You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Motivated by the fact that living cells use molecular circuits (i.e., a set of chemical reactions) for information processing, this paper investigates the problem of designing molecular circuits for demodulation. In our earlier work, we use a Markovian approach to derive a demodulator for diffusion-based molecular communication. The demodulation filters take the form of an ordinary differential equation, which computes the log-posteriori probability of a transmission symbol being sent. This paper considers the realization of these demodulation filters using molecular circuits assuming the transmission symbols are rectangular pulses of the same duration but different amplitudes, i.e., concentration modulation. This paper makes a number of contributions. First, we use time-scale separation and renewal theory to analytically derive an approximation of the demodulation filter from our earlier work. Second, we present a method to turn this approximation into a molecular circuit. By using simulations, we show that the output of the derived molecular circuit is approximately equal to the log-posteriori probability calculated by the exact demodulation filter if the log-posteriori probability is positive. Third, we demonstrate that a biochemical circuit in yeast behaves similarly to the derived molecular demodulation filter and is therefore a candidate for implementing the derived filter.

Cited Abstract(s):
[1]: This paper considers a diffusion-based molecular communication system, where the transmitter uses reaction shift keying (RSK) as the modulation scheme. We focus on the demodulation of RSK signal at the receiver. The receiver consists of a front-end molecular circuit and a back-end demodulator. The front-end molecular circuit is a set of chemical reactions consisting of multiple chemical species. The optimal demodulator computes the posteriori probability of the transmitted symbols given the history of the observation. The derivation of the optimal demodulator requires the solution to a specific Bayesian filtering problem. The solution to this Bayesian filtering problem had been derived for a few specific molecular circuits and specific choice(s) of observed chemical species. The derivation of such solution is also lengthy. The key contribution of this paper is to present a general solution to this Bayesian filtering problem, which can be applied to any molecular circuit and any choice of observed species.

[2]: 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.

[3]: Molecular Communication (MC) is a bio-inspired communication technique that uses molecules as a method of information transfer among nanoscale devices. MC receiver is an essential component having profound impact on the communication system performance. However, the interaction of the receiver with information bearing molecules has been usually oversimplified in modeling the reception process and developing signal detection techniques. In this paper, we focus on the signal detection problem of MC receivers employing receptor molecules to infer the transmitted messages encoded into the concentration of molecules, i.e., ligands. Exploiting the observable characteristics of ligand-receptor binding reaction, we first introduce a Maximum Likelihood (ML) detection method based on instantaneous receptor occupation ratio, as aligned with the current MC literature. Then, we propose a novel ML detection technique, which exploits the amount of time the receptors stay unbound in an observation time window. A comprehensive analysis is carried out to compare the performance of the detectors in terms of bit error probability. In evaluating the detection performance, emphasis is given to the receptor saturation problem resulting from the accumulation of messenger molecules at the receiver as a consequence of intersymbol interference. The results reveal that detection based on receptor unbound time is quite reliable even in saturation, whereas the reliability of detection based on receptor occupation ratio substantially decreases as the receiver gets saturated. Finally, we also discuss the potential methods of implementing the detectors.

[4]: In a diffusion-based molecular communication network, transmitters and receivers communicate by using signalling molecules (or ligands) in a fluid medium. This paper assumes that the transmitter uses different chemical reactions to generate different emission patterns of signalling molecules to represent different transmission symbols, and the receiver consists of receptors. When the signalling molecules arrive at the receiver, they may react with the receptors to form ligand-receptor complexes. Our goal is to study the demodulation in this setup assuming that the transmitter and receiver are synchronised. We derive an optimal demodulator using the continuous history of the number of complexes at the receiver as the input to the demodulator. We do that by first deriving a communication model which includes the chemical reactions in the transmitter, diffusion in the transmission medium and the ligand-receptor process in the receiver. This model, which takes the form of a continuous-time Markov process, captures the noise in the receiver signal due to the stochastic nature of chemical reactions and diffusion. We then adopt a maximum a posteriori framework and use Bayesian filtering to derive the optimal demodulator. We use numerical examples to illustrate the properties of this optimal demodulator.
Our assumption of using the continuous history of the number of active receptors for demodulation leads to a demodulator which uses analog filters. The use of analog filters for demodulation was studied in [4] [2] [1] , but no molecular circuit realisation was provided. A recent work [3] presented two different molecular circuits for demodulation but their circuits used one sample point per symbol for demodulation rather than continuous history.