# Majority Decision Aggregation with Binarized Data in Wireless Sensor Networks

## Abstract

**:**

## 1. Introduction

- The calculation method for defining the k value of k-means++ to ensure that the distance between nodes in the cluster is less than the threshold value between transmission and reception in the first-order radio model and provides further energy-saving efficiency and extends the overall network lifetime.
- The k value is defined as an odd number, which means that there will be an odd cluster and cluster head, and the purpose is to aggregate the binarized data to a BS to achieve a majority decision afterward.
- Once the nodes are deployed, the sensing nodes must operate for months or years without any additional power supply. Notably, the communication between nodes often consumes more energy than the computation. If the original sensing data are directly transmitted to the sink, it will consume much more energy. WSNs are often used in alarm applications. Moreover, we have assumed that a critical threshold value is the warning level and is asserted/deasserted a binary. Only binary values are transmitted, which conserves energy at the node and extends the network’s lifetime.
- The BS is fixedly deployed in the center of the sensing area. The sensing area consumes the center of the entire WSN and is used as the origin to further divide it into four quadrants. A data transmission chain is constructed in each quadrant. The chain starts from the CH farthest from the BS, and ends at the CH nearest to the BS. In each round, the CH transmits the majority binary value to the next hop until it reaches the BS by the chain. This is a proven method of reducing CH energy consumption.

## 2. Related Works

#### 2.1. Majority Rule and Hamming Weight

_{i}sets $Even{t}_{i}^{p}=1$, otherwise 0 using Equation (2). TED-FTR does not exhibit better performance in scenarios where more nodes are faulty or there are failures because the nodes responsible for reporting event information can quickly consume their energy.

#### 2.2. Spatial Correlation Model for Sensor Networks

#### 2.3. First-Order Radio Model

_{0}, $k{\epsilon}_{fs}{d}^{2}$ according to the free space model; otherwise, ${\mathsf{\epsilon}}_{mp}{d}^{4}$ uses the multipath model. In this study, we assumed that the radio model dissipates ${E}_{elec}$= 50 nj/bit, ${\epsilon}_{fs}=10\mathrm{pJ}/\mathrm{bit}/{\mathrm{m}}^{2}$ and ${\epsilon}_{mp}=100\mathrm{pJ}/\mathrm{bit}/{\mathrm{m}}^{2}$, where ${d}_{0}=\sqrt{\left({\epsilon}_{fs}/{\epsilon}_{mp}\right)}\cong \sqrt{\frac{10}{0.0013}}\cong 87.705802$ denotes the threshold distance between two nodes.

#### 2.4. Cluster-Based WSNs

#### 2.4.1. K-means++ Clustering Algorithm

_{i}is the ith clustering center for each $i\in \left\{1,\dots ,k\right\}$. Choosing the next center G

_{i+}

_{1}and selecting G

_{i}with probability ($p\left(n\right)=\frac{D{\left({n}^{\prime}\right)}^{2}}{\sum D{\left(n\right)}^{2}}$), the distance between two nodes was calculated using the Euclidean distance D(n). Therefore, we could use the k-means++ algorithm to divide the clusters evenly in the clustering phase.

#### 2.4.2. Cluster-Based Routing Protocol for WSNs

#### 2.4.3. Cluster Head Rotation in WSNs

_{xy}is the group center, and D(n

_{j}) is the Euclidean distance from the G

_{xy}to node (n

_{j}). The n

_{1}will be preferentially selected as the CH because it is closest to the group center.

## 3. The Proposed Approach (EEBDA)

#### 3.1. Cluster Formation

_{0}) of data transmission and reception between two nodes. Where ${d}_{0}=\sqrt{\left({\epsilon}_{fs}/{\epsilon}_{mp}\right)}\cong 87.7058$, d

_{0}= 87, simplifying the calculations to cut off the decimal points and take the distance threshold as an integer value of 87. At the beginning of the cluster formation, neighboring nodes were grouped into the same clusters using k-means++ clustering. Equation (6) is used to calculate the k value of k-means++, which is used to divide the cluster into k groups, as shown in Figure 7. In addition, the k value is defined as an odd value for the subsequent calculation of the majority decision making. In Equation (6), C is the length and width divided by d

_{0}individually and takes the ceiling value. If C is odd, then k = C; if C is even, then k = C + 1.

