## 3 Proposed Scheme
### Distributed and Reliable Data Transmission: DRDT  
The proposed scheme DRDT consists of two major phases: helper node selection phase using helper value and transmission phase. Performing the two phases repetitively, DRDT increases the reliability  
Figure 2: Overview of proposed DRDT scheme.  
of the data transmission in an energy-efficient way. We first propose the helper value, followed by the helper node selection phase using the helper value.  
**Helper Value (\(H\))**  
A helper node, which can retransmit data packet with low cost, should be selected among neighbor nodes that overhear the data packet sent to the receiver node in order for DRDT to provide reliability in an energy-efficient way. The expected cost is defined as the total transmitted bits until the receiver node obtains the data packet [19]. We first explain the procedure how the helper node retransmits the data packet when the receiver node fails to receive the data packet to calculate the expected cost (Figure 3).  
Step 1: Helper node transmits a control packet to prevent unnecessary retransmissions of the sender.  
Step 2: Helper node retransmits the overheard data packet to the receiver node.  
For the receiver node to obtain the data packet successfully, the expected number of data packet transmissions is \(\frac{1}{PRR_{h\to r}\times PRR_{r\to h}}\), where \(h\) is the helper and \(r\) is the receiver in these two steps. Similarly, the expected number of control packet transmissions is \(\frac{1}{PRR_{h\to s}\times PRR_{s\to h}}\), where \(s\) is the sender. We assume that the data packet size ratio of a control packet to a data packet is \(\lambda\) to calculate the expected cost. Therefore, the expected cost to perform retransmission using a helper node can be written as follows.  
\[Expected\ Cost=\frac{1}{PRR_{h\to r}\times PRR_{r\to h}}+\frac{ \lambda}{PRR_{h\to s}\times PRR_{s\to h}} \tag{2}\]  
As we can see in Equation (2), minimizing the cost required to use a helper node on behalf of the sender node demands the maximization of the PRR between a helper node and the sender node, as well as the PRR between the helper node and the receiver node. That is, in an attempt to maximize the energy-efficient retransmission using a helper node, a node with a high PRR to both the receiver and the sender nodes is selected as a helper node.  
Figure 3: Retransmission of the helper node.  
The _helper value_ (\(H\)) is the criterion to calculate the condition of such a helper node. The helper value is defined as follows:  
\[H=w_{1}H_{PRR}(s,c)+w_{2}H_{PRR}(r,c), \tag{3}\] \[w_{2}\geq w_{1}\geq 0\ and\ w_{1}+w_{2}=1,\]  
where \(c\) denotes a current node that is considered as a helper node. \(w_{1}\) and \(w_{2}\) are the weighting values. Generally, the data packet size is larger than the control packet size, and therefore, a larger weighting value is applied to the PRR of the receiver node than to that of the sender node. \(H_{PRR}(a,b)\) refers to the PRR between nodes \(a\) and \(b\). It is defined as follows:  
\[H_{PRR}(a,b)=1-min(1,-\log_{10}PRR_{a\to b}\times PRR_{b\to a}) \tag{4}\]  
In \(H_{PRR}(a,b)\), logarithm function rapidly decreases the selected probability when PRR approaches low. In [10] and [11], when the number of retransmissions exceeds 10, the transmission is assumed to have failed. Therefore, if the PRR is below 0.1, the helper node cannot retransmit the data packet. Thus, this paper assumes the base of the log to be 10; this value can be changed.