One of the main focus in federated learning (FL) is the communication efficiency since a large number of participating edge devices send their updates to the edge server at each round of the model training. Existing works reconstruct each model update from edge devices and implicitly assume that the local model updates are independent over edge devices. In FL, however, the model update is an indirect multi-terminal source coding problem, also called as the CEO problem where each edge device cannot observe directly the gradient that is to be reconstructed at the decoder, but is rather provided only with a noisy version. The existing works do not leverage the redundancy in the information transmitted by different edges. This paper studies the rate region for the indirect multiterminal source coding problem in FL. The goal is to obtain the minimum achievable rate at a particular upper bound of gradient variance. We obtain the rate region for the quadratic vector Gaussian CEO problem under unbiased estimator and derive an explicit formula of the sum-rate-distortion function in the special case where gradient are identical over edge device and dimension. Finally, we analyse communication efficiency of convex Minibatched SGD and non-convex Minibatched SGD based on the sum-rate-distortion function, respectively.
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