  In large scale distributed computing systems, communication overhead is one
of the major bottlenecks. In the map-shuffle-reduce framework, which is one of
the major distributed computing frameworks, the communication load among
servers can be reduced by increasing the computation load of each server, that
is, there is a trade-off between computation load and communication load.
Recently, it has been shown that coded distributed computing (CDC) improves
this trade-off relationship by letting servers encode their intermediate
computation results. The original CDC scheme does not assume any special
structures on the functions that servers compute. However, in actual problems,
these functions often have some structures, and the trade-off relation may be
further improved by using that structures. In this paper, we propose a new
scheme that further improves the trade-off relationship by utilizing the linear
dependency structure of the intermediate computation results. The intermediate
values computed in the map phase can be considered as vectors on
$\mathbb{F}_{2}$. In some applications, these intermediate values have a linear
dependency and in such cases, it is sufficient for each server to send a basis
of the linear subspace and linear combination coefficients. As a result, the
proposed approach improves over the best-known computation-communication
overhead trade-off in some applications.
