Plate structures are widely adopted in many industries and instruments. Guided ultrasonic wave communication has unique advantages, as it can transmit over long distances in plates unaffected by electromagnetic interference. This is particularly beneficial in scenarios where electromagnetic waves are shielded or severely influenced, and where wired communication is difficult to deploy. Meanwhile, the main challenges in air-coupled guided ultrasonic wave communication are wave conversion and multimodal nonlinear interference. Motivated by these issues, this paper proposes an air-coupled Lamb waves based non-contact communication system, which uses deep neural networks to decode received signals and address nonlinear interference during wave propagation. Additionally, to address the issue of increased bit error rates (BER) caused by transmission channel variations, a strategy (Adaptive-BPSK) combining a feedback mechanism and binary phase-shift keying (BPSK) is proposed, enhancing communication stability and robustness. It is noteworthy that traditional cross-correlation methods cannot effectively decode in this system, but deep neural network based decoding can achieve a BER of 0.19%.