  Coded distributed computing has been considered as a promising technique
which makes large-scale systems robust to the "straggler" workers. Yet,
practical system models for distributed computing have not been available that
reflect the clustered or grouped structure of real-world computing servers.
Neither the large variations in the computing power and bandwidth capabilities
across different servers have been properly modeled. We suggest a group-based
model to reflect practical conditions and develop an appropriate coding scheme
for this model. The suggested code, called group code, employs parallel
encoding for each group. We show that the suggested coding scheme can
asymptotically achieve optimal computing time in regimes of infinite n, the
number of workers. While theoretical analysis is conducted in the asymptotic
regime, numerical results also show that the suggested scheme achieves
near-optimal computing time for any finite but reasonably large n. Moreover, we
demonstrate that the decoding complexity of the suggested scheme is
significantly reduced by the virtue of parallel decoding.
