Network-Coded Broadcast Incremental PowerAlgorithm for Energy-Efficient Broadcasting

in Wireless Ad-Hoc Network

Sauradyuti Coondu, Anasua Mitra, Samiran Chattopadhyay, Matangini Chattopadhyay∗, Munmun BhattacharyaDepartment of Information Technology

∗School of Education TechnologyJadavpur University

Kolkata, IndiaEmail: {sauradyuti, anasuamitra2005, samirancju, matanginic, munmunds}@gmail.com

Abstract—An important operation in multi-hop wireless ad-hoc networks is broadcasting, which propagates informationthroughout the network. We are interested to explore the issueof broadcasting, where all nodes of the network are sources thatwant to transmit information to all other nodes, in an ad-hocwireless network. Our performance metric is energy efficiency, avital defining factor for wireless networks as it directly concernsthe battery life and thus network longevity. We show the benefitsnetwork coding has to offer in a wireless ad-hoc network as far asenergy-savings is concerned, compared to the store-and-forwardstrategy. Network coded broadcasting concentrates on reducingthe number of transmissions performed by each forwarding nodein the all-to-all broadcast application, where each forwardingnode combines the incoming messages for transmission. Thetotal number of transmissions can be reduced using networkcoding, compared to broadcasting using the same forwardingnodes without coding. In this paper, we present the performanceof a network coding-based Broadcast Incremental Power (BIP)algorithm for all-to-all broadcast. Simulation results show thatoptimisation using network coding method lead to substantialimprovement in the cost associated with BIP.

Keywords—Broadcast Incremental Power, Energy-Efficiency,Minimum Power Broadcast Problem, Network Coding, Wireless Ad-Hoc Network, Wireless Multicast Advantage

I. INTRODUCTION

The new breakthroughs in micro-mechano-electrical sys-tems, digital technology and wireless communications have ledto the advent of wireless ad-hoc networks. A popular operationin wireless ad-hoc networks, is to send one data from an iden-tified source node to all other nodes. This operation is widelyknown as broadcasting, and is useful in various contexts, i.e.,routing processes, network configuration processes, networktopology discovery processes, and so on [1].

One of the most important issues in the wireless ad-hocnetworks is energy efficiency, because in many applicationscenarios, nodes in wireless ad-hoc networks operate on batterypower and sometimes it is quite difficult or even impossible toreplace/recharge the batteries, when large number of wirelessnodes are located in averse or remote limited-energy environ-ments. The main source of energy consumption in wirelessad-hoc networks is radio, which is usually comprised of threeparts, i.e., transmission power, reception power and idle power,and the idle power is insignificant compared to the other

two [2]. Since in broadcast operation, all the nodes in thenetwork must receive messages, therefore, the reception poweris also not considered for determining energy consumption.That leaves us with only the transmission power as the energycost. It is very energy-consuming to transmit a signal to alonger range because of the non-linear attenuation propertiesof radio signals. Long distance transmissions also result inwidespread interference across the network and hence theyshould be avoided.

A. Wireless Multicast Advantage

The issues discussed above can be seen as correlated,and they can be handled together by taking advantage ofthe so-called wireless multicast advantage property [3]. Thisproperty is based on the observation that, in wireless networks,devices are usually equipped with omnidirectional antennae,and for this reason multiple nodes can be reached by a singletransmission, without the sender suffering from additionalenergy costs.

B. Minimum Power Broadcast (MPB) Problem

Given a network with an identified source node, the min-imum power broadcst (MPB) problem is to allocate trans-mission powers to the nodes such that the total power con-sumed is minimized and the network is connected [4]. TheMPB problem in wireless ad-hoc networks has been provedto be NP-complete in [5], implying that polynomial timealgorithms are not known to exist. An important issue inwireless ad-hoc networks is to provide an energy-efficientsolution to the MPB problem given that wireless nodes havelimited energy budget. In the case that transmission poweris similar for nodes in the network, the minimum-powerbroadcast problem is transformed to the problem of finding aspanning tree with a minimized number of intermediate nodes.Generally, a broadcast tree can be described as the source nodebeing the tree root and the intermediate nodes shall relay andretransmit the message to their children after reception.

