  In this paper, a new communication-efficient federated learning (FL)
framework is proposed, inspired by vector quantized compressed sensing. The
basic strategy of the proposed framework is to compress the local model update
at each device by applying dimensionality reduction followed by vector
quantization. Subsequently, the global model update is reconstructed at a
parameter server by applying a sparse signal recovery algorithm to the
aggregation of the compressed local model updates. By harnessing the benefits
of both dimensionality reduction and vector quantization, the proposed
framework effectively reduces the communication overhead of local update
transmissions. Both the design of the vector quantizer and the key parameters
for the compression are optimized so as to minimize the reconstruction error of
the global model update under the constraint of wireless link capacity. By
considering the reconstruction error, the convergence rate of the proposed
framework is also analyzed for a non-convex loss function. Simulation results
on the MNIST and FEMNIST datasets demonstrate that the proposed framework
provides more than a 2.4% increase in classification accuracy compared to
state-of-the-art FL frameworks when the communication overhead of the local
model update transmission is 0.1 bit per local model entry.
