Fountain Codes with XOR of Encoded Packets for Broadcasting and source independent backbone in Multi-hop Networks using Network Coding

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1 Fountain Codes with XOR of Encoded Packets for Broadcasting and source independent backbone in Multi-hop Networks using Network Coding Khaldoun Al Agha LRI, Paris XI University, Orsay, France Nour KADI LRI, Paris XI University, Orsay, France Ivan Stojmenovic SITE, University of Ottawa, Canada Abstract We consider multiple source asynchronous broadcasting problem. That is, in each broadcast, one of the nodes is the source, and the message is to be received, unaltered, by all the other nodes in the network. We propose to exploit LT code, which is one of the fountain codes, with the source independent backbone in order to reduce the number of transmissions for broadcasting with network coding in ad hoc wireless network. We use the principle of LT code to perform network coding in a simple distributed manner where encoding can be applied with both received singletons and non-singletons, and generated candidates can be used in an optimization criteria. We show by simulation that our approach reduces the number of transmissions required for flooding. I. INTRODUCTION Forward error correcting (FEC) schemes such as fountain codes [1], [2] are provided as a solution for reliable communication in lossy networks. They eliminate the need of retransmission request which increases the bandwidth consumption and increases the delay. The most important characteristic of these codes is its low complexity of encoding and decoding functions. These schemes is considered as endto-end approaches where the source node generates a flow of encoded packets and the destination starts decoding to get the source packets when it receives enough encoded packets. LT (Luby transform) codes [1] are special case of digital fountain s codes. LT encoder [1] chooses randomly from a set of K packets, and according to a distribution, a subset of d packets, and XOR them. In practice, decoding may be possible from a set S of such encoded packets, for S slightly larger than K. Decoding starts from packets with d =1(that we call here singletons), which are then removed (by applying ) from the encoded packets where they participate. The process is repeated until all packets are decoded, or there are no more singletons. This decoding algorithm forces the increased number of singletons to avoid halting decoding process. We are particularly interested in wireless ad hoc and sensor networks, in applications where multiple sources broadcast data to all other nodes. Broadcasting using network coding was studied in [3]. However, XOR and opportunistic listening to neighbor receptions was not applied. In XOR-based algorithm [4], forwarding nodes store only source packets, and also store subset of source packets received by each neighbor (via opportunistic listening). An encoded packet will benefit one of neighbors only if it contains exactly one new source packet. Greedy heuristic starts with one source packet at the head of output queue. Then sequentially other packets would be XORed to previously taken source packets only if they allow all neighbors to decode received packet. [4] chooses some of nodes to retransmit messages, independent on coding process. We refer to this set as backbone nodes. The proposed backbone construction used in [4] is very similar to MPR (multipoint relay). Each node selects its own MPR (multipoint relay) set which is set of one-hop neighbors that cover two-hop neighbors. Broadcasting from a source node then proceeds by retransmitting from any receiving node if it identifies that it is MPR node of sender node. Decoding process is improved in [5]. Their algorithm has similar goal like XORbased algorithm [4], to maximize the number of neighbors that can learn one new source packet. However, they do not require the ability of all neighbors to decode received packet in their greedy heuristics. Packet with longest queue delay is added first to the encoded packet. Each of the remaining source packets is tested for inclusion in the current set of source packets. If any of them would increase the number of neighbors that will benefit then the one with maximal such benefit will be added. Encoded packets are not memorized at sender or receiving nodes, as they all store only decoded source packets throughout the process. [4] also proposes a Reed-Solomon based coding algorithm. The main drawback of this algorithm is the need to send k (maximal number of missing packets at any neighbor) packets at once, and the need for neighbors to receive them all to complete decoding, otherwise the whole set of transmitted packets is wasted (even if a single failure happens at a single neighbor). The LT-code based algorithm from [5] allows nodes to store received encoding packets that couldn t be decoded immediately. Each time a node has a sending opportunity signaled by MAC, it applies LT code over native packets that are in need by at least one of neighbors, and are assigned for retransmission by the node with MPR based backbone. The number of native packets d to be encoded is decided /9/$2. 29 IEEE

