## 3 Learning-Automaton-Based Communication Protocol for a High Data Rate
The red line represents the signaling molecules with a speed of 45 \(\upmu\)m/s, the blue line a speed of 27 \(\upmu\)m/s and the green line a speed of 18 \(\upmu\)m/s. ity distribution for m actions at each instant n. It holds that \(\sum_{i=1}^{m}p_{i}(n)=1\). Initially, the LA has no prior knowledge about the environment it operates in, and as a consequence, all initial probabilities are the same. At each iteration n, the action \(b_{i}\), \(1\leq i\leq m\) is selected with probability \(p_{i}(n)\). The action taken by the automaton corresponds to a stochastic reaction \(A_{i}(n)\), which is used to update the probability vector. Upon completion of the n iteration, the LA selects the next action based on the updated probability vector \(p(n+1)\). This results in different update actions for each probability, based on the feedback received from the environment. After a number of iterations, the LA in its theoretical form will select the optimal action that has the minimum penalty probability vector. The use of LA, in the context of this study, is the detection of the optimal values for the numbers of ascensions and descensions that should be taken into consideration from the message detection algorithm. Via the operation of the LA, the response from the BS (stands as the environment for the LA) is being translated into the probabilities for each of the two parameters: to increase or to decrease. Figure 4b shows the 3 different set of actions followed by the LA. State 1 is the preferred state whenever the node misses a transmitted message (network environment \(b=-1\)), and the protocol must decrease the ascensions and increase the descensions. The opposite applies for state (2) (\(b=1\) and therefore an additional message has been sensed), and the third state (3) (\(b=0\)) is the one where the node successfully receives the message transmitted from the BS. In the latter state, only the number of descensions is decreased, seeking the maximum transfer data rate. The LA has to decide in each state which selection will minimize the penalty and will be the next state. Assuming that the LA is at state 1 (the orange cycle in Figure 4b) and the node running the LA receives a feedback of \(a_{i}=1\), then the algorithm will update the probability vector, and at the next iteration, the red cycle state will be the favorable one. Whenever the feedback is \(a_{i}=0\), the system will promote the transition to the state 3 (green cycle). Related to the specific actions, if the LA is at state 2 and the environmental response is translated to a lost message, then the favorable transition will be towards state 1. At the same time, the LA will relax the required number of ascensions, as the lost message is the result of a low density pulse. If the LA is at the state 1 and the system receives positive feedback, meaning that it sensed exactly the message that the BS sent, then the favorable direction would be towards the state 3. The system will remain at that state as long as it receives the exact number of messages that have been sent from the BS (action \(b=0\)). It should be noted that the most visited state should be state 3, as it means that the node has received successfully the message that the BS has sent (in that case, the action \(b=0\) will be selected again) and just relaxes the number of descensions in order to detect the message as fast it can in order initiate the response from the node and increase the transfer data rate between the communicating nodes. Figure 4: Learning automaton state principles and statechart. (**a**) Typical learning automaton interaction. (**b**) Learning automaton statechart with all the state transitions. The probability update scheme is described based on the following relations. Relations (1) are applied for environmental response \(b=-1\) (before normalization); relations (2) are applied for environmental response \(b=1\); and finally, relations (3) are applied most of the time, as the node operates towards the maximum transfer data rate (environmental response \(b=0\)).