The increasing amount of data generated at the edge/client nodes and the privacy concerns have resulted in learning at the edge, in which the computations are performed at edge devices and are communicated to a central node for updating the model. The edge nodes have low bandwidth and may be available only intermittently. There are helper nodes present in the network that aid the edge nodes in the communication to the server. The edge nodes communicate the local gradient to helper nodes which relay these messages to the central node after possible aggregation. Recently, schemes using repetition codes and maximum-distance-separable (MDS) codes, respectively known as Aligned MDS Coding (AMC) scheme and Aligend Repetition Coding (ARC) scheme, were proposed. It was observed that in AMC scheme the communication between edge nodes and helper nodes is optimal but with an increased cost of communication between helper and master. An upper bound on the communication cost between helpers and master was obtained. In this paper, a tradeoff between communication costs at edge nodes and helper nodes is established with the help of pyramid codes, a well-known class of locally repairable codes. The communication costs at both the helper nodes and edge nodes are exactly characterized. Using the developed technique, the exact communication cost at helper nodes can be computed for the scheme using MDS codes. In the end, we provide two improved aggregation strategies for the existing AMC and ARC schemes, yielding significant reduction in communication cost at helpers, without changing any of the code parameters.

中文翻译：

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编码渐变聚合：边缘节点和辅助节点上的通信成本之间的权衡

在边缘/客户端节点处生成的数据量的增加以及对隐私的关注已导致在边缘进行学习，其中在边缘设备处执行计算，并将计算结果传达给中央节点以更新模型。边缘节点具有低带宽，并且可能仅间歇性地可用。网络中存在帮助节点，以帮助边缘节点与服务器进行通信。边缘节点将本地梯度传递给辅助节点，该辅助节点在可能的聚合之后将这些消息中继到中心节点。最近，提出了使用重复码和最大距离可分离（MDS）码的方案，分别称为对准MDS编码（AMC）方案和Aligend重复编码（ARC）方案。已经观察到，在AMC方案中，边缘节点和辅助节点之间的通信是最佳的，但是辅助节点和主节点之间的通信成本增加。求助者和主人之间的通信成本达到了一个上限。在本文中，借助金字塔代码（一种众所周知的本地可修复代码）在边缘节点和辅助节点之间的通信成本之间进行权衡。准确描述了辅助节点和边缘节点的通信成本。使用开发的技术，可以使用MDS代码为该方案计算辅助节点上的确切通信成本。最后，我们为现有的AMC和ARC方案提供了两种改进的聚合策略，在不更改任何代码参数的情况下，大大降低了助手的通信成本。