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arXiv 2007.15480cs.ITeess.SPmath.IT
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无线信道下的远程分类容量

Capacity of Remote Classification Over Wireless Channels

Qiao Lan, Yuqing Du, Petar Popovski, Kaibin Huang

摘要:

无线连接创建了一个融合通信和推理的计算范例。在这个范例中的基本操作是设备将分类任务卸载到边缘服务器的操作。我们将这种远程分类称为智能应用。无线信道有限且可变的数据率对远程分类提出了挑战,这影响了传输高维特征的能力,从而限制了分类分辨率。我们引入了一组指标的分类能力的名称下,被定义为类的最大数量,可以辨别在一个给定的通信信道,同时满足目标分类错误概率。我们的目标是选择一个子集的类从一个图书馆,提供令人满意的性能在给定的通道。我们对待两种情况下的子集选择。首先,设备可以通过修剪类库来选择子集,直到达到满足目标错误概率的子集,同时最大化分类容量。采用子空间数据模型,证明了分类容量最大化与格拉斯曼装箱的等价性。结果表明,分类容量与瞬时通信速率呈指数增长,与每个数据簇的维数呈超指数增长。如果瞬时速率分别用平均速率和固定速率代替,则这也适用于具有衰落的遍历和中断容量。在第二种情况下,一个设备有一个优先级的类子集的每一个通信速率,这是建模为均匀采样库的实例。在没有类选择的情况下,分类容量及其遍历和中断对应物被证明与其相应的通信速率成线性比例,而不是在最后一种情况下的指数增长。

英文摘要:

Wireless connectivity creates a computing paradigm that merges communication and inference. A basic operation in this paradigm is the one where a device offloads classification tasks to the edge servers. We term this remote classification, with a potential to enable intelligent applications. Remote classification is challenged by the finite and variable data rate of the wireless channel, which affects the capability to transfer high-dimensional features and thus limits the classification resolution. We introduce a set of metrics under the name of classification capacity that are defined as the maximum number of classes that can be discerned over a given communication channel while meeting a target classification error probability. The objective is to choose a subset of classes from a library that offers satisfactory performance over a given channel. We treat two cases of subset selection. First, a device can select the subset by pruning the class library until arriving at a subset that meets the targeted error probability while maximizing the classification capacity. Adopting a subspace data model, we prove the equivalence of classification capacity maximization to Grassmannian packing. The results show that the classification capacity grows exponentially with the instantaneous communication rate, and super-exponentially with the dimensions of each data cluster. This also holds for ergodic and outage capacities with fading if the instantaneous rate is replaced with an average rate and a fixed rate, respectively. In the second case, a device has a preference of class subset for every communication rate, which is modeled as an instance of uniformly sampling the library. Without class selection, the classification capacity and its ergodic and outage counterparts are proved to scale linearly with their corresponding communication rates instead of the exponential growth in the last case.

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