2 by selected distribution [1]. If d > 1 then the receiver will eliminate from the encoded packet all native packets that are present in it and already received. After that, all remaining (and stored) encoded packets will be composed of only native packets which are not individually decoded. If the degree of encoded packet is reduced to 1 then new native packet is recognized, and it can be then used to reduce other, previously received and stored, encoded packets. The receiver then piggybacks IDs of newly recognized packets to the next packet data to inform neighbors. In this paper we propose to integrate the notion of network coding with the technique of connected dominating set which represents the source independent backbone in order to improve the broadcast process in ad hoc wireless network. When using the source independent backbone, the intermediate nodes are either responsible for retransmitting all or none of packets. This increases network coding efficiency since forwarder nodes use all available packets in encoding. We use a simple and distributed method to apply LT-based encoding at each forwarder. We propose to increase the options for encoding, by encoding together native packets and already encoded packets instead of only native ones. Our design uses the following principles: It is based on deterministic broadcasting as it employs a source independent backbone where only some forwarders are responsible for rebroadcasting the packets. This technique reduces the redundant retransmissions. It employs opportunistic network coding in order to overload each transmission with additional information as possible without delaying the packets. It implements the coding by using the principle of LT code which is rateless erasure code and is characterized by the simplicity of its encoding and decoding functions. Our simulation results show the efficiency of our approach as it reduces the number of transmissions required for flooding and reduces the packet delay as well. II. RELATED WORK A. Broadcasting with network coding Broadcasting using network coding was studied in [3]. Each node is a source that wants to transmit the same amount of information to all other nodes. Authors apply linear network coding from [6]. Intermediate nodes may combine incoming encoded packets, by making a random linear combination of them. The vector of coefficients (coding vector) over n source packets is transmitted together with the encoded message, and is collected in a decoding matrix G. A received packet is said to be innovative if its coding vector increases the rank of matrix G. Once a node receives n linearly independent combinations, it is able to decode and retrieve the information on n sources. Decoding amounts to solving linear equations with complexity bounded as O(n 3 ) [6]. [3] proposes algorithms for a random ad hoc wireless network. The main problem with linear algebra approaches is that the size of linear combination of packets is not controlled. Another problem is that the number of transmitted encoded packets is probabilistic and is not linked to the decoding needs of neighbors. That is, overhearing (opportunistic listening) neighbor receptions is not utilized, as the algorithm simply assumes that all neighbors need all the packets. Fountain codes were used in [7] to broadcast n packets from the same source. The source generates m encoded packets using LT codes, and floods each of them into the network. Each recipient retransmits each received packet with certain fixed probability. When a recipient has received enough data, it can decode original packets. This is a restricted problem statement, where encoding and decoding is done only at endpoints, while intermediate nodes only forward received packets. This problem can be solved by our techniques also, since it is a special case of our more general many to all asynchronous broadcasting process. Network coding was applied in [4] for deterministic broadcasting. In their XOR-based algorithm, forwarding nodes store only source packets, and also store subset of source packets received by each neighbor (via opportunistic listening). Greedy heuristic is provided to form the encoded packet in which all neighbors can decode received packet. [4] also proposes a Reed-Solomon based coding algorithm. Again, no memorization of received encoded packets is used for combining with future incoming encoded packets. Kadi and Al Agha [5] applied network coding to optimize MPR-based flooding. Each node selects its own MPR (multipoint relay) set which is set of one-hop neighbors that cover two-hop neighbors. Broadcasting from a source node C then proceeds by retransmitting from any receiving node if it identifies that it is MPR node of sender node. The algorithm from [8] allows nodes to store received encoding packets that couldn t be decoded immediately. Each time a node has a sending opportunity signaled by MAC, it applies LT code over native packets that are in need by at least one of neighbors, and are assigned for retransmission by the node with MPR based backbone. The number of native packets d to be encoded is decided by selected distribution [1]. If d>1 then the receiver will eliminate from