# Reduction of Complexity Design of SAC OCDMA Systems by Utilizing Diagonal Permutation Shift (DPS) Codes with Single Photodiode (SPD) Detection Technique

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## Abstract

**:**

## 1. Introduction

## 2. Code Construction and Code Properties

#### 2.1. Algorithm of Code Construction

#### 2.2. Code Properties

- A unity CC between any sequences.
- The number of users N = ${P}^{2}$.
- The code weight can be any prime number greater than 2.
- The code length equals ${P}^{2}+P$.
- Each code sequence has (P + 1) “1s” and (${P}^{2}$ − 1) “0s”.

#### 2.3. Code Examples

## 3. DPS System Description

_{1}, λ

_{5}, λ

_{8}, and λ

_{10}according to Table 3.

_{2}, λ

_{3}, λ

_{4}, λ

_{5}, λ

_{6}, λ

_{7}, λ

_{9}, λ

_{11}, and λ

_{12}according to Table 3.

_{2}, λ

_{3}, λ

_{4}, λ

_{5}, λ

_{6}, λ

_{7}, λ

_{9}, λ

_{11}, and λ

_{12}).

## 4. Detection Techniques Selection

#### 4.1. Complementary Detection Scheme (CDS)

#### 4.2. Single Photodiode (SPD)

#### 4.3. Pickup of Detection Scheme

## 5. Performance Analysis

## 6. Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Block diagram implementation of DPS code for P = 3: structure of (

**a**) transmitter, (

**b**) receiver.

**Figure 2.**Schematic diagram of DPS code using three users: (

**a**) transmitter; (

**b**) receiver using CDS detection technique.

**Figure 4.**BER versus number of users for DPS code at different detection techniques and different bit rates.

**Figure 5.**BER versus number of active users for DPS and RD codes at different detection techniques and different bit rates.

**Figure 6.**BER versus effective power for DPS code using different detection techniques and at 622 Mbps and 60 users.

**Figure 7.**SNR versus number of users for DPS code using different detection techniques at different bit rates Mbps.

**Figure 8.**BER versus transmission distance for DPS code using SPD detection scheme at 622 Mbps, 1 Gbps, and 2 Gbps.

**Figure 10.**Q-factor versus transmission distance for DPS code using SPD detection scheme at 622 Mbps, 1 Gbps, and 2 Gbps.

**Figure 12.**SNR versus transmission distance for DPS code using SPD detection scheme at 622 Mbps, 1 Gbps, and 2 Gbps.

i/j | 0 | 1 | 2 | $\cdots $ | P − 1 |

0 | 0 | 0 | 0 | $\cdots $ | 0 |

1 | 0 | 1 | 2 | $\cdots $ | P − 1 |

2 | 0 | 2 | 4 | $\cdots $ | P − 2 |

$\vdots $ | $\vdots $ | $\vdots $ | $\vdots $ | $\ddots $ | $\vdots $ |

P − 1 | 0 | P − 1 | P − 2 | $\cdots $ | 1 |

i | ${\mathit{A}}_{\mathit{i},\mathit{j}}$ j = 0, 1, 2, 3 | DPS Code | |||
---|---|---|---|---|---|

0 | 0110 | 100 | 010 | 010 | 100 |

1 | 1011 | 010 | 100 | 010 | 010 |

2 | 1102 | 010 | 010 | 100 | 001 |

3 | 1220 | 010 | 001 | 001 | 100 |

4 | 2121 | 001 | 010 | 001 | 010 |

5 | 2212 | 001 | 001 | 010 | 001 |

6 | 2000 | 001 | 100 | 100 | 100 |

7 | 0201 | 100 | 001 | 100 | 010 |

8 | 0022 | 100 | 100 | 001 | 001 |

Wavelength (nm) | 1550 | 1550.8 | 1551.6 | 1552.4 | 1553.2 | 1554 | 1554.8 | 1555.6 | 1556.4 | 1557.2 | 1558 | 1558.8 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{\lambda}}_{1}$ | ${\mathit{\lambda}}_{2}$ | ${\mathit{\lambda}}_{3}$ | ${\mathit{\lambda}}_{4}$ | ${\mathit{\lambda}}_{5}$ | ${\mathit{\lambda}}_{6}$ | ${\mathit{\lambda}}_{7}$ | ${\mathit{\lambda}}_{8}$ | ${\mathit{\lambda}}_{9}$ | ${\mathit{\lambda}}_{10}$ | ${\mathit{\lambda}}_{11}$ | ${\mathit{\lambda}}_{12}$ | |

