Overview

The main purpose of this demonstration is about testing and comparing the traffic throughput before the recovery operation and after factory recovery operation. The expected result is the unique factory data of our target cable modem which is fully recovered from our system quickly and flawlessly, so that this cable modem can achieve the ideal throughput.

We take the advantage of a special type network with the idea of a structure which has a normal inflected form called combination network. The combination network was presented in [18]

“Network coding gain of combination networks”. And this type of network, when the size of the network increases, can reach the unbounded NC gain which is calculated by the network throughput ratio with NC to without NC. As we know, the combination network is presented as a multicast network with a topology that conforming to a certain principle. For taking this advantage of the combination network, we make the topology of this system as a regular graph which is presented in Figure 4-10 Topology of the factory data distribution. This topology contains three kinds of nodes: (1) Factory Data, (2) Generated Blocks and (3) Receiver CM. We explain these nodes in the following descriptions.

(1) Factory Data: In our design, we tar (derived from tape archive and commonly referred to as

"tarball") the factory data files into one compressed file (named FactoryData.tgz). And then this factory data can be divided into the continuous parts. So that we can easily get back the original factory data when the source cable modem gets the continuous parts.

(2) Generated Blocks: As we discussed in chapter 3, this system gets the continuous parts by using Gaussian Elimination to solve linear equation method. Since we get the continuous parts from the tared factory data, the source cable modem can generated blocks by linear coding.

(3) Receiver CM: The nodes at the bottom of this topology are the receivers. These receiver

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cable modems which is used to receive certain generated blocks from the source cable modem. In our design, the edge vector of a receiver cable modem's incoming edges must be linear independent.

Figure 4-10 Topology of the factory data distribution

As we know, in the random network coding, because of the nodes encode the received data with the random coefficients. That is, the nodes generate random coefficients for the edge functions to determining the outgoing edges' function independently. This kind of feature makes the random network coding maintains a linear coding scheme among the nodes without any control overhead, and become the main advantage [15]. In the other hand, the receiver cable modem's edge vectors of the incoming edges may not be linear independent. But we can not make this system at the risk of fail in factory data recovery.

Here is our solution, we make the coefficients that were generated like the way what the deterministic network coding dose. As we present in the last chapter, the cable modem which is going to backup it's factory data, it receives the coefficients that were assigned by the system. In Figure 4-10 , the source cable modem can generates the blocks with these assigned coefficients for it's factory data. There are n (in Figure 4-10, the number is 4) blocks which were generated by the source cable modem with these known coefficients, and relay these to the receiver cable modems.

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There are k (in Figure 4-10, the number is 2) multicast capacities of the network, in another word, any one of the receiver cable modems which receives k generated blocks from the source cable modem. Thus, we can see that there are Cn

k receiver cable modems which receive the generated blocks from the source cable modem.

For this demonstration, the source factory data is divided into three equal continuous parts. The source cable modem generate four blocks with these equal continuous parts by the assigned coefficient. In Figure 4-10, any receiver cable modem gets two generated blocks from the source cable modem. As our design and the rules we set to receiver node, any receiver node can only have one block which is the same as another node. In Figure 4-10, the green block is G1, the purple block is G2, the blue block is G3 and the yellow block is G4. We can see that the leftmost receiver node gets G1 and G2, the second on the left node gets G1 and G3, the third on the left node gets G1 and G4, the 4th on the left node gets G2 and G3, the second on the right node gets G2 and G4 and the last node gets G3 and G4. For this designed model, there are 7 node available cases: all available, 5 available nodes, 4 available nodes, 3 available nodes, 2 available nodes, 1 available node and no available node. It is easy to understand that if the available nodes more than 4, there are more than 4 kinds of encoded block we can get. Obviously, the source cable modem only needs to get the generated blocks from any two receiver cable modems of these six ones successfully, and then the source cable modem must have three to four encoded blocks. These received blocks are sufficient to return to the original factory data by Gaussian Elimination. We can say that, in this demonstration system, we only need one third of the receiver cable modems which are available to response for the recovery operation, so that 1/3 is our required availability.

Since we consider the issue of the receiver cable modem is unavailable, it is taken for granted to think over the status, when the source cable modem is out of this system in some cases, there should have a method to ensure the distributed blocks available in the network. Let us consider about this case, we have to guarantee the online nodes have enough distributed blocks for maintaining the factory data. In our concept, we must shift the missed blocks to any available

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stocks. For implement details, there is a synoptic and schematic diagram in the Figure 4-11 Off line scheme. And we are going to present the solution below.

Figure 4-11 Off line scheme

We let the nodes N1, N2, N3 and N4 be the cable modems in the network, and all nodes distribute the source factory data in this network already. These are either source nodes or receivers.

In some cases, N2 enters the off line status. For keep enough numbers of receiver cable modems, as we present in past chapter, the source cable modems N1, N3 and N4 sending maintain message and detect the generated blocks in N2 is unavailable for recovery operation. To this step, all of these source cable modem enter the post status, broadcast it's requirement to look for a appropriate receiver cable modem to take the place of the node who leaves. Base on the maintain list, the source cable modems have to give a judgment on the selected receiver cable modem which been percolated through the responded message from all the available nodes in this network.

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