Distributed Data Aggregation Using Slepian–Wolf Coding in Cluster-Based Wireless Sensor Networks

2564 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 59, NO. 5, JUNE 2010

Distributed Data Aggregation Using Slepian–WolfCoding in Cluster-Based Wireless Sensor Networks

Jun Zheng, Senior Member, IEEE, Pu Wang, Student Member, IEEE, andCheng Li, Senior Member, IEEE

Abstract—In this paper, we study the major problems in ap-plying Slepian–Wolf coding for data aggregation in cluster-basedwireless sensor networks (WSNs). We first consider the clusteredSlepian–Wolf coding (CSWC) problem, which aims at selectinga set of disjoint potential clusters to cover the whole networksuch that the global compression gain of Slepian–Wolf codingis maximized, and propose a distributed optimal-compressionclustering (DOC) protocol to solve the problem. Under a clusterhierarchy constructed by the DOC protocol, we then considerthe optimal intracluster rate-allocation problem. We prove thatthere exists an optimization algorithm that can find an optimalrate allocation within each cluster to minimize the intraclustercommunication cost and present an intracluster coding protocolto locally perform Slepian–Wolf coding within a single cluster.Furthermore, we propose a low-complexity joint-coding schemethat combines CSWC with intercluster explicit entropy coding tofurther reduce data redundancy caused by the possible spatialcorrelation between different clusters.

Index Terms—Clustering, data aggregation, rate allocation,Slepian–Wolf coding, wireless sensor network (WSN).

I. INTRODUCTION

W IRELESS sensor networks (WSNs) have many applica-tions that require dense deployment of a large number

of sensor nodes in a field of interest with one or more data sinkslocated either at the center or out of the field [1]. The sensornodes observe the phenomenon at different points in the fieldand send the observed data to the sink(s). The observed phe-nomenon is usually a spatially dependent continuous processin which the observed data have a certain spatial correlation.In general, the degree of the spatial correlation in the dataincreases with the decrease in the separation between sensornodes. Therefore, spatially proximal sensor observations are

Manuscript received March 15, 2009; revised August 31, 2009; acceptedNovember 11, 2009. Date of publication February 2, 2010; date of currentversion June 16, 2010. This work was supported in part by the ResearchFund of National Mobile Communications Research Laboratory, SoutheastUniversity, under Grant 2009B07, by the Natural Sciences and EngineeringResearch Council of Canada under Grant 293264-07, and by the Funds from theWireless Communications and Mobile Computing Research Center, MemorialUniversity. The review of this paper was coordinated by Prof. Y. Xiao.

J. Zheng is with the National Mobile Communications Research Laboratory,Southeast University, Nanjing 210096, China (e-mail: [email protected]).

P. Wang is with the School of Electrical and Computer Engineering,Georgia Institute of Technology, Atlanta, GA 30308 USA (e-mail: [email protected]).

C. Li is with the Faculty of Engineering and Applied Science, Memor-ial University of Newfoundland, St. John’s, NL A1B 3X5, Canada (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2010.2042186

highly correlated, which leads to considerable data redundancyin the network [2]. To efficiently use network resources toincrease energy efficiency in data transmission, it is highlydesirable to remove such data redundancy through effectivedata-aggregation techniques.

Slepian–Wolf coding [3], [4] is a distributed source-codingtechnique that can completely remove data redundancy with noneed for intersensor communication and is therefore a promis-ing technique for data aggregation in a WSN. This technique isbased on the assumption that each sensor node has knowledgeof the correlation structure of the network a priori, whichdepends on the distances between sensor nodes and the char-acteristics of the observed phenomenon [4]. However, globallyapplying Slepian–Wolf coding to the whole network is difficult,because each sensor node needs to know the global correlationstructure to encode its own data, which would incur significantadditional costs. Moreover, Slepian–Wolf coding is not tolerantto communication failures, because the data from one node mayaffect the decoding of the data from other nodes [5]. For thesereasons, Slepian–Wolf coding is usually not suitable for globalapplication in a large network.

In a cluster-based network, however, each cluster covers asmaller number of sensor nodes within a smaller local rangeof the network. This makes it more feasible to locally ap-ply Slepian–Wolf coding within each cluster as, in this case,a sensor node only needs knowledge of a local correlationstructure to perform encoding. Moreover, it will not obviouslycompromise the compression performance, because the spatialcorrelation usually decreases with distance [2], [6]. Despitethe promising perspective, many technical issues remain to bestudied and resolved to put this technique into practical use.