the encoded packet all native packets that are present in it and already received. After that, all remaining (and stored) encoded packets will be composed of only native packets which are not individually decoded. If the degree of encoded packet is reduced to 1 then new native packet is recognized, and it can be then used to reduce other, previously received and stored, encoded packets. The receiver then piggybacks IDs of newly recognized packets to the next packet data to inform neighbors. B. Connected Dominating Set For each message, there exist a dedicated backbone set of nodes (called forwarders) that needs to retransmit it so that all other nodes receive the message. This type of backbones is also called connected dominating set. A set V is dominating set for G if each node from G is either in V or has a neighbor in V. We will describe here only one type of connected dominating sets, based on the concept of multipoint

3 Fig. 1. MPR-CDS algorithm. relays. It is called here MPR-CDS. Adjih, Jacquet and Viennot [9] proposed a MPR-based algorithm for CDS (MPR-CDS) backbone construction. Each node computes its multipoint relay set by selecting a subset of 1-hop neighbors which cover all 2-hop neighbors. The node attaches the relay list to a hello message which is broadcasted to its neighbors. Upon receiving the hello message, an intermediate node decides to join the CDS if it has either the smallest ID in its neighborhood or if it is the multipoint relay for the neighbor with the smallest ID. Wu [1] improved the rule by eliminating the node that has the smallest ID among its neighbors, but without two unconnected neighbors. The construction of MPR-CDS backbone requires 2-hop neighbor knowledge, plus a message containing the list of relay nodes of each node. This can be treated overall as CDS construction requiring three rounds of messages, plus another round if the CDS decisions are to be communicated to neighbors. Consider the example in Figure1. Since a and b are the nodes with the smallest ID amongst their neighbors, they decide to belong to the CDS. Node a computes its multipoint relay set {g, h} and then attaches the list to its hello message. Upon receiving the hello message, nodes g and h decide to belong to the CDS as well. Similarly, node f decides to belong to the CDS since it is the multipoint relays of b. Finally, nodes {a, b, f, g, h} form a CDS by the algorithm [9]. Using the improved algorithm [1], node b is not selected for CDS, and CDS set is {a, f, g, h}. III. CONTRIBUTIONS This article makes two main contributions to network coding based broadcasting. A. Source independent backbones As mentioned, source dependent backbones, like those defined by MPR, have intermediate nodes which retransmit some packets, but not the others. This means that the power of encoding and assisting neighbors is reduced. We propose to apply instead any source independent backbone concept. One such choice is MPR-DS [9]. There are other choices, and reader can consult [11] for their descriptions. It is obviously also important that the average number of nodes in the backbone is small, or close to the ones selected by MPR, as otherwise the benefits of shared backbones would be reduced. When applying source independent backbone concept, intermediate nodes are either responsible for retransmitting all or none of packets. B. LT encoding from singletons and non-singletons All existing methods are based on encoding and retransmitting native packets, that is, received and/or decoded singletons or native packets generated at the node itself. However, backbone nodes also store all received encoded packets which they could not decode, but are aware of the elements in the corresponding subsets. They can also be used to generate packet with certain desired degree (number of native packets). For example, if a relay node R has singletons x, u, and subset{y, z}, then a candidate subsets for encoding are also {x, y, z}, {u, y, z} and {x, u, y, z} in addition to {x, u}. For instance, if LT coding prefers to encode three variables into a packet, in this case it is possible only with the participation of {y, z} and joining either x or u. To achieve randomness, appropriate weights need to be calculated. In this case, the probability of selecting {y, z} should be.5 since they together represent 2 out of 4 possible variables. Further study is needed to identify proper soliton probabilities, that is probabilities for encoding a singleton, or encoding message with d native packets, for each d. These probabilities are expected to be lower for singletons and higher for others, leading to increased network coding benefits and reduction of overall number of transmitted messages. IV. : HIGHLIGHTS ON THE PROTOCOL Our protocol is an integration of the source independent backbone represented by the connected dominating set and the LT-based network coding. In the following subsections we give an overview of each of these techniques and how we use it. A. LT-based Network Coding The encoding operation is accomplished at each forwarder in a distributed manner. Unlike the original LT code, which use only native packets for the encoding operation, we use both singleton and