C. Broadcast Incremental Power

In numerous works, the minimum power broadcast problemis transformed to the problem of finding a spanning tree. Onenoteworthy paper in this regard was proposed by Wieselthier

���������� �������������� ���������������� ����������

��� � ���� !��� !"��"#!�$���%������&&& ��

et al. [3], who first noticed that the so-called ”node based” per-spective is more appropriate for wireless environment than thepreviously followed ”link-based” algorithms. They developedthe Broadcast Incremental Power (BIP) algorithm, which isa straightforward sub-optimal heuristic for building minimumpower broadcast trees in wireless ad-hoc networks. The mainpurpose of BIP is to construct a broadcast tree rooted at thesource node, and it is built in a similar way to Prims algorithmthat is used to construct the Minimum Spanning Tree (MST).

D. Network Coding

Network coding is a recently introduced concept to effi-ciently communicate data in wireless ad-hoc networks, wheredata flows coming from multiple sources are integrated toenhance robustness, reduce delay, and increase throughput.In contrast to the conventional store and forward approach,it implements a store, code, and forward technique, whereeach node stores incoming packets in its own buffer and trans-mits their combinations. This technique allows for increasedthroughput efficiency as well as scalability and robustness[6] leading to fewer transmissions and thus helps to savetransmission and reception energy [7]. Furthermore, they arenot limited to error-free communication networks, but can alsobe acquired in ad hoc networks [8].

Given the benefits that network coding has to offer forbroadcasting in wireless networks, in this work, we explore theimprovement in the performance of BIP when implemented inconjunction with network coding. Our interest is in the specificproblem of all-to-all broadcast communication. As figure ofmerit we use energy efficiency, calculated as the number oftransmissions required for an information unit to reach allnodes in the network. We evaluate the performance of ouralgorithms on random, realistic networks (where we obtainsimulation results). We show that the network coding-basedBIP substantially outperforms non-coded BIP.

The rest of the paper is organized as follows. In SectionII, we formulate the problem. Our approach of the networkcoding-based BIP is presented in Section III. Simulation resultsare presented in Section IV, while Section V concludes thepaper.

II. PROBLEM FORMULATION

A. System Model

We consider source-initiated, circuit-switched, all-to-allbroadcast sessions, where all nodes in the network have sourcedata to be broadcast. The network consists of N nodes, whichare randomly distributed over a specified region.

The connectivity of the network is dependent on the trans-mission power. We assume that each node can choose its powerlevel. We also assume that the received signal power varies asr−α, where r is the range and α is a parameter that generallyvaries between 2 and 4, depending on the properties of thecommunication medium. Based on this model the transmissionpower needed to sustain a link between two nodes separatedby range r is proportional to rα. Without loss of generality,the normalizing constant is set equal to 1, resulting in:pij = power needed for link between Node i and Node j

= rα,where r is the distance between Node i and Node j.

We assume the use of omnidirectional antennas; thus allnodes within communication range of a transmitting nodecan receive its transmission. It is important to note how thebroadcast property of wireless communication can be exploitedin broadcast applications. Consider the example shown in Fig.1, in which a subset of the broadcast tree involves Node i,which is transmitting to its neighbours, Node j and Node k.The power required to reach Node j is Pij and the powerrequired to reach Node k is Pik. A single transmission at powerPi,(j,k) = max{Pij , Pik} is sufficient to reach both Node j andNode k, based on our assumption of omnidirectional antennas.

Fig. 1: The wireless multicast advantage

As noted earlier, we address only the transmission energy.Thus, the total energy of the broadcast tree is simply the sumof the energy expended at each of the transmitting nodes inthe tree; leaf nodes (which do not transmit) do not contributeto this quantity. Therefore, the total transmission energy isproportional to the total power needed to maintain the tree.Hence, we evaluate performance in terms of the total powerrequired to maintain the tree.