In this paper, we study the major problems in applyingSlepian–Wolf coding for data aggregation in a cluster-basedWSN, with the objective of optimizing data compression, sothat the total amount of energy for transmitting data in thewhole network is minimized. The first problem is how to clusterthe sensor nodes, given the spatial correlation structure of thenetwork, such that the global compression gain of Slepian–Wolfcoding is maximized, or in other words, the total rate (bits)of the encoded data from all clusters is minimized. To solvethis problem, we propose a distributed optimal-compressionclustering (DOC) protocol based on an optimization algorithmto solve the minimum weight set cover (MWSC) problem ingraph theory. With a cluster hierarchy constructed by the DOCprotocol, the second problem is how to find an optimal rateallocation for each node within a cluster such that the intraclus-ter communication cost, which is defined as the total energy

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ZHENG et al.: DISTRIBUTED DATA AGGREGATION USING SLEPIAN–WOLF CODING IN CLUSTER-BASED WSNs 2565

consumed by all the sensor nodes in the cluster for sendingdata encoded with the allocated rates, is minimized. To addressthis problem, we first prove that there exists an optimizationalgorithm that can find an optimal rate allocation within eachcluster and then present an intracluster coding protocol tolocally perform Slepian–Wolf coding within a single cluster.Furthermore, we propose a joint clustered Slepian–Wolf coding(CSWC) and explicit entropy coding scheme to further reducepossible correlation in the data generated between differentclusters.

The rest of this paper is organized as follows: Section IIdescribes the considered problems and reviews related work.Section III presents the proposed DOC protocol. Section IVdiscusses optimal rate allocation and presents the intraclus-ter coding protocol to locally perform Slepian–Wolf coding.Section V presents joint CSWC and explicit entropy coding.Section VI shows simulation results to evaluate the compres-sion performance of the DOC protocol. Section VII concludesthis paper.

II. PROBLEM STATEMENTS

In this section, we introduce the concept of Slepian–Wolfcoding, describe the CSWC problem and the optimal intraclus-ter rate allocation problem, and review related work.

A. Slepian–Wolf Coding

Consider a network consisting of N sensor nodes uniformlydistributed in a region of interest, where each node i producesreading Xi, and all the readings constitute a set of jointlyergodic sources denoted by X = (X1,X2, . . . , XN ) with dis-tribution p(x1, x2, . . . , xN ), which corresponds to the spatialcorrelation structure known by each node a priori. To obtainthe spatial correlation structure, different estimation approachescan be employed. For example, Chou et al. proposed a cen-tralized approach in [7], where an intelligent data-gatheringnode estimates the degree of correlation between the data fromdifferent source nodes based on collected data. In [8], Daiand Akyildiz proposed a distributed approach that predictsthe correlation coefficient using a simple function of severalnetwork settings, such as sensing direction, sensing offset, andsensing range. As a result, little energy consumption is induced,because only short messages conveying the required settings areexchanged among the neighboring nodes.

According to the Slepian–Wolf Theorem [3], the nodes canjointly encode their data without internode communication,with a rate (in bits) R(U) that is lower bounded by their jointentropy H(X1,X2, . . . , XN ), as long as their respective ratessatisfy the constraints

R(U) ≥ H (X(U)|X(U c)) (1)

for all U ⊆ {1, 2, . . . , N}, where {1, 2, . . . , N} is a set of theindices of sensor nodes in the network, U c is the complemen-tary set of U , H(X) is the entropy of X , and

R(U) =∑

i∈U

Ri X(U) = {Xj |j ∈ U}.

For example, consider a simple case of two sensor nodesproducing readings X1 and X2. Their individual rates shouldbe subject to

R1 ≥ H(X1|X2), R2 ≥ H(X2|X1)

R1 + R2 ≥ H(X1,X2).

According to the chain theory [4], under the preceding con-straints, it is always possible to find a rate allocation for thetwo nodes, which makes the total rate (in bits) of the two nodesequal to their joint entropy, i.e.,

R1 + R2 = H(X1) + H(X2|X1) = H(X1,X2).

Correspondingly, for an arbitrary ordering of N nodes (e.g., inascending or descending order of the nodes’ ID numbers), thereexists a rate allocation (vector) {Ri}N

i=1 such that the numberof generated bits from all nodes can achieve the value of theirjoint entropy, e.g.,

N∑

i=1

Ri = H(X1,X2, . . . , XN )

where

R1 = H(X1)

Ri = H(Xi|Xi−1,Xi−2, . . . , X1), 2 ≤ i ≤ N.

