in Proc. ACM Int. Conf. on Nanoscale Computing and Communication (NANOCOM), Dublin, Ireland, Sep. 2019, pp. 1–6.
Abstract: This paper discusses and compares the performance of existing mod-
ulation schemes in diffusion-based molecular communication systems by means of extrinsic information transfer chart and bit error rate analysis. Additionally, a new modulation scheme called variable concentration shift keying is introduced with proven advantage over conventional concentration shift keying in terms of bit error rate performance.
[DS+19] M. Damrath, M. Schurwanz, and P. A. Hoeher, “The turbo principle in molecular communications,” in Proc. Int. ITG-Conf. on Systems, Commu- nications and Coding (SCC), Rostock, Germany, Feb. 2019, pp. 1–6.
Abstract: This work introduces the turbo principle into the area of diffusion-
based molecular communication (DBMC). By means of bit-interleaved coded modulation (BICM) at the transmitter side, channel encoder and modulator are serially concatenated with a random interleaver in-between. At the receiver side, iterative processing between detector and channel decoder is performed. The convergence of the iterative processing is investigated by an extrinsic information transfer (EXIT) chart analysis. In addition, the EXIT chart is used to predict the system performance and to determine the communication channel capacity including the DBMC channel. Bit-error-rate (BER) simulations are performed for advanced low-density parity-check (LDPC) codes. These numerical results confirm the benefit of turbo processing over non-iterative processing for DBMC applications.
1.5 Structure of Dissertation
The content of the dissertation is structured as follows. Chapter 2 deals with the modeling of the diffusion-based transmission channel and thus represents the basis for the analy- ses presented in the subsequent chapters. First, the system model and its assumptions are described. Three different methods for determining the channel impulse response are then presented and the equivalent discrete-time channel model is established including different approximations. Finally, a macroscopic alcohol-based testbed setup, for which a channel impulse response is determined, is described as proof of concept. This channel impulse response is used for prediction of a sequence transmission and compared with testbed measurements. Chapter 3 deals with transmitter and receiver algorithms based
on the channel model presented in Chapter 2. The focus is on modulation schemes at the transmitter side and on detectors and channel equalizers at the receiver side. Furthermore, orthogonal frequency-division multiplexing is regarded as a multi-carrier method which elegantly combines modulation and channel equalization/detection. Chapter 4 examines the improvement of transmission by utilizing channel codes. In addition to classical block and convolutional FEC codes, line codes, spreading codes and spatial codes are analyzed as well. The analysis of the codes is performed under different aspects of normalization and shows corresponding gains and losses. Chapter 5 deals with advanced channel coding apply- ing the turbo principle, in which the decoder and detector are connected by an interleaver and exchange extrinsic information. Using an extrinsic information transfer chart analysis, the communication channel capacity is determined, the iterative detection performance is predicted and an adapted irregular convolutional code is designed. The performance is evaluated using bit error rate simulations. Chapter 6 concludes the dissertation with a summary of the contents. In addition, an outlook gives inspiration for further research.
The notation throughout the dissertation, which comprises amongst others acronyms and mathematical notations, is listed in Appendix A. Appendix B collects supporting mathematical derivations. Furthermore, Appendix C summarizes the simulation parameters of all simulations presented in this dissertation. The listed values are intended as default values, which are fixed if the parameters are not varied throughout the simulation.
2
Diffusion-Based Channel Modeling
This chapter forms the basis for the transmission algorithms examined in the following chapters. In addition to a description of the system model and its assumptions, various methods for channel characterization are presented. Based on these, a channel model is introduced. Finally, a testbed setup is presented as a proof of concept.
2.1 System Model and Assumptions
ρy ρx ρz Transmitter r Receiver d Messenger molecule
Figure 2.1: Visualization of the diffusion-based molecular communication scenario
under investigation.
In this dissertation, a three-dimensional communication scenario is assumed, which is shown in Fig. 2.1 [DH16]. The unbounded environment is filled with a fluid medium, which
together with the diffusing particle is defined by its diffusion coefficient [NE+13]
D = kBϑ
6πηrmol, (2.1)
where kB ≈ 1.38 × 10−23J/K is the Boltzmann constant, ϑ and η are the temperature and viscosity of the medium respectively, and rmol is the hydrodynamic radius of the diffusing particle. It is assumed that the medium is stationary and homogeneous, i. e., it does not change its temperature and viscosity over time or location. Furthermore, the medium is free of any form of drift/flow.
