The Asymmetric-Distance Metrics for Decoding of Convolutional Codes in Diffusion-Based Molecular Communications

In this paper, we focus on the channel coding for diffusion-based molecular communications (MC) with information conveyed in the time of molecules released. The symbol error probability (SEP) is theoretically derived for multiple channel use. The conception called asymmetric-distance is introduced as the metric from the transmitted codeword to the received codeword. A new decoding scheme based on asymmetric-distance is proposed for convolutional codes, which significantly enhances the communication reliability. Biological circuits for the implementation of the proposed channel coding scheme in MC systems are designed by bio-nanomachines. The theoretical analysis indicates that the proposed decoding scheme provides an approximately maximum likelihood estimation. Compared with uncoded systems, Hamming codes, convolutional codes based on Hamming distance (CCHD) and some new coding schemes for molecular communications, numerical results show that the proposed convolutional codes based on asymmetric-distance (CCAD) offer better bit error ratio (BER) performance with the same throughput. The simulation results illustrate that the proposed channel coding scheme is efficient for a larger range of channel environment than other conventional channel coding schemes.