Therefore, a cluster of nodes A can be encoded withH(X1,X2, . . . , X|A|) bits using Slepian–Wolf coding withoutcommunicating with each other, where |A| is the numberof nodes in cluster A, and there always exists an optimalrate allocation to achieve this local maximum compressionperformance.

B. CSWC Problem

Consider a network that consists of a finite set of sensornodes V . Every sensor node in the network is initially a clusterhead candidate. We assume that each candidate has an identicalcluster diameter within which all other nodes may become itscluster members. The nodes within the cluster diameter of acandidate v form a finite point set Nv with the cardinalityof |Nv|, which is called the neighbor set of candidate v. Thepower set of Nv , which was denoted by P (Nv), is a set whoseelements are the subsets of Nv . P (Nv) contains all possiblecombinations of nodes in Nv . Thus, the cardinality of P (Nv)is 2|Nv |. Since a candidate v associated with each combinationof nodes (cluster members) within its cluster diameter [e.g.,a set of nodes Bv , where Bv ∈ P (Nv)] can form a uniquepotential cluster (e.g., A := Bv ∪ {v}), a candidate v can gen-erate up to 2|Nv | potential clusters. Recall that, initially, everynode in the network is a candidate; thus, there are a totalnumber of |V | candidates. Therefore, there exists a cluster setS consisting of

∑v∈V 2|Nv | potential clusters in the whole

network. Meanwhile, each potential cluster A can be encodedwith H(X1,X2, . . . , X|A|) bits using Slepian–Wolf coding inthat cluster.


With the preceding assumptions, the CSWC problem is toselect a set of disjoint potential clusters C∗ from the cluster setS to cover the whole network such that the global compressiongain of Slepian–Wolf coding is maximized or, more specifi-cally, the total rate (in bits) of the encoded data generated byall the clusters (or all the nodes) in the network is minimized,i.e.,

C∗ = arg minC⊆S

∑

A∈C

H (X(A)) (2)

where ∪A∈C∗A = V , ∩A∈C∗A = φ, and X(A)={Xj |j ∈ A}.

C. Optimal Intracluster Rate-Allocation Problem

Suppose that a cluster hierarchy has already been constructedin the CSWC problem. Consider a cluster A with |A| sensornodes, and let {Ri; i = 1, 2, . . . , |A|} be a rate vector allocatedto the nodes in the cluster. In addition, let di be the distancebetween node i and the cluster head v, which is used toestimate the energy consumed by node i for sending one bit datato the cluster head v, because normally, transmission energydissipation is proportional to the signal-propagation distance.Then, the objective of the intracluster rate allocation problemis to find a rate vector for the nodes in the cluster under theconstraints given by (1) such that the total energy consumed byall nodes to send the data encoded with their individual rates tothe cluster head is minimized, i.e.,

{R∗i}

|A|i=1 = arg min

{Ri}|A|i=1

|A|∑

i=1

d2i Ri (3)

subject to∑

i∈Y

Ri ≥ H (X(Y )|X(Y c)) ∀Y ⊆ {1, 2, . . . , |A|}

where {1, 2, . . . , |A|} is a set of the indices of the sensor nodesin the cluster A. Note that the CSWC problem assumes thatthere exists a rate allocation such that the total rate of encodeddata in a cluster is equal to the joint entropy of readings orobservations. However, a solution to the intracluster rate allo-cation problem considered may generate a rate allocation thatis not subject to that assumption. We will prove in Section IV-Athat the obtained solution conforms to the assumption in theCSWC problem.

D. Related Work

Data redundancy caused by spatial correlation has motivatedthe application of Slepian–Wolf coding [6], [9] for data ag-gregation in WSNs. Recent advances in practical codes forSlepian–Wolf coding have paved the way to perform dataaggregation based on this promising coding technique [10]–[13]. In [10], Pradhan and Ramchandran proposed a DistributedSource Coding Using Syndromes (DISCUS) method based onthe coset coding of linear codes. According to DISCUS, twosignals X and Y are independently compressed, and insteadof sending the codeword representing X , the syndrome of thecodeword coset is sent and the receiver decodes by choosing the

codeword in the given coset that is closest to Y . In [11], Aaronand Girod proposed a coding method based on turbo codes,which can achieve a performance close to that of Slepian–Wolfcoding. In [12], Lan et al. studied practical Slepian–Wolf codedesigns for more than two sources, in which multilevel codeswith low-density-parity-check codes at each level are used toapproach the Slepian–Wolf limit.