B. Construction of Energy-Efficient Broadcast Trees using BIP

In this section, we review the well-known traditional broad-casting algorithm, BIP. After the development of this algo-rithm, there hasn’t been any remarkable progress in the fieldof broadcasting in wireless networks due to the complexityof the problem. Most of the authors who have proposed anynewer algorithm [4], [9], [10], [11], [12] have considered BIPas a benchmark to compare the performance of their algorithm.This is why we have considered BIP, among other algorithms,for the construction of broadcast trees.

Taking into account the wireless multicast advantage, useof omnidirectional antennas and adjustable transmission powerof the nodes, discussed in the previous section, BIP proceedsas follows. Given a random deployment of wireless nodes, theprocess of tree construction starts from the source node, whichbecomes the root of the broadcast tree. Then, the node, sayNode i, nearest to the source node is added to the tree, withthe source node, say Node s, transmitting at power level Psi.Thereafter, at each step, the node which can be reached, fromany node already in the tree, with the minimum incrementalcost [3] is added to the tree. After a new node is added tothe tree, the cost to reach the other nodes, which are not inthe tree yet, from the nodes present in the tree is dynamically

�!

updated. Proceeding in this way, till all the nodes are addedto the tree, the final broadcast tree is obtained. Examples andpseudo-code can be found in [3].

Since we are focused on all-to-all broadcasts, all the nodesin the network follow the same procedure separately to buildtheir broadcast trees. The nodes in any particular broadcasttree do not necessarily have to use the same power levels;moreover, a node may use different power levels for the variousbroadcast trees in which it participates.

C. Network Coding in Broadcasting

Network coding [13] can be used to enable the intermediatenodes to integrate packets before retransmitting. Therefore,network coding can be used for efficient broadcasting byreducing the total number of transmissions [14]. In [15],Fragouli et al. has shown the quantitative energy savings thatnetwork coding has the capability to render in broadcasting.

The following example illustrates the concept of networkcoding. Fig. 2 depicts two spacecrafts, labelled SA and SB ,of a communication network at a distance twice the wirelesstransmission range. The two spacecrafts want to transmit datato each other, which is possible only via a satellite Satgeographically positioned between the two spacecrafts. Fig.2a shows the situation where spacecraft SA sends its dataA to spacecraft SB relayed by the satellite Sat, resulting intwo transmissions (SA → Sat and Sat → SB). Similarly,spacecraft SB sends its data B to spacecraft SA taking twomore transmissions (SB → Sat and Sat → SA). But, ifthe satellite Sat used network coding to facilitate this dataexchange then only three transmissions would’ve sufficed asdepicted in fig. 2b. In the first two transmissions (SA → Satand SB → Sat), the relay transceiver receives one data fromeach side. In the third transmission, the satellite broadcasts theexclusive-OR bit to both spacecrafts. Because of the broadcastnature of wireless medium, this transmission can be heard byboth SA and SB . SA then receives A⊕B, and recovers SB’sdata B as B = A ⊕ (A ⊕ B). Similarly SB can recover A.Therefore only three transmissions are needed in this case,which represents a 25% throughput improvement for bothsenders.

(a) Without Network Coding (b) With Network Coding

Fig. 2: Simple Network Coding Example

We consider the RLNC paradigm of [16], which is im-plemented as presented in [17]. At any given node, every

new encoded packet is obtained as the linear combinationof all packets in its receiving buffer, where the combinationcoefficients are scalars randomly picked in GF (q). Thesescalars are then stored in an encoding vector which is sentalong with the encoded packet, see [17] for further details.

III. NETWORK CODING-BASED BROADCASTINCREMENTAL POWER

Our objective is the exploration of performance improve-ment in BIP when implemented in conjunction with networkcoding. In this section, we describe the basic operation ofnetwork-coded BIP by presenting a simple example.

Step 1: All the wireless nodes in the network build theirrespective broadcast trees using BIP. Two such broadcast treesare shown in fig. 3 (example from [3]). During the constructionof any broadcast tree, all intermediate nodes store their hopcount from the source, apart from storing their transmissionpower level and their neighbouring nodes.

(a) Broadcast Tree of Node 3

(b) Broadcast Tree of Node 4

Fig. 3: Broadcast Tree Examples

The hop count values, neighbouring nodes and transmissionpower level of Node 9 for the 10 different broadcast treesare tabulated in table I. Where Ti is the broadcast tree ofsource Node i. From this, we can observe that Node 9 is anintermediate node in all the broadcast trees, except in T9 whereit is the source node.

