## 2 Unipolar Optical Digital Modulation Schemes and Spreading Codes
### Unipolar Optical Digital Modulation Schemes
In DPPM, an \(M\)-bit input block maps to one of \(L=2^{M}\) unique DPPM symbols, including \(L-1\) empty slots and a pulse [40; 41; 42; 44; 45; 46]. The DPPM symbol is derived from the corresponding PPM symbol by removing all empty slots following the pulse, thus reducing the average symbol length  
Figure 2: Time waveforms for on–off keying (OOK), pulse position modulation (PPM), differential PPM (DPPM), multipulse PPM (MPPM), digital pulse interval modulation (DPIM), and dual-header pulse interval modulation (DH-PIM) signals. The different symbols for the different modulation schemes shown in the figure are denoted by different colors. and increasing bandwidth efficiency. DPPM indicates its own symbol synchronization when all symbols end with a pulse. For a long sequence of zeros, there may be a slot synchronization problem that can be handled using a guard slot (GS) immediately after the pulse is removed. The DPPM improves bandwidth and power efficiency over the PPM for a fixed average bit rate and fixed available bandwidth. As the level of coding increases, the number of PPM slots and the required transmission bandwidth both increase exponentially. To overcome these limitations, MPPM was introduced as a way to improve the bandwidth utilization of PPM. MPPM is a generalization of PPM that allows more than one pulse per symbol. Moreover, \(w\)-pulse \(n\)-slot MPPM has \(\binom{n}{w}\) unique symbols that correspond to filling \(n\) slots with \(w\) pulses in a frame [40; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52]. This approach reduces the bandwidth to half of that in the traditional PPM at the same transmission efficiency. That is, a single frame can carry information of size \(\log_{2}\binom{n}{w}\) bits. By contrast, for PPM, this rate is \(\log_{2}L\) bits. The amount of information that the MPPM can transfer increases with the number of pulses in the fixed-length frame. The disadvantage is that if one or more of these pulses are erroneous, the frame is incorrectly demodulated. Therefore, too many source bits are affected. MPPM provides half the information capacity of the PPM, and is inferior to it in terms of error performance. DPIM has built-in symbol synchronization that improves bandwidth efficiency and data speed compared to PPM and power efficiency compared to OOK [40; 41; 42; 44; 31]. The waveform of DPIM is similar to that of DPPM, except the variable frame length and the pulse are located at the beginning of the frame. In DPIM, each symbol starts with a pulse of short duration after the optional GS, followed by the number of empty time slots, which is determined by the decimal value of the bit input block. In other words, a symbol is represented by a discrete interval between consecutive pulses belonging to two consecutive frames. The GS consists of zero or more empty slots, and is vital to avoiding continuous pulses when the input symbol is zero. The frame length of the DPIM may vary depending on the bit input block. The number of DPIM and DPPM slots increases exponentially with OOK bit rates as bit resolution increases. If two systems are included in the GS, this increase is even greater. As the slot frequency increases, bandwidth requirements also increase. In DH-PIM, a symbol consists of two sections: A heading that starts a symbol and an ending information section. The \(n\)th symbol \(S_{n}(h_{n},d_{n})\) starts with the header \(h_{n}\) of duration \(T_{h}=(\alpha+1)T_{s}\) and ends with the sequence of \(d_{n}\) empty slots, where \(\alpha>0\) is an integer [40; 31]. Depending on the most significant bit (MSB) of the input block, two headers are considered, \(H_{1}\) and \(H_{2}\), corresponding to \(MSB=0\) and \(MSB=1\), respectively. \(H_{1}\) and \(H_{2}\) have pulses of \(0.5\alpha T_{s}\) and \(\alpha T_{s}\), respectively. Each pulse is followed by a GS of appropriate length \(T_{g}\in\big{\{}\big{(}\frac{\alpha}{2}+1\big{)}\ T_{s},T_{s}\big{\}}\).