In [13] and [14], Cristescu et al. studied data aggregationusing global Slepian–Wolf coding. It is assumed that eachnode uses multihop flat routing for sending data to the datasink, and complete knowledge of the correlation between thereadings produced by all nodes is available at each node. In thiscase, global Slepian–Wolf coding and shortest-path routing arejointly considered, aiming to minimize the total cost for sendingcompressed data. Although it is shown that globally applyingSlepian–Wolf coding is difficult in these studies, optimallyconstructing a cluster hierarchy with Slepian–Wolf coding ina distributed manner is not considered.

In [5], it has been shown that locally applying Slepian–Wolfcoding within each cluster is able to overcome the effect ofnode and relay failures on the data reconstruction at the remotesink. However, no clustering protocol has been proposed toconstruct a cluster hierarchy, and no work has taken accountinto the intracluster transmission cost, which depends on therate allocation within each cluster. On the other hand, existingclustering protocols for WSNs [15]–[20] are generally corre-lation structure blind and are not born to maximally exploitSlepian–Wolf coding with respect to global compression gain.In addition, little work has been conducted on the optimizationof data compression in the context of node clustering. The effectof spatial correlation on MAC protocols and routing algorithmshas been investigated in [21] and [22].

E. Main Contributions of This Paper

This work focuses on distributed data aggregation usingSlepian–Wolf coding in cluster-based WSNs. The main contri-butions of this paper include the following:

1) study the CSWC problem, the optimal rate-allocationproblem, and the joint Slepian–Wolf and explicit entropycoding problem in applying Slepian–Wolf coding for dataaggregation in WSNs;

2) DOC protocol proposed to solve the CSWC problem;3) proof of the existence of an optimization algorithm that

can find an optimal rate allocation within each cluster;4) joint CSWC and explicit entropy-coding scheme pro-

posed to reduce the possible correlation in the data re-ceived from different clusters.

III. CLUSTERING USING SLEPIAN–WOLF CODING

In this section, we present a DOC protocol to solve theCSWC problem.

A. Optimal-Compression Clustering Algorithm

The CSWC problem is similar to the MWSC problem ingraph theory [23]. Given a set of points, a collection of sets


Fig. 1. Chvátal’s algorithm.

Fig. 2. Heuristic algorithm.

of these points (or potential sets), and a nonnegative weightassigned to each potential set, the MWSC problem is to finda subset of the collection of potential point sets such that eachelement in the given set of points belongs to at least one ofthe point sets in the subset so that the sum of the weights ofall point sets in the subset is minimized. The only differencebetween the two problems is that a point in the MWSC problemcan be covered by more than one point set, whereas a sensornode in the CSWC problem will be covered by one and onlyone cluster.

The MWSC problem has been proven to be NP-hard [24].To solve this problem, Chvátal proposed an approximationalgorithm based on a sequential greedy method [23]. Fig. 1gives the pseudocode of Chvátal’s algorithm, where S is acollection of potential point sets, C∗ is a collection of pointsets we would like to find, A is a set (called “qualified” set)with minimum W (A)/|A − Q|, W (A) is the weight assignedto A, Q is a set consisting of all nodes that are covered by all“qualified” sets already added to C∗, and A − Q is a set ofelements that are members of A but not members of Q. Hence,|A − Q| is the number of new nodes to be covered by C∗ if anew “qualified” set A is added to C∗. This means that a selected“qualified” set A may have members in common with the setsalready in C∗, which is not allowed in the CSWC problem.Chvátal’s algorithm starts with C∗ ← φ, and each time greedilyadds one “qualified” set to C∗ until the sets in C∗ include allpoints.

To solve the CSWC problem, we propose a heuristic al-gorithm based on Chvátal’s algorithm to generate a pairwisedisjoint C∗, in which any two distinct sets are disjoint. Fig. 2gives the pseudocode of the heuristic algorithm, where H(·)

corresponds to W (·) in the MWSC problem, H(X({v} ∪B))/|{v} ∪ B| can be considered as the average entropy ofcluster {v} ∪ B, and A is a “qualified” cluster with the mini-mum average entropy. Since, each time, we only consider one“qualified” cluster A, which has no element in common withthe clusters that have already been selected (i.e., A ∩ Q = φ,because {v} ∩ Q = φ and B ∪ Q = φ), we can guarantee thatthe generated C∗ is pairwise disjoint.

