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Machine learning methods are ubiquitous in communication systems and have proven powerful for applications including radio-frequency (RF) fingerprinting, automatic modulation classification, and signal recovery in communication systems. However, the high throughput requirement of a communication link makes AI models difficult to implement in real-time on edge devices. In this work, we address this issue by improving both the algorithm and hardware to target real-time AI processing in communication systems. For algorithm development, we propose the first compact deep network consisting of a silicon photonic recurrent neural network model in combination with a simplified convolutional neural network classifier to identify RF emitters by their random transmissions. Our model achieves 96.32% classification accuracy over a set of 30 identical ZigBee devices when using 50 times fewer training parameters than an existing state-of-the-art CNN classifier (Merchant et al., 2018). Thanks to the large reduction in network size, we emulate the system using a small-scale FPGA board, the PYNQ-Z1, and demonstrate real-time RF fingerprinting with 0.219 ms latency. In addition, for hardware implementation, we further demonstrate a fully-integrated silicon photonic neural network for fiber nonlinearity compensation (Huang et al., 2021), which improves the received signal by 0.60 dB.