Task-oriented communication improves communication efficiency by transmitting semantic information required for downstream tasks, but may incur redundancy with previously transmitted information. To address this issue, we propose a variational directed information bottleneck joint source-channel coding (VDIB-JSCC) framework that transmits only previously unacquired information. Specifically, we use directed information to characterize the causal flow of task-relevant incremental information and theoretically demonstrate its advantages over mutual information and conditional mutual information. Based on this metric, we formulate a directed information bottleneck (DIB) objective that balances task-relevant information preservation and redundant information compression. We further derive a variational formulation, termed VDIB, whose tractable upper bound serves as the training loss. The encoder integrates a Vision Transformer for frame-wise semantic extraction and a Mamba-based causal state-space model for capturing temporal dependencies and extracting incremental information, while the decoder uses a Mamba-based state-space model for task inference. Experiments on CIFAR-10 and CIFAR-100 video streams demonstrate that VDIB-JSCC achieves higher classification accuracy with less transmitted information than state-of-the-art semantic communication methods. These results show that leveraging historical knowledge enables task completion with less information, improving communication efficiency.

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