We discuss a federated learned compression problem, where the goal is to learn a compressor from real-world data which is scattered across clients and may be statistically heterogeneous, yet share a common underlying representation. We propose a distributed source model that encompasses both characteristics, and naturally suggests a compressor architecture that uses analysis and synthesis transforms shared by clients. Inspired by personalized federated learning methods, we employ an entropy model that is personalized to each client. This allows for a global latent space to be learned across clients, and personalized entropy models that adapt to the clients' latent distributions. We show empirically that this strategy outperforms solely local methods, which indicates that learned compression also benefits from a shared global representation in statistically heterogeneous federated settings.

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