We propose a task-oriented multiuser wireless communication framework for distributed classification based on a MAP-driven system design under wireless channel impairments. \textcolor{black}{By deriving tractable approximations of the MAP error bound}, the proposed approach enables the design of learning-based feature extraction and precoding strategies. Unlike existing approaches that optimize intermediate reconstruction, information-theoretic, or feature-separability objectives, the proposed formulation directly optimizes objectives derived from the MAP decision error, thereby providing a more direct connection to the final classification performance. Simulation results demonstrate that the proposed schemes achieve higher classification accuracy than their counterparts, with lower or comparable computational complexity.

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