Coding for edge-facilitated wireless distributed computing with heterogeneous users

We consider the edge-facilitated wireless distributed computing with three users, each communicating with the other two users via the help of an access point (AP) only. Motivated by the idea of MapReduce-based wireless coded distributed computing (CDC) proposed by Li et al. in [1] for homogeneous systems where each user's file storage size is identical, we attempt to extend MapReduce-based CDC to heterogeneous systems where each user has arbitrary file storage size. In this paper, we provide an achievable communication load region of the uplink-downlink transmission pair by appropriately designing file placement over the users and developing coding schemes at both the users and the AP. Moreover, we provide the converse for the communication load region, by decoupling the uplink and downlink transmissions. Finally, we provide a discussion on the shape of the load region for several examples and observations.