Deep joint source--channel coding (Deep JSCC) enables visual semantic transmission by mapping inputs directly to channel symbols and task outputs, but its performance can deteriorate under distribution shifts between training and deployment domains. We study single-source domain adaptation for task-oriented Deep JSCC and formulate a classification-capacity-invariance (CCI) function to characterize how the available channel capacity and class-conditional cross-domain invariance affect target domain classification accuracy. A scalar linear analysis of source-domain-optimal solutions and a controlled shallow nonlinear validation show that target domain classification accuracy can vary non-monotonically with the invariance constraint and with available capacity along separate control paths obtained by varying the transmitted dimension or CSNR. We then propose a domain-adaptive Deep JSCC framework that combines pseudo-label-based class-level adversarial alignment with supervised contrastive learning on confidence-filtered target samples. Experiments on digit and PACS datasets over AWGN and Rayleigh fading channels demonstrate improved target domain generalization without introducing additional inference-time networks. On SVHN $\rightarrow$ MNIST, the proposed method achieves 98.15\% target-domain accuracy at a CSNR of 10 dB.

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