communication systems in which the central server equipped with a massive
antenna array communicates with the wireless devices. One major challenge in
system design is to reconstruct local gradient vectors accurately at the
central server, which are computed-and-sent from the wireless devices. To
overcome this challenge, we first establish a transmission strategy to
construct sparse transmitted signals from the local gradient vectors at the
devices. We then propose a compressive sensing algorithm enabling the server to
iteratively find the linear minimum-mean-square-error (LMMSE) estimate of the
transmitted signal by exploiting its sparsity. We also derive an analytical
threshold for the residual error at each iteration, to design the stopping
criterion of the proposed algorithm. We show that for a sparse transmitted
signal, the proposed algorithm requires less computationally complexity than
LMMSE. Simulation results demonstrate that the presented approach outperforms
conventional linear beamforming approaches and reduces the performance gap
between federated learning and centralized learning with perfect
reconstruction.

本文提出了一种基于压缩感知的联邦学习算法，通过传输策略构造稀疏的梯度向量信号，利用压缩感知算法迭代地求解线性最小均方误差 (LMMSE) 估计量。通过仿真实验，证明了该方法在无线设备通信系统中具有比传统线性波束赋形方法更好的性能，并减小了联邦学习和中央学习的性能差距。