#### 3.2. Cluster Head Selection and Rotation

_{t}), and is closest to the group center as the cluster head. Other nodes then join the nearest cluster head, and their probability of being selected as the cluster head increases the next time. The CH rotation aims to show the advantages of being cluster based and selecting a plentiful energy sensor node to be a CH in a cluster; the energy load can be dispersed in the cluster. In this study, a threshold value of the residual energy was considered when selecting the CHs in each subsequent round. The nodes near the cluster head dissipate less energy as the relay data of these nodes is a shorter distance. Likewise, more energy is consumed if the nodes are far away from the CH. If the current CH energy is less than the energy threshold, it triggers the rotation CH procedure, where the energy threshold (E

_{t}) is the overall average residual energy of a cluster in which the current CH is located. Equation (7) shows that the node with the highest score in each cluster is selected as the CH. In Algorithm 1, R

_{min}and R

_{max}denote the scanning range with a radius of 10 m and 25 m, respectively [35]. Any nodes beyond the R

_{max}range are already far from the cluster (group) center and are not ideal candidates as CHs. The process of accessing the nearest nodes from the group center and finding a node with the maximum residual energy uses Algorithm 1 at each rotation CH phase.

Algorithm 1 Cluster head rotation |

Input: R_{min}, R_{max}, G_{xy}, CH_{k}, ${n}_{k}$(x), E_{t}, E_{r}Output: New_CH_{k}For each node ${n}_{k}$(x) in {1, 2, …, K}IF CH_{k}.Er <= E_{t}//Check if the residual energy of the current CH_{k} is less than or equal to the energy threshold (Et). Scan G _{xy}.radius = R_{min}//Scanning all nodes in the 10 m radius of a group center
IF Find a MAX{$Score\left({n}_{k}\left(\mathrm{x}\right)\right)$}//Find the node with maximum residual energy, ref Equation (7)Broadcast New_CH _{k} = ${n}_{k}\left(x\right)$ selected
ELSEScan G _{xy}.radius = R_{max}//Scanning all nodes in the 25 m radius of a group center
IF Find a MAX{$Score\left({n}_{k}\left(x\right)\right)$}
Broadcast New_CH _{k} = ${n}_{k}\left(x\right)$ selected
ELSEIF Random selection of a MAX{$Score\left({n}_{k}\left(\mathrm{x}\right)\right)$}
Broadcast New_CH _{k} = ${n}_{k}\left(x\right)$ selected
END IFEND IFEND IFELSEThe CH _{k} to continues as the CH
END IFEND FOR |

#### 3.3. The Majority Result of a Binarized Aggregation

_{k}has a number of members n

_{k}(1), n

_{k}(2),…,n

_{k}(x) with binary decisions $B{n}_{k}^{{C}_{k}}\left(1\right)$, $B{n}_{k}^{{C}_{k}}\left(2\right)$,…, $B{n}_{k}^{{C}_{k}}\left(x\right),k\in \left\{1,\dots ,k\right\}$ as given in Equation (8), where $C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}$ denotes the majority result of each CH in the network. The final majority result of the entire network ($\sum B{S}^{maj}$) can be determined by Equation (9). Finally, the pseudo-code of the network’s final majority result algorithm is presented in Algorithm 2. An illustration is shown in Figure 8, where the one-dimensional matrix represents binarized aggregation data and then computes the Hamming weight in each matrix to obtain the majority result.

Algorithm 2 Find the majority result of a cluster |

Input: ${C}_{k\in \left\{1,\dots ,k\right\}}$, CH_{k}, ${n}_{k}$(x),$\text{}B{n}_{k}^{{C}_{k}}\left(x\right)$,
Output: Majority result of a cluster ($\sum C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}$)
For each node ${n}_{k}$(x) in ${C}_{k\in \left\{1,\dots ,k\right\}}$$C{H}_{k\in \left\{1,\dots ,k\right\}}=\left\{B{n}_{k}^{{C}_{k}}\left(x\right)\right\}$ //each cluster head (CH _{k}) receives binary values from its own member nodes $B{n}_{k}^{{C}_{k}}\left(x\right)$
IF $\sum C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}=1$//where $\sum C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}$ can be calculated by using Equation (7). Send $C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}=1$ to BS//Send cluster final majority result one value to the BS ELSESend $C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}=0$ to BS END IF$B{S}^{maj}$ = {$C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}\left(k\right)$} //BS receives binary values from $C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}$ IF $\sum B{S}^{maj}=1$//where $\sum B{S}^{maj}$ can be calculated by using Equation (8). final majority result of the entire network is true ELSEfinal majority result of the entire network is false END IFEnd For |

#### 3.4. CH Chain Formation Phase

#### 3.5. Overhead Cost Analysis

_{total}= k × n. The binary value is transmitted to the CH through the sensor nodes in the majority decision part, and the CH stores binarized aggregation data in the one-dimensional matrix to perform Hamming weight operations. Therefore, the time complexity is O(n), and no additional space is consumed; hence, the space complexity is O(1) [12,39].