non-singleton to generate the encoding packet. This can speed up the flooding operation as the node doesn t have to wait any successful decoding before it can submit a packet. So when a forwarder has an opportunity to send signaled by MAC, it checks if it has any native or encoded packets in its buffers, and then choose randomly some of these packets to mix (XOR) together and broadcast it to its neighbors. XOR (bitwise sum modulo 2) is used as coding operation to control the bit length of transmitted messages. To choose the degree of the encoded packet we use a simple distribution such as p(d) = 1 ; <d k where d is the 2 d degree of the encoded packet ( the number of native packets XORed together) and k is the total number of native packets available at the forwarder either decoded or embedded within an encoded packet. For example, suppose that node x has 3 native packets p, q, r and one encoded packet z w. Then x can send packet of degree from 1 to 5, where p(1) = 1 2 represents the probability of node x to send a native packet and p(2) = 1 4 represents the probability to send an encoded packet of degree 2...etc. Note that if the selected length exceeds the maximal one, or is impossible to combine from existing packets, then

4 new value of d is generated. Then, choosing the d packets (coding candidates) to XOR is done randomly. In our previous example if x choose to XOR three packets, it can choose one of the following cases {p q r, p z w, q z w, r z w}. B. Packet Decoding The node needs to retrieve the native packets from the received packet by using the decoding process as follow: 1) If the received packet R is of degree d>1, the node tries to reduce this degree by processing the packet R against all native packets it has stored in the buffer. That means to XOR the packet R with all the native packets stored in the buffer which are coding candidates of R. Each coding candidate found in the buffer reduce the degree of R by 1. If the reduced degree of R is still greater than 1 then R will be stored in the buffer (and used later for encoding future packets). For example, suppose that node x has 2 packets P 1, P 2 in the buffer, and it receives an encoded packet R = P 2 P 3 P 4 of degree 3. By XORing P 2 with R we get R = R P 2 = P 2 P 3 P 4 P 2 = P 3 P 4 which has degree 2. 2) If the received packet R has degree 1 or its degree has been reduced to 1 in the previous step, it is inserted into the buffer as it is a native packet. This native packet is then used to reduce the degree of the other encoded packets by matching it against all the encoded packets residing in the buffer. 3) Whenever the previous step succeeds to reduce degree of any packet in the buffer to 1, this packet is processed against the other encoded packets remaining in the buffer. V. SIMULATION To evaluate the efficiency of the integration of source independent backbone with LT-based Network coding for broadcasting in wireless multi-hop networks, we implemented in a custom network simulator written in C++. At the beginning of the simulation, nodes are placed randomly on the simulation area and don t move during the simulation process. Transmissions are received by all nodes within transmission range. A packet transmission takes exactly one time unit. A node can either send or receive only one packet at a time unit. For network traffic, we assume that each node has one packet to broadcast to all the nodes in the network. All of these packets are generated at the beginning of the simulation, and then the simulation continues to run without inserting further packets until all the packets are delivered to the entire network. We assume that only one node can send at a given time unit and in this way we avoid packet collisions. We compare the performance for different density (average number of neighbors) values. We suppose that the number of nodes is 15. The nodes are placed randomly in a square network area whose size is chosen according to the desired density and selected fixed transmission radius. The average number of neighbors changes from 2 to 7. We only consider Nb. of Transmissions Avg. Delay MPR (a) Number of transmissions MPR (b) Average packet delay Fig. 2. (a) number of transmissions required to broadcast all the packets into the entire network. (b) average delay for a packet to be delivered to all the nodes. connected networks. Our performance metrics are the number of transmissions needed for flooding and average packet delay. Packets delay is measured by the average time needed for one packet to be delivered to the entire network. We compare the performance of three approaches. The first approach is MPRbased flooding. The second approach is the original LT code used in flooding where each forwarding node (in addition to the source node) performs LT code over the packets it has received. The third is, our previous approach [8] that combines the Multi Point Relay (MPR) technique with LT code [1] to perform network coding at each MPR node. The last approach is which combines CDS with LT-based network coding, described in section IV. Figure 2 shows the efficiency of our approach in term of the number of transmissions required for flooding all the packets and the packet delay. Our gain is about 8% in comparison to MPR approach, and is especially notable for low densities. We see that for sparse networks, MPR technique doesn t perform very well in term of number of transmissions required. So exploiting the network coding technique can significantly reduce the number of transmissions as done in and. Further, we observe that the delay of is superior to by about 4%. This is due to two reasons. First, using source independent backbone (CDS) instead of source dependent backbone (MPR) increases the benefit of network coding because all the packets pass through