As shown in Fig. 2.1, the communication scenario consists of a transmitter and a receiver. It is assumed that the transmitter is a point source with an infinitesimally small volume. In the sense of a point source, it is able to release an impulse of messenger molecules at its location at any time. Without loss of generality, it is assumed that the transmitter is in the coordinates origin of the three-dimensional environment. The receiver is assumed to have a spherical shape defined by the radius r. It is located at a distance d > r away from the transmitter, where d is defined as the distance between the centers of the receiver and the transmitter, respectively. The surface of the receiver consists of ideal receptors which are sensitive to the messenger molecules. Whenever a messenger molecule hits a receptor, it is immediately counted and removed from the environment. The removal of message molecules after reaching the receiver is a natural phenomenon. In nature, receiving cells often modify or degrade signal molecules [LB+00]. For example, acetylcholines are degraded by acetylcholinesterase in neuromuscular junctions [KY+13]. The spatial expansion of the receptors is assumed to be infinitesimally small. The density of receptors on the surface is assumed to be high enough to count messenger molecules every time they hit the surface of the receiver. Consequently, the receiver is modeled as an ideal absorbing receiver. Throughout this dissertation, it is assumed that the receiver performs energy detection, i. e., it is capable to sum up the number of molecules received over a symbol duration T . It is also assumed that the transmitter and receiver are perfectly synchronized in time. Time synchronization can be achieved, for example, by an external signal such as the human heartbeat or, as described in [MN13], by the release of inhibitory molecules.
The messenger molecules, emitted by the transmitter and detected by the receiver, act as information carriers in the communication system. It is assumed that they are all of the same type and are the only molecules in the environment. They propagate independently of each other, do not collide, and can be in the same position at the same time. Consequently, the messenger molecules follow the principle of Brownian motion. The stochastic propagation
2.1 System Model and Assumptions
of the messenger molecules by diffusion leads to a diffusion noise, which describes the deviation from the expected propagation. In this dissertation, it is assumed that this is the only noise source in the system.
This system model modulates a diffusion-based intercellular transmission for example between two bacteria or two nanomachines. It is a rather simple model, which has its advantages in its comparatively simple description. Moreover, the model focuses on the diffusion propagation of the molecules without considering other effects such as additional molecules in the environment, a heterogeneous fluid medium, receptor binding processes, or interactions between molecules. This is consistent with the focus of the dissertation on the effect of diffusion.
Table 2.1: Assumed default parameters for the scenarios theoretically examined in
this dissertation. While the results are presented only for microscopic parameters, the macroscopic parameters lead to equivalent results.
Parameter Microscopic Value Macroscopic Diffusion coefficient D 4.367 64 × 10−10m2/s 4.367 64 × 10−4m2/s
Receiver radius r 4.5 µm 4.5 mm
Transmission distance d 10 µm . . . 150 µm 10 mm . . . 150 mm
Tab. 2.1 presents the default parameters for the scenario which is the basis for the theoretical investigations carried out in this dissertation. While results for the microscopic parameters are presented in the following, the macroscopic parameters lead to equivalent results. Thus, the presented results can also be interpreted for macroscopic molecular communication.
The microscopic parameters are biologically motivated and inspired by “System 1” ap- plied in [NC+14a]. Water is considered as a transmission medium at a temperature of ϑ= 25 °C with a viscosity of η = 1 × 10−3kg/m/s. The radius of the messenger molecules is assumed to be rmol = 0.5 nm, which corresponds to the size of common small organic molecules such as glucose, amino acids, and nucleotides [NC+14a]. These values result in the diffusion coefficient D according to equation (2.1). In contrast to [NC+14a], the receiver radius is set to r = 4.5 µm instead of 45 nm, which is a more realistic value for a cell. The size of prokaryotic cells ranges typically between 1 µm and 10 µm [NE+13].
The macroscopic parameters are obtained by upscaling the microscopic parameters under the constraint of providing equivalent results. Nevertheless, they represent realistic values for a macroscopic scenario. The receiver radius of r = 4.5 mm is feasible as the size of the sensitive layer of a sensor (see Section 2.4). The diffusion coefficient D is in the order of
magnitude of diffusing substances in gases. Typical values ranges between 0.1 × 10−4m2/s and 1 × 10−4m2/s at a pressure of 1 atm and near room temperature [Cus09].
The resulting transmission distances in the interval of seconds by pure diffusion are in micrometers in the microscopic scenario, while millimeters are reached in the macroscopic scenario. It should be noted that a significant increase in range can be achieved by a favorable drift in the medium. Thus the transmission distances can be increased as shown for example in [DH18] to millimeters in the microscopic scenario and to meters in the macroscopic scenario. The macroscopic testbed presented in Section 2.4 also demonstrates transmission in the meter range.