## 4. Experimental Analysis

#### 4.1. Experiment Setting

#### 4.2. The Energy Consumption Performance

^{2}and 200 m

^{2}, respectively.

^{2}and 200 m

^{2}, and the number of network nodes is 100, 200, and 500 for LEACH, LEACH-C, DEEC, and EEBDA.

#### 4.3. The Variance of the Residual Energy

## 5. Discussion

## 6. Conclusions and Future Works

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Average residual energy relative to the number of rounds in EEBDA, LEACH, LEACH-C, and DEEC protocols. (

**a**) 500 nodes in 100 m

^{2}area; (

**b**) 200 nodes in 100 m

^{2}area; (

**c**) 100 nodes in 100 m

^{2}area; (

**d**) 500 nodes in 200 m

^{2}area;

**(e**) 200 nodes in 200 m

^{2}area; (

**f**) 100 nodes in 200 m

^{2}area.

**Figure 11.**Number of alive nodes over rounds. (

**a**) 500 nodes in 100 m

^{2}area; (

**b**) 200 nodes in 100 m

^{2}area; (

**c**) 100 nodes in 100 m

^{2}area; (

**d**) 500 nodes in 200 m

^{2}area; (

**e**) 200 nodes in 200 m

^{2}area; (

**f**) 100 nodes in 200 m

^{2}area.

**Figure 12.**Comparison of the variance of the residual energy. (

**a**) 500 nodes in 100 m

^{2}area; (

**b**) 200 nodes in 100 m

^{2}area; (

**c**) 100 nodes in 100 m

^{2}area; (

**d**) 500 nodes in 200 m

^{2}area; (

**e**) 200 nodes in 200 m

^{2}area; (

**f**) 100 nodes in 200 m

^{2}area.

Notation | Definition |
---|---|

${d}_{0}$ | distance threshold based on the first-order radio model |

K | the number of clusters |

${n}_{k}$(x) | the nodes x in cluster {1, …, K} |

E_{t} | energy threshold for CH rotation |

Er | the residual energy |

E_{in} | the initial energy |

G_{xy} | location of the group center |

D(${n}_{k}$(x)) | Euclidean distance between ${n}_{k}$(x) and G_{xy} |

R_{min} | scanning range at given cluster center with radius 10 m |

R_{max} | scanning range at given cluster center with radius 25 m |

${C}_{k\in \left\{1,\dots ,k\right\}}$ | cluster {1, …, K} of the deployed area |

$C{H}_{k\in \left\{1,\dots ,k\right\}}^{maj}$ | the final majority value of cluster {1, …, K} |

$C{H}_{k}$ | cluster head {1, …, K} |

$B{n}_{k}^{{C}_{k}}\left(x\right)$ | a binary value of node x in cluster {1, …, K} |

BS^{maj} | the final majority value of a BS |

Parameters | Values |
---|---|

Size of the WSN | 100 m^{2}, 200 m^{2} |

Number of sensor nodes | 100, 200, and 500 |

Position of BS (m, m) | (50, 50), (100, 100) |

Packet size | 4000 bits |

Initial energy (E_{0}) | 0.5 J |

Energy for data aggregation | 5 nJ/bit/signal |

Deployment type | Random deployment |

Energy model | First-order radio model |

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**MDPI and ACS Style**

Liu, F.
Majority Decision Aggregation with Binarized Data in Wireless Sensor Networks. *Symmetry* **2021**, *13*, 1671.
https://doi.org/10.3390/sym13091671

**AMA Style**

Liu F.
Majority Decision Aggregation with Binarized Data in Wireless Sensor Networks. *Symmetry*. 2021; 13(9):1671.
https://doi.org/10.3390/sym13091671

**Chicago/Turabian Style**

Liu, Fanpyn.
2021. "Majority Decision Aggregation with Binarized Data in Wireless Sensor Networks" *Symmetry* 13, no. 9: 1671.
https://doi.org/10.3390/sym13091671