5 Avg. nb. of coded packets Avg. nb. of decoded packets (a) average packet degree (b) Packet delivery Fig. 3. (a) average number of native packet XORed and sent at each transmission, (b) average number of native packets delivered at each transmission. the same forwarder nodes and this enhances the encoding process. Second, the optimization accomplished in the encoding function increases the number of packets delivered in single transmission as shown in fig3-b. Our new LT probability distribution function proposed in section IV-A decreases the average number of coded packets (fig3-a) and also it speeds up the decoding process (fig3-b). VI. CONCLUSION AND FUTURE WORK We have proposed, an approach which exploit the source independent backbone with LT-based network coding to improve the performance of broadcast process in ad hoc wireless network. We use a connected dominating set definition as the backbone. For network coding, we make use of the principle of LT code which is one of the fountain codes. LT coding is applied at each forwarder in a simple distributed manner. Instead of using soliton distribution we propose a simpler distribution which give us better performance as shown in our simulation. We leave the analysis of this distribution for future work. Another modification proposed here is to use both singleton and non-singleton in the encoding function. Our future work is to optimize LT code furthermore to speed up the decoding process by combining the stored encoding packets instead of waiting to receive more singletons, in order to avoid halting decoding process. We also propose to apply the same algorithm for the secure multi-path routing process between a fixed source-destination pair. Encoded packets are sent over two or more disjoint paths toward destination. All nodes, including intermediate ones, apply the same algorithm, and forward according to selected routing scheme. However, only destination receives enough packets to decode native ones. In some algorithms, the decision on selecting the encoded subset for transmission is based on a criterion, such as maximizing the number of recognized singletons at neighbors, instead of generating one at random. Further, the ability of neighbors to decode certain variable packets should be judged not only on their recognized singletons, but also on other packets they store. Current node may, by having two-hop knowledge, keep a list of received and generated encoded nonsingleton packets and use them in judging the quality of a candidate subset. Further, the optimization criterion itself may go beyond just counting recognized singletons. It could include also the number of newly generated subsets at each neighbor, with proper weights that could depend on the size of these subsets. This also increases the ability of neighbors to decode future incoming packets. ACKNOWLEDGMENTS This research was supported by NSERC Canada Strategic Grants STPSC and STPGP REFERENCES [1] Luby, LT codes, in FOCS: IEEE Symposium on Foundations of Computer Science (FOCS), 22. [2] A. Shokrollahi, Raptor codes, IEEE Transactions on Information Theory, vol. 52, no. 6, pp , 26. [3] C. Fragouli, J. Widmer, and J.-Y. L. Boudec, Efficient broadcasting using network coding, IEEE/ACM Trans. Netw, vol. 16, no. 2, pp , 28. [Online]. Available: [4] E. L. Li, R. Ramjee, M. M. Buddhikot, and S. C. Miller, Network coding-based broadcast in mobile ad-hoc networks, in INFOCOM. IEEE, 27, pp [Online]. Available: [5] N. Kadi and K. A. Agha, Optimized MPR-Based Flooding in Wireless Ad Hoc Network using Network Coding, in IFIP/IEEE Wireless days 8. Dubai, UAE: IEEE Explorer, November 28. [6] P. A. Chou, Y. Wu, and K. Jain, Practical network coding, in Allerton Conference on Communication, Control, and Computing, Monticello, IL, 23. [7] R. Kumar and A. Paul and U. Ramachandran, Fountain broadcast for wireless networks, in IEEE Int. Workshop on Network Sensing Systems, San Diego, USA, 25. [8] N. Kadi and K. A. Agha, Network coding based flooding using fountain codes, Technical Report 15 LRI, Univ. Paris-Sud XI, Tech. Rep. 15, 28. [9] C. Adjih, P. Jacquet, and L. Viennot, Computing connected dominated sets with multipoint relays, Oct. 22. [1] J. Wu, An enhanced approach to determine a small forward node set based on multipoint relay, vol. 4. Vehicular Technology Conference VTC 23-Fall IEEE 58th, 23, pp [11] D. Simplot-Ryl, I. Stojmenovic, and J. Wu, Energy efficient backbone construction, broadcasting, and area coverage in sensor networks,, ser. in: Handbook of Sensor Networks: Algorithms and Architectures (I. Stojmenovic, ed.). Wiley, 25.