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 channel decoding 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 provided 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 an existing approach.
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