We propose a task-oriented multiuser wireless communication framework for distributed classification based on a MAP-driven system design under wireless channel impairments. By deriving a tractable class-mean separation objective, the proposed approach enables low-complexity design of both learning-based feature extraction and precoding strategies. Unlike existing covariance-based and reconstruction-oriented methods, the proposed formulation avoids repeated covariance inversions and eigen-decomposition operations while directly improving class separability after channel distortion. Simulation results demonstrate that the proposed method achieves higher classification accuracy than existing schemes, while simultaneously reducing computational complexity.

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