In the heuristic algorithm, the first step is to find out allcluster head candidates left in the network, i.e., the nodes thathave not been covered by the clusters already added into C∗

(e.g., Z ← V − Q). Each candidate v then constructs its ownpotential clusters by combining with every possible combina-tion of the nodes that are in its neighbor set Nv but have notbeen covered by the clusters already in C∗, i.e., P (Nv − Q).For each candidate v, it first calculates the entropy of each of itsown potential clusters, i.e., H(X({v} ∪ B) and B ∈ P (Nv −Q). Then, it selects the potential cluster Rv with minimumaverage entropy to be the representative cluster of candidate v.After that, it compares the average entropy of the representativeclusters of all candidates and selects the representative clusterA with the minimum average entropy as a “qualified” clusterto be added into C∗. The corresponding candidate becomes acluster head. The preceding procedures are repeated until theclusters in C∗ cover all nodes in the network.

B. DOC Protocol

The heuristic algorithm described in Section III-A is a cen-tralized clustering algorithm, which can be performed at acentral node (e.g., a data sink) and is thus relatively simpleto implement. In a distributed network, node clustering isindependently performed at each node based on the local infor-mation that each node maintains. For this reason, a distributedclustering protocol is more complicated to implement.

According to the heuristic algorithm, whether a candidatev can become a cluster head is determined by whether itscorresponding representative cluster A has minimum averageentropy H(X(A))/|A| among all candidates in the network.However, the value of H(X(A))/|A| of a candidate v canonly be changed if any of the candidates within a distanceof at most two times the cluster diameter (two-hop range)becomes a cluster head. This is because only the candidateswithin two-hop range may cover common nodes, and if oneof them becomes a cluster head, the number of nodes withinthe diameter of other candidates will decrease, thus affectingthe H(X(A)) and |A| of those candidates. Therefore, if thevalue of H(X(A))/|A| of candidate v is smaller than that ofany other candidates within a distance of at most two-hop rangefrom candidate v, v is selected as the cluster head before any ofthe candidates within that two-hop range.

Based on the preceding observation, we present a DOCprotocol to solve the CSWC problem. In the DOC protocol,a candidate generates its potential clusters by searching everypossible combination of elements in its uncovered neighbor set;calculates each potential cluster’s entropy, which only dependson the distances between the nodes in the cluster; selects arepresentative cluster; and sends the average entropy of the


Fig. 3. DOC protocol.

representative cluster to all candidates within its two-hop range.A candidate collects the average entropies sent by all candidateswithin its two-hop range. If the candidate itself has minimumaverage entropy, it becomes a cluster head and advertises anINVITE message to all the nodes in its representative clusterto invite them to become its cluster members. Otherwise, if anINVITE message is received by a candidate and the destinationof this message is the candidate, the candidate first changesits candidate status to a cluster member. Then, it extracts thecluster head ID from the INVITE message and broadcasts aJOIN message to all the nodes within its cluster diameter. ThisJOIN message will acknowledge the receipt of the INVITEmessage and, at the same time, notify the other candidateswithin the cluster diameter that the candidate has become acluster member of some cluster head. If no INVITE messageis received or some INVITE messages for other nodes arereceived, the candidate stays in its candidate status and reselectsits representative cluster, because some elements in its uncov-ered neighbor set might have been covered by some clusterheads or have become cluster heads.

The preceding procedures are performed by all candidatesuntil each of them becomes either a cluster head or a clustermember. Fig. 3 gives the pseudocode of the preceding proce-dures, where Av is the representative cluster of candidate v,arg(v) is the average cost of Av , Xv is the set containing thecluster members of Av , head is a flag indicating a cluster head,cand is a flag indicating a candidate, memb is a flag indicating acluster member, G is a set containing the average costs sentby other cluster heads within two-hop range of a candidate,

INV ITE(v,Xv) is a message inviting the nodes in set Xv tobecome the cluster members of candidate v, and JOIN(v, u)is a message acknowledging that node v received the INVITEmessage sent by candidate u and joins the cluster as a clustermember of candidate u.

C. Computational Complexity

Consider a network consisting of |V | sensors uniformlydistributed over a region with a predefined node density ρ toguarantee the sensing coverage. The computational complexityof the heuristic algorithm is O(|V |). This is because, at everyiteration, the algorithm selects at least one cluster with a clusterhead v from the 2|Uv | potential clusters generated by v, whereUv is the uncovered neighbor set of v. Since |Uv| ≤ |Nv|,where Nv is the neighbor set of v, the algorithm terminatesin O(

∑v∈V 2|Nv |) iterations. Furthermore, let r be the clus-

ter diameter of v. The number of nodes within the limitedcluster diameter of v is |Nv| = ρπr2, where ρ is the sensordensity. Therefore, 2|Nv | can be denoted by a constant D, andthe heuristic algorithm terminates in O(

∑v∈V D) = O(|V |)

iterations. Similarly, the DOC protocol also has a computationalcomplexity of (O|V |).