Step 2: After the broadcast trees have been built, thebroadcast operation can start. The entire process of all-to-all broadcasting has been divided into sequential rounds ofbroadcast, with the first round (round-0) being the sourcebroadcasts (fig. 4). In the first round, all the nodes broadcasttheir source packets to the hop-1 neighbours according to therespective broadcast trees created in the previous step.

��

TABLE I: Hop count, neighbouring nodes and transmissionpower level of Node 9 in the 10 different broadcast trees

BroadcastTree

T1 T2 T3 T4 T5 T6 T7 T8 T10

Hopcount

1 2 1 2 3 2 2 3 1

Neigh.nodes

10 1,3 10 10 1,2,3,4

1,2,3,4 1,2 1,2,

3,41,2,3,4

Trans.power 0.25 3.25 0.25 0.25 8.5 8.5 8.5 8.5 8.5

Fig. 4: A subgraph of the round-0 source transmissions

Step 3: In the second round (round-1), the hop-1 nodes ofall broadcast trees encode and forward packets to the hop-2nodes, in all the broadcast trees, in a single transmission.

For example, from table I, Node 9 is at hop-1 in threebroadcast trees (T1, T3, T10), as such, it will transmit theencoded packets in round-1, to all its neighbouring nodes(Nodes 1, 2, 3, 4 and 10) comprising of the three broadcasttrees in a single transmission, at a power levelP9,(1,2,3,4,10) = max(P9,1, P9,2, P9,3, P9,4, P9,10)

= 8.5.

Step 4: Proceeding in this manner, nodes at hop-i transmittheir encoded packets in round-i to all its neighbours, com-prising all such broadcast trees where the transmitting node isat hop-i from the source. After all the rounds are complete,it is guaranteed that all nodes have received all source data,since all edges of all the broadcast trees have been traversed.Now, all the nodes can decode the received packets.

IV. SIMULATION RESULTS & DISCUSSION

We have simulated the performance for numerous exam-ples. Networks comprising of a specified number of nodes(typically 10 to 100) are randomly generated in a specifiedsquare area, i.e., the coordinates of nodes are randomlygenerated. There is no restriction placed on the maximumtransmission power (i.e. pmax = ∞). The transmitter poweractually used (rα) depends on the distance (r) to the farthestneighbour to which a node is transmitting. We have consideredpropagation loss exponent of α = 2. In all cases, (i.e. for aspecified region and specified network size), our results arebased on the performance of 10 randomly generated networks.

Our performance metric is the number of transmissions andtotal power of the broadcast tree. Table II summarizes perfor-mance comparison of BIP with network coded-BIP (BIP-NC).Tw denotes the number of transmissions in BIP, Tnc denotesthe number of transmissions in BIP-NC, Ew denotes the energyconsumed in BIP and Enc denotes the energy consumed inBIP-NC. The performance of BIP-NC substantially improvesover BIP, as the number of nodes increases, as is evident fromthe two comparative parameters Tnc

Twand Enc

Ew.

TABLE II: Performance comparison of BIP with BIP-NC

No. of Nodes Tw TncTncTw

Ew EncEncEw

10 47.21 27.8 0.5890 468.8 325.4 0.6941

20 237.6 103 0.4335 3701.4 1936.2 0.5231

30 565.6 236.2 0.4176 12440 6075.2 0.4884

40 997.6 367.6 0.3685 32078.8 14096.8 0.4394

50 1632.4 597.2 0.3658 64384.8 27695.2 0.4302

60 2291.6 783.2 0.3418 97718.8 37494.8 0.3837

70 3183.8 1013 0.3182 168195.4 62261.4 0.3702

80 3989.2 1353.2 0.3392 240499.2 92168.8 0.3832

90 5392.4 1548.2 0.2871 337944.6 113230.8 0.3351

100 6401.8 1837.4 0.2870 472275.6 162695 0.3445

The performance comparison graphs for the two parame-ters, Tnc vs. Tw and Enc vs. Ew, are shown in fig. 5 and fig.6 respectively.

