## 2 The Pulsed Coding Technique: Theory, Modelling and Methods of the Optical Approach
Then, at half bit period \(T/2\), if the symbol 1 has to be transmitted, a second laser pulse is generated, while for the transmission of the symbol 0 the VCSEL driving current is maintained at the value \(I_{\mathrm{min}}\). In this way, the transmitter power consumption is mainly due to the current \(I_{\mathrm{min}}\) that is constant during each bit period \(T\), while the contribution of the current pulses, with an amplitude equal to \(I_{\mathrm{max}}\), is minimal due to the very small duty cycle. These operating conditions allow us to strongly reduce the system overall power consumption and the VCSEL response time. Figure 2: Example of a timing diagram describing the proposed data coding process and the corresponding laser operating conditions. Figure 3 shows the logic block level implementation of the coding and decoding systems inside the transmitter and the receiver, respectively. The coding system receives in input \(\mathrm{CLK}_{T}\) and \(S_{T}(t)\) considering the bit period \(T\) equal to the clock period (i.e., one bit transmitted at each bit period \(T\)), as shown in Figure 2 and detailed in Figure 4a. Thus, the coding system generates a train of \"rect\" pulses \(P_{\mathrm{RECT}}\left(t\right)=\sum_{n=-\infty}^{+\infty}\left[\mathrm{rect}_ {T_{0}}\left(t-nT\right)\right]\) having a period \(T\) with a very small duty cycle \(T_{0}\) and the same signal, delayed by a time period \(\tau=T/2\), defined as \(P_{\mathrm{RECT}}\left(t-\tau\right)=\sum_{n=-\infty}^{+\infty}\left[\mathrm{ rect}_{T_{0}}\left(t-nT-\tau\right)\right]\). The transmitted pulsed signal \(U_{T}(t)\) is obtained as the combination of \(P_{\mathrm{RECT}}(t)\) and \(P_{\mathrm{RECT}}(t-\tau)\) and can be expressed as follows:  
\[U_{T}\left(t\right)=\sum_{n=-\infty}^{+\infty}\left[\mathrm{rect}_{T_{0}} \left(t-nT\right)+S_{T}\left(t\right)*\mathrm{rect}_{T_{0}}\left(t-nT-\tau \right)\right] \tag{1}\]  
On the other hand, \(U_{T}(t)\) contains the constant pulses \(P_{\mathrm{RECT}}(t)\) used for the clock recovery and the pulses \(P_{\mathrm{RECT}}(t-\tau)\) related to the transmitted data \(S_{T}(t)\) (i.e., the bit symbols 1 or 0). Inversely, \(U_{R}(t)\) is the input of the decoding system that operates clock and data recovery so providing the synchronisation signal \(\mathrm{CLK}_{R}\) and the decoded data stream \(S_{R}(t)\). In particular, the decoding system integrates the signal \(U_{R}(t)\) during a bit period \(T\), starting from \(T/2\) after the first synchronisation pulse through the \"Timer\" block (see Figure 3), according to the following relation:  
\[S_{R}\left(t\right)=\left\{ \begin{array}{l}1\ \mathrm{if}\ \int_{T/2}^{T}U_{R} \left(t\right)dt\geq t_{H}\\ \\ 0\ \mathrm{if}\ \int_{T/2}^{T}U_{R}\left(t\right)dt\leq t_{L}\end{array} \right. ; \ \mathrm{Err}\ \forall \tag{2}\]  
where \(t_{H}\) and \(t_{L}\) are the high and low threshold levels defined by the decoding system. Consequently, the generated output signals \(S_{R}(t)\) and \(\mathrm{CLK}_{R}\) can be described as detailed in Figure 4b. More in detail,  
Figure 4: Correlations between the signals \(\mathrm{CLK}_{T,R}\), \(S_{T,R}(t)\) and the corresponding coded data \(U_{T,R}(t)\) related to the coding (**a**); and decoding (**b**) systems. Figure 3: Description, at logic block level, of the implementation of the coding (on the **left**); and decoding (on the **right**) systems. since the clock recovery as well as the synchronisation between the transmitter and the receiver is a critical issue in communication systems, the \"Timer\" block includes a control unit. Starting from the pulsed signal \(U_{R}(t)\), the control unit operates the clock recovery by managing the regeneration of the new clock signal CLK\({}_{R}\) and its synchronisation with the received pulses \(U_{R}(t)\). Simultaneously, the overall \"Timer\" block also controls the synchronisation between the recovered clock CLK\({}_{R}\) and the integrator block that, in turn, performs the recovery and regeneration of the data stream \(S_{R}(t)\).