IV. INTRACLUSTER RATE ALLOCATION

Under a cluster hierarchy constructed by the DOC protocol,we now consider the optimal intracluster rate allocation prob-lem described in Section II-C.

A. Optimal Intracluster Rate Allocation

The intracluster rate-allocation problem can be analogized tothe global rate-allocation problem discussed in [13]. Given amultihop sensor network consisting of N nodes, where eachnode i produces reading Xi and uses the shortest path withweight e(i, s) to reach a common sink s, the global rate-allocation problem is to find an optimal rate vector {R∗

i}Ni=1

for all N nodes so that the total flow cost∑N

i=1 e(i, s)R∗i under

the constraints given by (1) is minimized. According to [13],the optimal rate vector is given by

R∗1 =H(X1)

R∗i =H(Xi|Xi−1,Xi−2, . . . , X1), 2 ≤ i ≤ N (4)

where the nodes (i = 1, 2, . . . , N) with the observations of(X1,X2, . . . , XN ) are organized in descending order of theweights of the shortest paths, i.e.,

e(1, s) ≤ e(2, s) ≤ · · · ≤ e(N, s).

The analogies between these two problems are given here.

1) In the intracluster rate-allocation problem, each clusteris analogous to the whole network in the global rate-allocation problem, because it performs coding indepen-dently of all other clusters.

2) In the intracluster rate-allocation problem, the clusterhead of each cluster can be considered as a local virtualdata sink. Thus, the cluster head is analogous to the data


sink, and each cluster member is analogous to a sensornode in the global rate-allocation problem.

3) In the intracluster rate-allocation problem, the shortestpath between a cluster member i and the cluster head v isa single-hop path with a distance di, which is analogousto the weight e(i, s) of the shortest path between a sensornode i and the data sink s in the global rate-allocationproblem.

Given the preceding analogies, we can use the same opti-mization algorithm to solve the global rate-allocation problemin [13] to solve the intracluster rate-allocation problem. Theoptimal intracluster rate allocation has the same form as (4).However, we still need to prove that this solution is valid, i.e.,the rate allocation obtained using (4) does not contradict theassumption in the CSWC problem, where the rate allocation foreach cluster must satisfy the condition that the total rate of thecoded sensor readings in a cluster (e.g., a whole network inthe extreme case) is equal to their joint entropy. According tothe chain theory, we can easily prove the validity of the solutiongiven by (4) if the whole network is considered as a singlecluster, i.e.,

N∑

i=1

R∗i = H(X1) +

N∑

i=2

H(Xi|Xi−1,Xi−2, . . . , X1)

= H(X1,X2, . . . , XN ).

Therefore, let {R∗i}

|A|i=1 be a rate vector to be allocated to

the nodes in a given cluster A consisting of |A| sensor nodesand Xi be the observation at node i in the cluster. The optimalintracluster rate allocation is given by

R∗1 = H(X1)

R∗i = H

(Xi

∣∣{Xj |dj ≤ di, j ∈ A}), 2 ≤ i ≤ |A| (5)

where d1 = 0 denotes the distance between the cluster head vand itself. Here, the cluster head with zero distance to itselfis encoded with a rate equal to its unconditional entropy, andeach of the cluster members in the cluster is encoded with arate equal to its respective entropy conditioned on all the othernodes in the cluster that are closer to the cluster head than itself.According to the chain theory, we have

|A|∑

i=1

R∗i = H

(X1,X2, . . . , X|A|

).

Therefore, {R∗i}

|A|i=1 is a valid rate vector for the optimal CSWC

problem.

B. Intracluster Slepian–Wolf Coding Protocol

Given an intracluster rate allocation, we now discuss how toperform CSWC within a single cluster. Consider a cluster Awith |A| sensor nodes shown in Fig. 4, where the node in blackrepresents the cluster head, and the nodes in white representcluster members. The cluster head produces reading X1. Fromleft to right, the first cluster member is the closest one to thecluster head and produces reading X2, the next closest one

Fig. 4. Slepian–Wolf coding within a cluster.

produces reading X3, and so on. Therefore, the intraclustercoding protocol can be described here.

1) The cluster head schedules the cluster members in de-scending order of their distances to the cluster head itself,as shown in Fig. 4.

2) The cluster head generates a list for each cluster memberi, which contains the indices (or IDs) of all the othernodes that are closer to the cluster head than clustermember i. For example, the list for cluster member 3contains (2, 1).

