# Constant Transmission Efficiency Dimming Control Scheme for VLC Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

- a.
- The channel state information (CSI) is available both at the receiver and the transmitter.
- b.
- c.
- A static link should be supposed in the proposed scheme because the channel is slow time-varying.

## 3. The Proposed Dimming Control Scheme

#### 3.1. Motivation of the ECWCS Scheme

#### 3.2. Construction of the Codeword Set

- (1)
- When the dimming factor $\gamma =\frac{i}{n}$, the code weight of every codeword in the codeword set $\mathcal{S}$ is i. Therefore, we can not only guarantee the dimming factor $\gamma =\frac{i}{n}$ but also ensure the Hamming distance of the codewords in the codeword set $\mathcal{S}$ is 2 to improve the error performance.
- (2)
- When the dimming factor $\gamma \ne \frac{i}{n}$ and $\frac{1}{n}<\gamma <\frac{n-1}{n}$, the construction of the codeword set is more complicated. First we find the range $\frac{i}{n}<\gamma <\frac{i+1}{n}$. Then we encode the original binary codes like the last case which makes all the code weight of every codeword in set $\mathcal{S}$ is i. At last, we calculate $m=n\times {2}^{k}\times \gamma $, $q=(m-{2}^{k}i)/2$, select q codewords in $\mathcal{S}$ and replace two bit ‘0’ with two bit ‘1’ of the q codewords respectively.

**Example**

**1.**

**Example**

**2.**

Algorithm 1: Construction of the Codeword Set. |

Input: The dimming factor $\gamma $, the length of original binary sequence k and the original binary signal $\mathbf{s}$Fix proper the length of the coded binary sequence n by the constraint: $n\u2a7e{2}^{k}$. If $\gamma =\frac{i}{n}$, where i is a positive integer and $0<i<n$Construct the codeword set $\mathcal{S}$ in which the code weight of every codeword is i. Else If $\gamma \ne \frac{i}{n}$ and $\frac{1}{n}<\gamma <\frac{n-1}{n}$Find the range $\frac{i}{n}<\gamma <\frac{i+1}{n}$ Construct the codeword set $\mathcal{S}$ in which the code weight of every codeword is i. Calculate $m=n\times {2}^{k}\times \gamma $ and $q=(m-{2}^{k}i)/2$ Select q codewords in $\mathcal{S}$ and replace two bit ‘0’ with two bit ‘1’ of the q codewords respectively. EndEndOutput: The codeword set $\mathcal{S}$ |

#### 3.3. Encoding/Decoding Procedure the ECWCS Scheme

- (1)
- When the dimming factor $\gamma =\frac{i}{n}$, the code weight of every codeword in the codeword set $\mathcal{S}$ is i. Thus we can utilize the proposed decoding algorithm directly.
- (2)
- When the dimming factor $\gamma \ne \frac{i}{n}$ and $\frac{1}{n}<\gamma <\frac{n-1}{n}$, the code weight of every codeword in set $\mathcal{S}$ is not a constant. First we find the range $\frac{i}{n}<\gamma <\frac{i+1}{n}$ and calculate $m=n\times {2}^{k}\times \gamma $, $q=(m-{2}^{k}i)/2$. Then we find the q codewords the code weight of which is not i in $\mathcal{S}$. At last, replace two bit ‘1’ with two bit ‘0’ of the q codewords respectively. That is the inverse process of the codeword set construction and requires the decoder to know the details of the construction process. In this way, we can utilize the proposed decoding algorithm.

Algorithm 2: Decoding Procedure. |

Input: The dimming factor $\gamma $, the length of original binary sequence k,the length of received binary sequence n, and the received sequence $\mathbf{r}$ If $\gamma \ne \frac{i}{n}$ and $\frac{1}{n}<\gamma <\frac{n-1}{n}$Find the range $\frac{i}{n}<\gamma <\frac{i+1}{n}$ Calculate $m=n\times {2}^{k}\times \gamma $ and calculate $q=(m-{2}^{k}i)/2$ Replace two bit ‘1’ with two bit ‘0’ of the q codewords respectively. Else If $\gamma =\frac{i}{n}$, where i is a positive integer and $0<i<n$EndEndFind the position of bit ‘1’ in $\mathbf{c}$, sum the elements at the same position in $\mathbf{r}$, and obtain the estimated sequence $\widehat{\mathbf{r}}$ of $\mathbf{r}$. Recover the original binary data by looking up from the table like Table 1 and Table 2. Output: The estimated signal $\widehat{\mathbf{s}}$ of the original binary signal $\mathbf{s}$. |

