As mentioned in the previous section, the grid network is practical, scalable, simple im-plemented, and will be applied to many elds in the future. In general, most grid network applications, such as agriculture monitoring in paddy elds, tracking of an object and others, are served by multi-hops communication. Moreover, the advancement of technology has led to great progress in computers, and as more kinds of network applications are invented in the upcoming years, the computers can not only become cheaper but would also be able to take up many more tasks than in the past. The grid network density and the utility rate of network communications can be increased enormously year by year. Since the grid net-work throughput and capacity directly aect the e ciency in services involving grid netnet-work applications, the improvement of both is a critical issue. Fortunately, a novel and powerful tool, network coding, is proposed by Ahlswede et al. [13] in recent years to improve network
throughput and capacity, which seems to have provided a solution to the above-mentioned problem.
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Figure 2.4: Butter y example
The butter y network is a well-known example [13] for illustrating the idea underlying network coding. In Figures 2.4(a) and 2.4(b), it is assumed that the capacity of each link is one message stream during one unit of time, and the middle routers W and X only forward received message stream. S1 and S2 represent two source nodes, which prepare for transmission message stream of both P1 and P2 to both destinations D1 and D2. In Figure 2.4(a), in the network without network coding, it is easy to predict that the bottleneck will happen at the middle routers W and X, because the middle routers W and X can only relay one message stream P1 or P2 during one unit of time. Hence, it leads to the conclusion that
2.4(b) describes the network with network coding. When the middle router W receives the message streams of both P1 and P2, it combines them into P1⊕ P2 by mixing two message of bits and forwards it to the destinations D1 and D2. The destinations D1 and D2 receive the message stream of both P1 and P2 by extracting its message stream from P1⊕ P2 using one of received message stream of P1 and P2. Thus, the network throughput with network coding is 2 message stream per unit of time, and is better than that without network coding.
Network coding was rst proposed in the pioneering work by Ahlswede et al. [13] in which they showed that multicast capacity can be increased by properly mixing information from dierent sources at intermediate nodes. Following Ahlswede's work, a large number of works are focused on coding packets based on network topology to improve network capacity. Li et al. [14] extend the work and show that a linear coding scheme for multicast tra c that can achieve the max ow from the source to each receiving node that is the maximum capacity bound [15]. In [16], polynomial time encoding and decoding algorithms are presented by Koetter and Me'dard and are extended to random coding by Ho et al. [17].
In the sensor network, Dimakis and Dan et al. [18,19] exploit the network coding approach to achieve e cient data storage, collection, and dissemination. Recent researches show that network coding in speci c unicast topologies can induce better throughput than in traditional transmissions [2022]. Moreover, [5, 23] indicate that implementing network coding using XOR coding on the MAC layer of IEEE 802.11 can eectively improve end-to-end unicast throughput.
Most of the works described above focus on the coding algorithms. There are also some theoretic works on analyses of the impact of network coding on network throughput. In [24], the authors developed the theoretical foundation for analyses of the throughput capacity of wireless network. The main results are fold. First, the throughput capacity of two-dimensional arbitrary wireless networks is in the order of O(√
n), where n is the number of nodes in the network; and second, for random wireless network, the throughput capacity will
scale with O(lognn ). Since such results were published, the throughput capacity of random wireless networks has been studied extensively in the literatures [2527]. In the random wireless network, Lu et al. [28] show that network coding on the physical-layer can improve the throughput capacity substantially, minimize delay and provide con dentiality. It also derives tighter bounds in two-dimensional random wireless networks with unicast tra c, which is uniformly distributed among all nodes. Except for adapting network coding to networks, MAC, physical layers, David et al. [29] proposed a modi cation for TCP of IEEE 802.11 back-o mechanism using the feedback approach. It XORs the forwarding ow of TCP data packets and reverses the owing TCP data packets to improve the throughput.
In [30], the authors show that the total number of transmissions with network coding, as compared to that without network coding, is a constant factor under the xed network, such as the circular network and the grid network. According to related works, network coding is a powerful tool which, unquestionably, can improve the network throughput of multicasts, broadcasts, TCP mechanisms, and other network transmission mechanisms. To implement network coding, the network should include two properties: path diversity and multicast.
In wireless networks, the broadcast nature of wireless communications provides an envi-ronment for implementing network coding schemes. In other words, packets are transmitted by a transmitter over the air interface. Thus, wireless devices can receive the packets while located within the radio range of the transmitter. Moreover, while a wireless device transmits packets to the nexthops by broadcasting, it is very likely for one-hop neighbor devices to overhear packets. The broadcasting feature can satisfy both requirements for implementing network coding: path diversity and multicast. Hence, the environment of the wireless grid network is applicable for implementing network coding.