## 4 Experimental Results
### Optical Comparison Operation  
The author experimentally demonstrated an 8-bit optical comparison operation to evaluate the constellations obtained from the four comparators when several patterns of 8-bit code, consisting of four QPSK symbols, were injected into the comparators. In this experiment, the author previously evaluated the constellation of either the first + third or second + fourth symbols. Based on the situation, the coupled symbols were detected by a BPD, which gave a difference vector of the signal between the first + third and second + fourth symbols. Here, as we know the pattern of either the first + third or second + fourth symbols, the other constellation can be estimated by using the difference vector. Consequently, from the vector sum of the obtained first + third and second + fourth constellations, the constellation for the given 8-bit code was achieved. Figure 5 shows the obtained constellations of the \"00 00 00 00\" and \"11 00 11 00\" comparators. In this case, twelve 8-bit codes were injected into the two comparators, whose patterns were \"00 00 00\", \"01 00 01 10\", \"00 10 00 11\", \"10 01 10 01\", \"11 00 01\", \"01 01 10\", \"00 11 00 11\", \"01 01 01 01\", \"10 10 10 10\", \"11 01 10\", \"11 01 11 00\", \"10 01 10 11\", and \"11 11 11 11\", respectively. In the case of the \"00 00 000\" comparator, every pattern was divided into five classes in terms of its _Hamming_ distance of \(d_{H}(00000000,\mathbf{c})\), where \(\mathbf{c}\) is a given 8-bit code. The twelve 8-bit codes were classified as follows:  
\[d_{H}(00000000,\mathbf{c}) =0: \quad 00\ 00\ 00\ 00;\] \[d_{H}(0000000,\mathbf{c}) =3: \quad 01\ 00\ 01\ 10\ 00\ 10\ 00\ 11;\] \[d_{H}(0000000,\mathbf{c}) =4: \quad 10\ 01\ 01\ 01\ 11\ 00,\ 01\ 10\ 01\ 10,\ 00 11\ 00\ 11\ 00\ 11,\ 01 01\ 01\ 01,\] \[d_{H}(0000000,\mathbf{c}) =5: \quad 11\ 01\ 11\ 00\ 10\ 10\ 11;\] \[d_{H}(0000000,\mathbf{c}) =8: \quad 11\ 11\ 11\ 11.\]  
As in Figure 5a, all Hamming distances were accurately equal to the distance from the base-constellation in the complex plane. As an example, the \"00 00 00 00\" constellation corresponds to the base constellation due to its design concept. Meanwhile, the two constellations of \"01 00 01 10\" and \"00 10 00 11\", whose Hamming distance is given by 3, were located 3-bit length away from the base constellation. Furthermore, the \"11 11 11 11\" constellation was located at the farthest position. The distance coincides with the Hamming distance of \(d_{H}(00\ 00\ 00\ 00,11\ 11\ 111)=8\). Similarly, in Figure 5b, the \"11 00 11 00\" comparator generates the constellations to be located in conformity with a Hamming distance based on the \"11 00 11 00\" code. In particular, the constellations whose patterns are similar to \"11 00 11 00\" were located near the base constellation, in contrast, the constellations having different patterns from \"11 00 11 00\" were located away from the base  
Figure 4: Transmission spectra of the 8-bit optical comparator: (**a**) “00 00 00” and “11 00 11 00” comparator. (**b**) “11 10 10 00” and “00 10 01 00” comparator. In these figures, the “00 00 00 00” and “11 10 10 00” spectra exactly overlap the “11 00 11 00” and “00 10 01 00” spectra with 0.04 nm wavelength shift, which correspond to a \(\pi\) phase different at 10 GHz DLI. constellation. As an example, the \"11 00 11 00\" constellation, which is completely equal to the comparator code, was at the base constellation: \(d_{H}(11\,00\,11\,00,11\,00\,11\,00)=0\). Additionally, the \"00 11 00 11\" constellation, which is completely different from the comparator code, was located at furthest position in the complex plane: \(d_{H}(11\,00\,11\,00,00\,11\,00\,11)=8\). Figure 6 shows the constellations of the \"11 10 10 00\" and \"00 10 01 00\" comparators with eleven 8-bit codes of \"00 00 01 01\", \"10 10 00 00\", \"00 01 01 01\", \"10 10 00 10\", \"10 01 10 11\", \"11 11 10 10\", \"10 11 11\", \"01 01 01 11\", \"01 11 11\", \"01 11 11\", and \"11 11 11 10\".