## 4. Simulation Results

#### 4.1. Dimming Range

#### 4.2. Error Performance

#### 4.3. Spectral Efficiency

#### 4.4. Analysis

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**System model of the proposed dimming control scheme applied to on-off keying (OOK) modulation.

**Figure 2.**Dimming range of the block coding scheme and the extensional constant weight codeword sets (ECWCS) scheme under different k.

**Figure 4.**Spectral efficiency of variable on-off keying (VOOK), variable pulse position modulation (VPPM) and ECWCS.

**Table 1.**The mapping between the original binary sequence and the dimming coded binary sequence with $k=3$, $n=8$, and $\gamma =1/8$.

Original Binary Sequence | Dimming Coded Binary Sequence | Original Binary Sequence | Dimming Coded Binary Sequence |
---|---|---|---|

000 | 00000001 | 100 | 00010000 |

001 | 00000010 | 101 | 00100000 |

010 | 00000100 | 110 | 01000000 |

011 | 00001000 | 111 | 10000000 |

**Table 2.**The mapping between the original binary sequence and the dimming coded binary sequence with $k=3$, $n=8$, and $\gamma =5/16$.

Original Binary Sequence | Dimming Coded Binary Sequence | Original Binary Sequence | Dimming Coded Binary Sequence |
---|---|---|---|

000 | 00000011 | 100 | 00110000 |

001 | 00000110 | 101 | 01100000 |

010 | 00001100 | 110 | 11000011 |

011 | 00011000 | 111 | 10000111 |

k | ${\mathit{\gamma}}_{\mathbf{min}}$ | ${\mathit{\gamma}}_{\mathbf{max}}$ | ${\mathit{\gamma}}_{\mathit{r}}$ |
---|---|---|---|

2 | $\frac{1}{4}$ | $\frac{3}{4}$ | $\frac{1}{2}$ |

3 | $\frac{1}{6}$ | $\frac{5}{6}$ | $\frac{2}{3}$ |

4 | $\frac{1}{8}$ | $\frac{7}{8}$ | $\frac{3}{4}$ |

k | $\frac{1}{2k}$ | $\frac{2k-1}{2k}$ | $\frac{k-1}{k}$ |

k | ${\mathit{\gamma}}_{\mathbf{min}}$ | ${\mathit{\gamma}}_{\mathbf{max}}$ | ${\mathit{\gamma}}_{\mathit{r}}$ |
---|---|---|---|

2 | $\frac{1}{4}$ | $\frac{3}{4}$ | $\frac{1}{2}$ |

3 | $\frac{1}{8}$ | $\frac{7}{8}$ | $\frac{3}{4}$ |

4 | $\frac{1}{16}$ | $\frac{15}{16}$ | $\frac{7}{8}$ |

k | $\frac{1}{{2}^{k}}$ | $\frac{{2}^{k}-1}{{2}^{k}}$ | $\frac{{2}^{k-1}-1}{{2}^{k-1}}$ |

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**MDPI and ACS Style**

Guo, J.-N.; Zhang, J.; Xin, G.; Li, L.
Constant Transmission Efficiency Dimming Control Scheme for VLC Systems. *Photonics* **2021**, *8*, 7.
https://doi.org/10.3390/photonics8010007

**AMA Style**

Guo J-N, Zhang J, Xin G, Li L.
Constant Transmission Efficiency Dimming Control Scheme for VLC Systems. *Photonics*. 2021; 8(1):7.
https://doi.org/10.3390/photonics8010007

**Chicago/Turabian Style**

Guo, Jia-Ning, Jian Zhang, Gang Xin, and Lin Li.
2021. "Constant Transmission Efficiency Dimming Control Scheme for VLC Systems" *Photonics* 8, no. 1: 7.
https://doi.org/10.3390/photonics8010007