  In many distributed learning setups such as federated learning (FL), client
nodes at the edge use individually collected data to compute local gradients
and send them to a central master server. The master server then aggregates the
received gradients and broadcasts the aggregation to all clients, with which
the clients can update the global model. In this paper, we consider
multi-server federated learning with secure aggregation and unreliable
communication links. We first define a threat model using Shannon's
information-theoretic security framework and propose a novel scheme called
Lagrange Coding with Mask (LCM), which divides the servers into groups and uses
Coding and Masking techniques. LCM can achieve a trade-off between the uplink
and downlink communication loads by adjusting the number of servers in each
group. Furthermore, we derive the lower bounds of the uplink and downlink
communication loads, respectively, and prove that LCM achieves the optimal
uplink communication load, which is unrelated to the number of collusion
clients.
