  Graph neural network (GNN) is an efficient neural network model for graph
data and is widely used in different fields, including wireless communications.
Different from other neural network models, GNN can be implemented in a
decentralized manner with information exchanges among neighbors, making it a
potentially powerful tool for decentralized control in wireless communication
systems. The main bottleneck, however, is wireless channel impairments that
deteriorate the prediction robustness of GNN. To overcome this obstacle, we
analyze and enhance the robustness of the decentralized GNN in different
wireless communication systems in this paper. Specifically, using a GNN binary
classifier as an example, we first develop a methodology to verify whether the
predictions are robust. Then, we analyze the performance of the decentralized
GNN binary classifier in both uncoded and coded wireless communication systems.
To remedy imperfect wireless transmission and enhance the prediction
robustness, we further propose novel retransmission mechanisms for the above
two communication systems, respectively. Through simulations on the synthetic
graph data, we validate our analysis, verify the effectiveness of the proposed
retransmission mechanisms, and provide some insights for practical
implementation.
