Entropy-Adaptive Federated Learning with Efficient Bit Allocation over Wireless Channels

A key bottleneck in federated learning (FL) is the high communication cost of transmitting large local model updates. This paper proposes Entropy-Adaptive FL (EA-FL), a novel framework that integrates information-theoretic coding into the FL pipeline to reduce the bit rate of encoded updates. In EA-FL, clients train local models under an entropy constraint on their updates, ensuring they are compressible and require fewer bits when entropy coded. Accounting for wireless channel imperfections, we analyze the statistical behavior of the decoded updates at the server and derive bounds on the first and second derivatives of the EA-FL loss function, establishing its Lipschitz continuity. These results enable a convergence analysis that explicitly captures the effects of quantization error, channel noise, and aggregation. Building on this, we develop an optimization framework for efficient bit allocation across clients under a fixed total quantization budget. Extensive experiments show that (i) EA-FL outperforms state-of-the-art quantized FL methods in rateaccuracy trade-offs, and (ii) the proposed bit allocation scheme significantly improves over uniform allocation under the same bit budget.