User#1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |

User#2 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |

User#3 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |

Decoder (User#1) | 100010010100 |

User#2 (first interference with user#1) | 010100010010 |

User#3 (second interference with user#1) | 010100010010 |

(Decoder × User#2) | 000000010000 |

CC of (Decoder × User#2) | 1 |

$\overline{\mathrm{Decoder}}$ | 011101101011 |

(User#2 × User#3) | 010000000000 |

S-Decoder = $\overline{\mathrm{Decoder}}\times \left(\mathrm{User}\#2\times \mathrm{User}\#3\right)$ | 010000000000 |

(User#2 × S-Decoder) | 010000000000 |

CC of (Decoder × User#2) | 1 |

CC of (Decoder × User#2)—CC of (Decoder × User#2) | 1-1 0 |

Components | FBGs | Subtractor | PIN | LPF | |
---|---|---|---|---|---|

User#1 | Complementary | 4 FBGs in the decoder branch and 8 FBGs in complementary | One | 2 | One |

SPD | 4 FBGs used as decoder and one FBG as S-Decoder | One | One | One | |

User#2 | Complementary | 4 FBGs in the decoder branch and 8 FBGs in complementary | one | 2 | One |

SPD | 4 FBGs used as decoder and one FBG as S-Decoder | One | One | One | |

User#3 | Complementary | 4 FBGs in the decoder branch and 8 FBGs in complementary | One | 2 | One |

SPD | 4 FBGs used as decoder and one FBG as S-Decoder | One | One | One | |

Total | Complementary | 36 FBGs | 3 | 6 | 3 |

SPD | 15 FBGs | 3 | 3 | 3 |

Parameter | Value |
---|---|

Transmitter optical power | 9 dBm |

Bo: Optical bandwidth | 3.75 MHz |

Rb: Data bit rate | 622 Mbps |

Be: Electrical bandwidth | 0.75 Rb |

Single mode fiber dispersion | 17 ps/nm/km |

Single mode fiber slope | 0.075 ps/nm^{2}/km |

Single mode fiber attenuation | 0.25 dB/km |

$\Re $: Responsivity | 0.7 |

e: Electron charge | 1.6 × 10^{−19} C |

h: Planck’s constant | 6.66 × 10^{−34} J·S |

Kb: Boltzmann constant | 1.38 × 10^{−23} J/K |

Tn: Receiver noise absolute | 300 K |

RL: Receiver load resistance | $1030\Omega $ |

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**MDPI and ACS Style**

Ahmed, H.Y.; Zeghid, M.; Bouallegue, B.; Chehri, A.; Abd El-Mottaleb, S.A.
Reduction of Complexity Design of SAC OCDMA Systems by Utilizing Diagonal Permutation Shift (DPS) Codes with Single Photodiode (SPD) Detection Technique. *Electronics* **2022**, *11*, 1224.
https://doi.org/10.3390/electronics11081224

**AMA Style**

Ahmed HY, Zeghid M, Bouallegue B, Chehri A, Abd El-Mottaleb SA.
Reduction of Complexity Design of SAC OCDMA Systems by Utilizing Diagonal Permutation Shift (DPS) Codes with Single Photodiode (SPD) Detection Technique. *Electronics*. 2022; 11(8):1224.
https://doi.org/10.3390/electronics11081224

**Chicago/Turabian Style**

Ahmed, Hassan Yousif, Medien Zeghid, Belgacem Bouallegue, Abdellah Chehri, and Somia A. Abd El-Mottaleb.
2022. "Reduction of Complexity Design of SAC OCDMA Systems by Utilizing Diagonal Permutation Shift (DPS) Codes with Single Photodiode (SPD) Detection Technique" *Electronics* 11, no. 8: 1224.
https://doi.org/10.3390/electronics11081224