## 3 The Problem  
This paper proposes a perceptual routing decision model, named ANCR. Different from the previous models which require not only the same transmission success rate on all links, but also the same transmission success rate in two directions of each link, our model assumes that the transmission success rates on all links are different, and the transmission success rates in two directions of a link are also different. A network coding strategy is proposed under these new and more practical assumptions. Here is an example, as shown in Figure 3a. It is assumed that the network meets the preconditions above-mentioned and the success transmission rates of all the links are all 100%. There are two data streams in two directions in the network. One is from the node A to the node E, whose path is \(A\to B\to D\to E\), and the number of transmission is three. The other is from the node F to the node B, whose path is \(F\to E\to C\to B\), and the number of transmission is three. Thus, finishing transmitting the two packets, the total number of transmission is six. Now, if we consider network coding opportunities and introduce the network coding strategy, the path from F to B will be changed to \(F\to E\to D\to B\). It is obvious that D has a coding opportunity, which makes the number of  
Figure 2: Illustration of “Alice-Bob structure” network coding. (**a**) Transmission without network coding; (**b**) Transmission with network coding. transmission of the node D change from two to one. Thus, the total number of transmission changes to five and the network performance is promoted by about 17%. However, in a real WSN, such as monitoring the environment where wildlife lives, military investigation and so on, link quality [15] is always affected by many unpredicted and uncertain external environmental factors, such as temperature, humidity and electromagnetic waves, etc [16]. In addition, the network's own factors, such as the nodes' transmitting power and working frequency, etc., also affect the link quality. These factors usually cause packet loss in data transmission processes [17; 18]. Therefore, in an actual network, there are various transmission success rates on different links and in the two directions of a link, which makes the above-mentioned traditional network coding unusable. As shown in Figure 3a,b, they have the same network topology, but there is the different link quality in the latter (The numbers marked on each link represent the transmission success rate of the link. For example, the transmission success rate of the link BC is \(1/3\), which means that, on average, if the number of transmission is three, only once is successful.). Without considering the transmission success rates of the links and the coding opportunities, the optimal paths should be \(A\to B\to D\to E\) and \(F\to E\to C\to B\). However, retransmitting caused by unsuccessful transmission leads to the total number of transmission of the two data streams is ten \(((1+1+3)+(1+1+3)=10)\). To introduce the coding opportunities, we need to appropriately adjust the paths. If the path \(A\to B\to D\to E\) is not changed, the other path will be changed to \(F\to E\to D\to B\). Then the node D has a new code opportunity. Unlike the network where there is no difference in link quality, the transmission success rate of the link DE is \(1/3\). So after calculating, the total number of transmission of the two data streams is nine \(((1+1)+(1+3)+3=9)\) although D can encode the two packets from the different data streams into a big one and broadcast it to B and E. The network performance is improved by only 10%. Therefore, in a network with different-success-rate links, though the network coding strategy could be used, the improvement of the whole network performance would be discounted, due to the influence and restriction of the low link quality.