In addition to the need for security, everyday information exchange must be able to cope with noise and interference. We discuss the noise robustness of a recently-introduced communications protocol inspired by the human cardiorespiratory interaction, based on analysis methods originally developed for reconstructing coupling functions between oscillatory processes underlying the biological signals. Security is assured by use of multiple, time-varying, coupling functions between two or more dynamical systems, and the protocol allows for multiplexing of the information transfer. We focus on the exceptional noise-robustness that arises from the application of dynamical Bayesian inference to the stochastic differential equations. A particular advantage of the protocol is that it facilitates an effective separation between the deterministic information signals and the dynamical (channel) noise perturbations. We define reliability in terms of the bit-error-rate (BER) as a function of noise strength, expressed as the signal-to-noise ratio (SNR). We present results confirming that the coupling function protocol is highly noise robust, and that it outperforms other known communications protocols. In the broader context, we point out that this use of coupling functions between dynamical systems is a modular construct that can be extended to implement a range of different encryption concepts. Similarly, the method of dynamical Bayesian inference carries wider implications for future applications to noise reduction in communications using other protocols.