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Considering the increasing demand for large-scale MapReduce distributed computing, coded distributed computing (CDC) has become a promising technology to reduce the significant bottleneck of MapReduce computation. Despite its importance, most of the works on CDC have assumed homogeneous environments, where the nodes have the same storage, computing, and communication capacities. However, since many practical scenarios involve heterogeneous environments, heterogeneous CDC design is highly demanded to reduce communication load. Under consideration of full heterogeneity among workers, this paper addresses the joint design of function assignment and coded shuffling to reduce communication load effectively. We first devise a new embedded index coding (EIC) solution for the device-to-device (D2D) environment and prove its optimality. By extending our novel approach, we propose …