Distributed computing frameworks such as MapReduce and Spark are often used to process large-scale data computing jobs. In wireless scenarios, exchanging data among distributed nodes would seriously suffer from the communication bottleneck due to limited communication resources such as bandwidth and power. To address this problem, we propose a coded parallel computing (CPC) scheme for distributed computing systems where distributed nodes exchange information over a half-duplex wireless interference network. The CPC scheme achieves the multicast gain by utilizing coded computing to multicast coded symbols {intended to} multiple receiver nodes and the cooperative transmission gain by allowing multiple {transmitter} nodes to jointly deliver messages via interference alignment. To measure communication performance, we apply the widely used latency-oriented metric: \emph{normalized delivery time (NDT)}. It is shown that CPC can significantly reduce the NDT by jointly exploiting the parallel transmission and coded multicasting opportunities. Surprisingly, when $K$ tends to infinity and the computation load is fixed, CPC approaches zero NDT while all state-of-the-art schemes achieve positive values of NDT. Finally, we establish an information-theoretic lower bound for the NDT-computation load trade-off over \emph{half-duplex} network, and prove our scheme achieves the minimum NDT within a multiplicative gap of $3$, i.e., our scheme is order optimal.

翻译：MapReduce和Spark等分布式计算框架常被用于处理大规模数据计算任务。在无线场景中，受限通信资源（如带宽与功率）将导致分布式节点间的数据交换严重受制于通信瓶颈。针对该问题，我们提出一种适用于半双工无线干扰网络中分布式节点间信息交换的编码并行计算（CPC）方案。该方案通过编码计算向多个接收节点组播编码符号以获得组播增益，同时允许多个发送节点利用干扰对齐联合传输消息以获取协作传输增益。为衡量通信性能，我们采用广泛使用的延迟导向指标：归一化传输时间（NDT）。研究表明，CPC通过联合利用并行传输与编码组播机会可显著降低NDT。令人惊讶的是，当K趋于无穷且计算负载固定时，CPC的NDT趋近于零，而现有最优方案仍为正值。最后，我们建立了半双工网络下NDT-计算负载权衡的信息论下界，并证明所提方案可在3倍乘法因子内达到最小NDT，即实现顺序最优性。