1 Multi Ratio Shift Keying (MRSK) Modulation for Molecular Communication Boran A. Kilic, , O. B. Akan, Fellow, IEEE Abstract—Molecular Communication (MC) leverages the power of diffusion to transmit molecules from a transmitter to a receiver. A wide variety of modulation techniques based on molecule concentration, type, and release time have been extensively studied in the literature. In this paper, we propose a novel modulation technique that encodes the information into the relative concentrations of multiple molecules called Multi Ratio Shift Keying (MRSK) designed for diffusion-based MC without drift. We show that leveraging all possible ratios in a set of molecules can help mitigate the effects of intersymbol interference (ISI) and provide a flexible communication channel. To evaluate the performance of the MRSK, we develop a mathematical framework for studying the statistics of the ratio of random variables, focusing on noncentral Gaussian distributions. We then assess MRSK performance both analytically and through particle-based simulations under various channel conditions, identifying potential sources of error in our system model. Additionally, we conduct a comparative analysis of commonly used modulation schemes in the literature based on bit error rate (BER). The results show that MRSK significantly outperforms all traditional modulation schemes considered in this study in terms of BER. MRSK offers a promising, flexible, and more reliable communication method for the future of the MC paradigm. Index Terms—molecular communications, shift keying, mod- ulation, bit error rate, multi ratio shift keying, fixed threshold decoding, memory cancellation, ratio of random variables I. I NTRODUCTION M OLECULAR communication is a highly promising paradigm for realizing nano-networks, due to its bio- logically inspired approach and close resemblance to commu- nication mechanisms found in nature. Unlike electromagnetic communication systems, MC uses molecules as carriers of information, making it particularly suitable for medical and biological applications, including intrabody nano-networks for continuous health monitoring and targeted drug delivery [1], [2]. Among the various methods explored, diffusion-based MC has been widely studied. However, due to the inherent randomness of diffusion, such systems often face significant challenges, especially ISI, impacting reliability. Over the past decade, a range of modulation schemes have been introduced, primarily encoding information into three key molecular properties: concentration, molecule type, and release time. Modulation techniques such as On-Off Keying The authors are with the Center for neXt-generation Communications (CXC), Department of Electrical and Electronics Engineering, Koc¸ Uni- versity, Istanbul 34450, Turkey (e-mail: boran.kilic@std.bogazici.edu.tr, akan@ku.edu.tr). Ozgur B. Akan is also with the Internet of Everything (IoE) Group, Electrical Engineering Division, Department of Engineering, University of Cambridge, Cambridge, CB3 0FA, UK (email: oba21@cam.ac.uk). This work was supported by the AXA Research Fund (AXA Chair for Internet of Everything at Koc¸ University) (OOK) [3], Concentration Shift Keying (CSK) [4], Pulse Amplitude Modulation (PAM) [5], Molecule Shift Keying (MoSK) [6], and Release Time Shift Keying (RTSK) [7] have been widely explored and extensively studied in the literature. In this work, we depart from conventional techniques and focus on the novel concept of encoding information via relative ratios of different carrier molecules, which offers several distinct and practical advantages over traditional schemes. Research suggests that complex stimuli, such as odors, may be recognized in a concentration-invariant manner, relying primarily on ratio information. For example, studies have shown that rats are capable of distinguishing binary odor mixtures based on the molar ratios of the components, allow- ing the recognition of mixtures even at varying concentration levels [8]. In metabolic networks, the relative concentrations of enzymes and substrates can dictate the direction and rate of biochemical reactions. In glycolysis, the balance between ATP and ADP ratios (rather than their absolute quantities) affects regulatory enzyme activity, controlling the pathway’s overall flux. Additionally, when the diffusion coefficients of molecules are similar or nearly identical, their spatiotemporal distribution remains consistent, which is particularly benefi- cial for maintaining communication integrity under rapidly changing conditions. Furthermore, ratio-based MC allows the same ratio combination to be achieved with any number of molecules, providing flexibility in energy consumption, a critical advantage in resource-limited environments. To the best of our knowledge, the concept of ratio-based molecular communication is first introduced in Isomer Ratio Shift Keying (IRSK) [9], where it is presented as an extension of concentration-based modulation using isomers as messenger molecules. However, the statistical analysis in this study is limited. A more detailed statistical model is later developed in Ratio Shift Keying (RSK) for ligand binding in both stationary and mobile molecular communication systems [10]. Never- theless, these studies do not consider the impact of channel memory, assuming sufficiently large intervals. Additionally, in both works, encoding is limited to the ratio of two types of molecules, meaning only a single ratio is utilized to carry information. We argue that the effectiveness of ratio-based modulation increases as the number of molecule types used in- creases and introducing a general M-ary scheme presents great flexibility for different channel conditions. This is especially relevant in high data rate scenarios where symbol time can be extended by encoding more information in each symbol. Moreover, the statistical properties of the ratio of Gaussian random variables have not yet been thoroughly investigated in the context of molecular communication. We propose a novel modulation scheme, Multi Ratio Shift