Multimodal learning commonly assumes paired or synchronized observations, yet independently collected datasets rarely provide such correspondence. We introduce CIIR, a modular encoder--decoder framework that connects heterogeneous datasets through a class-indexed address space while preserving each dataset's native input format and output module. A known local index selects address $k$, and an input-dependent 128-dimensional address representation Z_k(x) is written to that address. To demonstrate CIIR, we learn this address space from handwritten digits, clothing images, spoken-digit spectrograms, and hand signs without synchronized or instance-matched samples. Newly trained label-free receivers recover the requested addresses with 94.7% macro-average Address Realization Accuracy. We then attach the unseen SVHN dataset after freezing the base address space and train only lightweight adapters, achieving 90.2% MNIST>SVHN and 82.3% SVHN>MNIST end-to-end Address Transfer Accuracy without target-side decoder labels. To demonstrate generalizability of CIIR, we reuse the ten addresses as code elements in collision-free arithmetic and hierarchical address codes for all 100 CIFAR-100 classes and evaluate direct arithmetic-code realization through the existing receivers. These results establish CIIR as a compact interface for modular cross-dataset communication and post-hoc dataset attachment without exhaustive paired multimodal supervision.

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