3) The cluster head distributes the generated lists withinthe cluster. After receiving the list, a cluster member iencodes its reading with a rate equal to its respectiveentropy conditioned on all the nodes in the received list,i.e., cluster member 3 encodes its data with a rate equal toH(X3|X2X1) = H(X3X2X1) − H(X2X1). Note that,in this case, only distances among (X3,X2,X1) areneeded to calculate the rate and perform encoding withknowledge of the correlation structure.

4) After the cluster head receives the compressed data fromall its cluster members, it relays the data to the data sink,where conditional decoding is performed on the collecteddata. The sink decodes the cluster head’s reading X1 en-coded with a rate equal to H(X1) without using any sideinformation, whereas all other readings are decoded withknowledge of the readings of the nodes that are closerto the cluster head. For example, reading X2, whichis encoded with a rate of H(X2|X1), is decoded withknowledge of X1, and reading Xi, which is encoded witha rate equal to H(Xi|Xi−1, . . . , X1), can be decodedwith knowledge of (X1,X2, . . . , Xi−1). Thus, loss of thedata from one sensor node may affect the reconstructionof the sensor values from other nodes within the samecluster but does not affect the decoding of the data fromother clusters.

V. JOINT CLUSTERED SLEPIAN–WOLF CODING AND

EXPLICIT ENTROPY CODING

Slepian–Wolf coding can completely remove the dataredundancy within each cluster with knowledge of the corre-lation structure. However, the encoded data from two phys-ically separated clusters may still have a certain amount of


Fig. 5. Joint clustered Slepian–Wolf coding and explicit entropy coding.

information in common or redundancy, even though the cor-relation degree generally decreases quickly with the spatialseparation between clusters. Explicit entropy coding is a low-complexity in-network data-aggregation technique, where eachsensor node encodes/decodes its reading only conditioned onthe readings (explicit side information) that it has alreadyreceived from other nodes with no need to know the correlationstructure a priori [22], [25]. Since, in a cluster-based network,a cluster head uses other cluster heads as a relay, data (sideinformation) from one cluster are available at the relay clusterheads. In this case, explicit entropy coding can be used tofurther reduce the potential correlation in the data from differentclusters without significantly increasing coding complexity.

Based on the preceding observation, we propose a joint cod-ing scheme in which the Slepian–Wolf coding is first appliedwithin each cluster. If a relay cluster head receives data fromother cluster heads, it performs explicit entropy encoding onlyon its own sensed data, which cannot be compressed via clus-tered Slepian–Wolf encoding because the optimal intraclusterrate allocation requires the cluster head to encode its own datawith a rate equal to the unconditional entropy. The codingscheme is briefly shown in Fig. 5, where nodes 1, 2, and 3are three cluster heads, and cluster head i produces readingXi (i = 1, 2, 3). Initially, a cluster head i encodes its readingXi with a rate equal to H(Xi) due to the requirement of CSWC,and when cluster head i receives data (side information) fromother cluster heads, it reencodes Xi with a new rate equal to itsrespective entropy conditioned on all other cluster heads fromwhich the side information has been received and to which ithas been forwarded.

In summary, when explicit entropy coding is jointly appliedwith CSWC, the data sent by a given cluster head dependnot only on the received data from cluster members in itsown cluster but on the data from other clusters whose clusterheads use that cluster head as a relay to the data sink as well.Therefore, the additional compression gain obtained by explicitentropy coding actually depends on the routing structure, asshown in Fig. 5. We can see that a cluster head that is closer tothe data sink encodes its own data with a smaller rate, which canmore evenly distribute the traffic load throughout the network,helping to avoid the formation of hot spots around the data sink.

It should be pointed out that routing is an important aspectthat must be considered in the joint coding scheme. There aretwo types of routing protocols suitable for the proposed jointcoding scheme, i.e., opportunistic compression routing (OCR)and dedicated compression routing (DCR). In OCR, clusterheads use shortest-path routes to relay the received data withcompression opportunistically performed wherever these routeshappen to overlap. In DCR, a route is selected in such a way thatthe received data are forwarded to the most correlated clusterhead to maximize the compression gain. Since the correlationintensity is proportional to the spatial separation, the next-hop

node in DCR will be the cluster head closest to the data sink onthe way. Therefore, the route selected by DCR is not necessarilythe shortest path as selected by OCR. Since routing is not thefocus of this paper, we do not go to more detail.

VI. JOINT CLUSTERED SLEPIAN–WOLF CODING AND

EXPLICIT ENTROPY CODING

In this section, we evaluate the effects of the spatial correla-tion degree and the network size on the compression perfor-mance of the DOC protocol through simulations using ns-2.In addition, we investigate the performance of intracluster rateallocation with respect to the intracluster communication costunder a cluster hierarchy constructed by the DOC protocol.