Fig. 5: Comparison of the no. of transmissions in BIP withoutcoding (Tw) and with coding (Tnc)

A. Reduction in Number of Transmissions

The substantial improvement in BIP when implementedin conjunction with the concept of network coding is evidentfrom the simulation results shown in the preceding section. In

�'

Fig. 6: Comparison of the energy consumed in BIP withoutcoding (Ew) and with coding (Enc)

this section, we investigate how the network coding operationreduced the number of transmissions significantly. We returnto the problem of all-to-all broadcast, where, all the nodes inthe network want to send data to all other nodes. The broadcastincremental power algorithm accomplishes this by creating thebroadcast trees for each node and separately traversing themone by one. For example, if there are n nodes in the network,then n broadcast trees will be created using BIP for each node.Then each node i broadcasts their source data, say Di, bysimply traversing its broadcast tree. A part of this operationis shown in fig. 7, where, nodes 1, 3 and 10, broadcasts theirsource data, D1, D3 and D10 respectively. We note that fig.7c is the same as presented in [3].

Now, when the same all-to-all broadcast operation is per-formed using network coding, the broadcast trees do not haveany individual existence. Rather, they can be thought of asa hop-by-hop graph formed by clubbing the broadcast treestogether. To illustrate this, the broadcast trees of fig. 7 areclubbed together upto hop-2 as shown in fig. 8.

On clubbing the trees hop-by-hop, multiple transmissions,from the individual broadcast trees overlap. Such overlappingtransmissions are merged to obtain a single transmission andthe data they were carrying are encoded to get a network-coded packet. For example, in fig. 7, Node 9 occurs at hop-1in all the three broadcast trees receiving source data D1, D3

and D10 from the respective source nodes. After receiving thesource data, Node 9 transmits D1 and D3 to node 10 in T1

and T3 respectively and D10 to nodes 1, 2, 3 and 4 in T10,accounting for three separate transmissions. On clubbing thesebroadcast trees, these transmissions are merged to get a singletransmission of D1 ⊕ D3 ⊕ D10 to all the five nodes. Thus,resulting in a reduction of two transmissions.

Formally, we can say that, if a particular node i occurs at aparticular hop h in k number of broadcast trees, then, there willbe a reduction of k − 1 transmissions. It is important to notethat, the hop h is an intermediate hop value, because networkcoding is performed only at the intermediate nodes.

B. Reduction in Energy Consumption

In lines with the reduction in the number of transmissions,it can be shown that network coding helps in reducing theenergy consumption as well. When multiple transmissions,each having a transmission power, are merged to obtain asingle transmission, the resulting transmission power is less

(a) Broadcast Tree of Node 1

(b) Broadcast Tree of Node 3

(c) Broadcast Tree of Node 10

Fig. 7: Broadcast Tree Examples

than the sum of the individual transmission powers. From theexample in the previous section, node 9 transmits D1 and D3

separately to node 10, each at a power level of 0.25 (fromtable I), and transmits D10 to nodes 1, 2, 3 and 4 at a powerlevel of 8.5, summing up to total energy consumption of 9(0.25+0.25+8.5). But, when using network coding, it needsto transmit at a power level of 8.5 (max(0.25, 0.25, 8.5)) toreach all the five nodes, saving 0.5 (9− 8.5) units of energy.

Formally, it can be said that, when multiple transmissionseach of power level Pi, Pj ,...Pk are network-coded to obtain asingle transmission of power Pmax = max(Pi, Pj , ...Pk), then,the reduction in energy consumption is (Pi +Pj + ...+Pk)−Pmax.

�(

Fig. 8: Reduced transmission on network coding

V. CONCLUSION

In this paper, we have presented a comprehensive perfor-mance evaluation of the BIP algorithm with network coding.The results confirm findings from previous studies that networkcoding improves the performance of broadcast operation inwireless ad-hoc networks. On the other hand, our paper alsopresents new findings that have not been reported in literature.That is, how much improvement can be obtained when theconcept of network coding is used in BIP, which is a well-known traditional broadcasting algorithm for wireless ad-hocnetworks. This has been demonstrated by simulation for a largenumber of random networks.

