Maximum A-Posteriori Decoding for Diffusion-Based Molecular Communication Using Analog Filters

Molecular communication is a promising approach to realize the communication between nanoscale devices. In a diffusion-based molecular communication network, transmitters and receivers communicate by using signalling molecules. The transmitter uses different time-varying functions of concentration of signalling molecules (called emission patterns) to represent different transmission symbols. The signalling molecules diffuse freely in the medium. The receiver is assumed to consist of a number of receptors, which can be in ON or OFF state. When the signalling molecules arrive at the receiver, they react with the receptors and switch them from OFF to ON state probabilistically. The receptors remain ON for a random amount of time before reverting to the OFF state. This paper assumes that the receiver uses the continuous history of receptor state to infer the transmitted symbol. Furthermore, it assumes that the transmitter uses two transmission symbols and approaches the decoding problem from the maximum a posteriori (MAP) framework. Specifically, the decoding is realized by calculating the logarithm of the ratio of the posteriori probabilities of the two transmission symbols, or log-MAP ratio. A contribution of this paper is to show that the computation of log-MAP ratio can be performed by an analog filter. The receiver can therefore use the output of this filter to decide which symbol has been sent. This analog filter provides insight on what information is important for decoding. In particular, the timing at which the receptors switch from OFF to ON state, the number of OFF receptors and the mean number of signalling molecules at the receiver are important. Numerical examples are used to illustrate the property of this decoding method.