  One of the most critical challenges for deploying distributed learning
solutions, such as federated learning (FL), in wireless networks is the limited
battery capacity of mobile clients. While it is a common belief that the major
energy consumption of mobile clients comes from the uplink data transmission,
this paper presents a novel finding, namely the channel decoding operation also
contributes significantly to the overall energy consumption of mobile clients
in FL. Motivated by this new observation, we propose an energy-efficient
adaptive channel decoding scheme that leverages the intrinsic robustness of FL
to model errors. In particular, the robustness is exploited to reduce the
energy consumption of channel decoders at mobile clients by adaptively
adjusting the number of decoding iterations. We theoretically prove that
wireless FL with communication errors can converge at the same rate as the case
with error-free communication as long as the bit error rate (BER) is properly
constrained. An adaptive channel decoding scheme is then proposed to improve
the energy efficiency of wireless FL systems. Experimental results demonstrate
that the proposed method maintains the same learning accuracy while reducing
the channel decoding energy consumption by 20% when compared to existing
approaches.
