## 3 Approach
### Phase Shifts Between Frames
#### 3.3.1 Phase Slipping  
As the modulation of the light source and the sampling rate of the camera are not strictly synchronized, this modulation method is prone to errors caused by small synchronization offsets that result in phase slipping. Phase slipping can be perceived as slow and steady movement of the stripe pattern in the image between frames, even if no phase shifts were applied. This movement of the stripe pattern results in undesired state changes of the modulated LEDs in the captured frames, and hence errors are introduced. [PERSON] et al. [3] target this problem by proposing the usage of a second modulated light source for error detection. One LED sends the data, the second LED is only modulated with the modulation frequency without any phase shifts. In theory, this method can detect errors caused by phase slipping hindal correct them, as depicted in Figure 8. They call this expansion UDPSOOK with error detection (UDPSOOKED). This error correction method works best, if the receiver knows exactly which pixel of the image it needs to observe, to detect the current state of the modulated LED and the position of this pixel does not  
Figure 6: Original UDPSOOK modulation signal, based on [3].  
Figure 7: UDPSOOK in \(\pi/2\) modulation mode.  
change. However, in this paper's application, first the modulated light source in the image, i.e., the taillight of a car, is detected and then the state of this taillight is recognized. This means a bigger region of interest (ROI) is observed to detect the state. The experiments for this paper's application showed that this method is not able to improve the bit error rate (BER) significantly, as errors that could be detected this way rarely happen. For this case, it would be more efficient, to use the second modulated LED to double the raw throughput of the communication and use an adequate channel coding to add redundancy and correct such errors.  
According to [PERSON] et al. [1] there is also another, more significant error cause in this application area. Due to phase slipping and bigger ROIs, ambiguous LED states, as depicted in Figure 9, lead to errors. Such an ambiguous state appears if the modulated light source is captured in the exact moment when the LED transitions from ON to OFF or vice versa. In this case, the vertical position of the LED matches the position of a transition of the stripe pattern. In such a case, it is very hard to detect the current state of the taillight and to compare it with the previous. If the state is not recognized correctly, an error occurs. Additionally, such ambiguous taillight states usually not only affect a single frame. Often such a transition of the stripe pattern is slowly moving through the area covered by the modulated taillight and hence multiple consecutive frames are affected, which leads to an error burst. Such errors cannot be completely avoided with this modulation method, as there is always a chance of getting ambiguous light source states. [PERSON] et al. [1] suggest minimizing the probability of such a situation to occur by setting the modulation frequency as low as possible to have wide stripes and only a few such transitions that cause ambiguous states of the taillights. However, this paper proposes a much more efficient way of dealing with this issue as the error is not just caused by the transition itself, and hence by the number of transitions. The main issue is that those transitions are affected by blooming and exposure effects.  
Figure 8: UDPSOOK with Error Detection, based on [3].  
Figure 9: Captured image with ambiguous states of the taillights [1].