  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.
