The fog computing architecture is considered to be one of the important directions of the Internet of Things. The key problems on the theoretical study and industrial implement of fog computing network are: 1) how to establish a fog computing system model and extract key system parameters, such as communication rate (regions), communication delay, computing performance and storage resources; 2) how to theoretically establish the fundmamental limits of these parameters. In our work, we try to address these two questions from information theor perspective. We firstly studied various networks including multicast network and relay broadcast channels, and proposed lower (inner) and upper (outer) bounds on the capacity (region), by which we established capacity (region) for some special channels. Then, we dervied order optimal trade-off between the communication delay and caching storage for relay network and server-aided device-to-device (D2D) network, respectively. Our work could provide theoretical guidance for the industrialization of fog computing networks
A. Capacity results on multi-terminal network:
We studied discrete memoryless multicast network and relay broadcast channel. New coding schemes are proposed to improve the best known schemes. Inner and outer bounds are established on the capacity (regions) which shows that our schemes are optimal form some special channels, e.g., degraded relay broadcast channels.
B. Trade-off between communication and caching in Fog networks:
We developed coded caching schemes for the server-aided D2D network and a two-layer caching-aided network, repsetively. For each considered setup, we proved that the proposed caching scheme is order optimal and can further reduce the transmission delay compared to the previously known caching schemes.