  The increasing amount of data generated at the edge/client nodes and the
privacy concerns have resulted in learning at the edge, in which the
computations are performed at edge devices and are communicated to a central
node for updating the model. The edge nodes have low bandwidth and may be
available only intermittently. There are helper nodes present in the network
that aid the edge nodes in the communication to the server. The edge nodes
communicate the local gradient to helper nodes which relay these messages to
the central node after possible aggregation. Recently, schemes using repetition
codes and maximum-distance-separable (MDS) codes, respectively known as Aligned
MDS Coding (AMC) scheme and Aligend Repetition Coding (ARC) scheme, were
proposed. It was observed that in AMC scheme the communication between edge
nodes and helper nodes is optimal but with an increased cost of communication
between helper and master. An upper bound on the communication cost between
helpers and master was obtained. In this paper, a tradeoff between
communication costs at edge nodes and helper nodes is established with the help
of pyramid codes, a well-known class of locally repairable codes. The
communication costs at both the helper nodes and edge nodes are exactly
characterized. Using the developed technique, the exact communication cost at
helper nodes can be computed for the scheme using MDS codes. In the end, we
provide two improved aggregation strategies for the existing AMC and ARC
schemes, yielding significant reduction in communication cost at helpers,
without changing any of the code parameters.