REFERENCES

[1] N. Xiong, X. Huang, H. Cheng and Z. Wan, ”Energy-Efficient Algorithmfor Broadcasting in Ad Hoc Wireless Sensor Networks,” Sensors, 13, pp.4922-4946, 2013.

[2] A. Sinha and A. Chandrakasan, ”Dynamic Power Management in Wire-less Sensor Networks,” IEEE Design & Test of Computers, 18, pp. 62-74,2001.

[3] J. E. Wieselthier, G. D. Nguyen and A. Ephremides, ”On the Constructionof Energy-Efficient Broadcast and Multicast Trees in Wireless Networks,”Mobile Networks and Applications, 7, pp. 481-492, 2002.

[4] R. Montemanni, L. M. Gambardella and A. K. Das, ”The MinimumPower Broadcast Problem for Wireless Networks,” Wireless Communi-cations and Networking Conference, 4, pp. 2057-2062, 2005.

[5] M. Cagalj, J. P. Hubaux and C. Enz, ”Minimum-Energy Broadcast inAll-Wireless Networks,” Proceedings of the 8th Annual InternationalConference on Mobile Computing & Networking, pp. 172-182, 2002.

[6] D. Tuninetti and C. Fragouli, ”Processing Along the Way: Forwardingvs. Coding,” International Symposium on Information Theory & itsApplications, 2004.

[7] A. Asterjadhi, E. Fasolo, M. Rossi, J. Widmer and M. Zorzi, ”TowardNetwork Coding-Based Protocols for Data Broadcasting in Wireless AdHoc Networks,” IEEE Transactions on Wireless Communications, 9, pp.662-673, 2010.

[8] C. Fragouli, J. Widmer and J. Y. Le Boudec, ”Efficient Broadcastingusing Network Coding,” IEEE/ACM Transactions in Networking, 16, pp.450-463, 2008.

[9] N. Rahnavard, B. N. Vellambi and F. Fekri, ”Efficient Broadcasting viaRateless Coding in Multihop Wireless Networks with Local Information,”Proceedings of the International Conference on Wireless Communica-tions and Mobile Computing, Honolulu, Hawaii, USA, 2007, pp. 85-90.

[10] N. Rahnavard, B. N. Vellambi and F. Fekri, ”Distributed Protocols forFinding Low-Cost Broadcast and Multicast Trees in Wireless Networks,”5th Annual IEEE Communications Society Conference on Sensor, Meshand Ad Hoc Communications and Networks, San Francisco, CA, 2008,pp. 551-559.

[11] M. K. An, ”Building Energy-Efficient Broadcast Trees using a GeneticAlgorithm in Wireless Sensor Networks,” M.S. thesis, Department ofComputer Science and Engineering, University of Texas, Arlington,Texas, 2007.

[12] F. Ingelrest and D. Simplot-Ryl, ”Localized Broadcast IncrementalPower Protocol for Wireless Ad Hoc Networks,” 10th IEEE Symposiumon Computers and Communications, 2005, pp. 28-33.

[13] R. Ahlswede, N. Cai, S. Y. R. Li and R. W. Yeung, ”NetworkInformation Flow,” IEEE Transactions on Information Theory, 46, pp.1204-1216, 2000.

[14] D. Nguyen, T. Nguyen and B. Bose, ”Wireless Broadcasting usingNetwork Coding,” IEEE Transactions on Vehicular Technology, 58, pp.914-925, 2009.

[15] C. Fragouli, J. Widmer and J. Y. Le Boudec, ”A Network CodingApproach to Energy Efficient Broadcasting: from Theory to Practice,”IEEE InfoCom, 2006.

[16] T. Ho, M. Medard, R. Koetter, D. R. Karger, M. Effros, J. Shi andB. Leong, ”A Random Linear Network Coding Approach to Multicast,”IEEE Transactions on Information Theory, 52, pp. 4413-4430, 2006.

[17] P. A. Chou, Y. Wu and K. Jain, ”Practical Network Coding,” AllertonConference on Communication, Control, and Computing, 2003.

��