Unless otherwise specified, we consider a network with100 sensor nodes uniformly deployed in a sensing regionmeasuring 100 m × 100 m and a sink located at the center ofthe region. The simulation results are based on the average of30 experiments, and each experiment uses a different randomlygenerated topology.

For the correlation structure, we assume that the observationsX1,X2, . . . , XN at N sensor nodes are modeled as anN -dimensional random vector X = [X1,X2, . . . , XN ]T ,which has a multivariate normal distribution with mean(0, 0, . . . , 0) and covariance matrix K, i.e., the density of X is

f(X) =1

(√

2π)N |K|1/2e−

12 XT K−1X

and the differential entropy of (X1,X2, . . . , XN ) is

h(X1,X2, . . . , XN ) =12

log(2πe)N |K| bits

where |K| denotes the determinant of the matrix K [4]. Inthe simulation, we use an exponential model of the covariancekij = exp(−d2

ij · θ) to model the observed physical event suchas electromagnetic waves [2], where dij denotes the distancebetween the nodes measuring Xi and Xj , respectively. Theparameter θ controls the relation between the distance dij andthe covariance kij , and it can be set to different values toindicate different levels of correlation within a given distance.For the sake of simplicity and without loss of generality, weuse differential entropy, instead of discrete entropy, becausewe assume that the sensor readings from different nodes arequantized with an identical and sufficient small quantizationstep, in which case, the differential entropy differs from discreteentropy by only a constant [4], [9].

The energy-consumption model used is similar to that in[15] and [17]. To send an n-bit message over a distance d, atransmitter consumes

ETX = Eelec + Eampd2

where Eelec = 50 nJ/bit is the energy consumption to run theradio circuit, and Eamp = 10 pJ/bit/m2 is the energy consump-tion to run the power amplifier.

Fig. 6 shows the effects of the correlation degree and thenetwork size on the compression performance. The compres-sion performance is measured in an overall compression ratio,which is the total amount of data produced in the whole network


Fig. 6. Impacts of the degree of correlation and the network size on the overallcompression ratio.

after CSWC is applied over the total number of bits gener-ated by all nodes without using this distributed source-codingscheme. The network size or the total number of sensor nodesn is set to be {80, 90, 100, 110, 120}. The parameter θ in thecovariance model is set to be {0.01, 0.009, . . . , 0.0003}, whereθ = 0.01 indicates low correlation, and θ = 0.0003 indicateshigh correlation. From the figure, it is seen that, in the caseof higher correlation, a better compression performance isachieved, because the Slepian–Wolf coding can remove moreredundancy caused by the higher spatial correlation among thereadings of different sensor nodes. In addition, the compressionperformance is improved as the network size or the density ofsensor nodes increases. This behavior is due to the fact that thedenser sensor deployment results in more sensor nodes residingwithin each cluster while CSWC can completely get rid of thehighly redundant data generated by these sensor nodes that arein closer proximity to each other.

Fig. 7 shows the intracluster communication cost with theoptimal rate allocation and an ID-based rate allocation, re-spectively. As described in Section II-A, the ID-based schemefirst schedules nodes in a cluster A in ascending (or de-scending) order of the nodes’ ID numbers. Thus, the rateassigned to the node i with ID number ID(i) is given by Ri =H(Xi|{Xj |ID(j) ≤ ID(i), j ∈ A}). The intracluster commu-nication cost is given by (3), and we use parameter θ = 0.006to model moderate spatial correlation. The result shown is anaverage of the intracluster communication costs of all clustersin the network, varying the network size. As expected, theoptimal intracluster rate allocation results in less communica-tion cost, compared with the one only based on the node’s ID,because the former scheme jointly considers rate assignmentsand transmission distances between the cluster members andthe cluster head.

Fig. 8 compares the intracluster communication cost of thedistributed data-aggregation technique using the CSWC withthat of a widely used centralized data-aggregation technique[15], [17] under different cluster sizes n and a moderate correla-

Fig. 7. Intracluster communication cost with optimal rate allocation and ID-based rate allocation.

Fig. 8. Intracluster communication cost with distributed data aggregation andcentralized data aggregation.

tion degree (θ = 0.006). With the centralized aggregation tech-nique, each cluster member periodically sends its original datato the cluster head, and the data from all cluster members areaggregated at the cluster head. It is observed that the distributedaggregation technique using Slepian–Wolf coding leads to lessintracluster transmission cost than that with the centralized ag-gregation technique. This is because the distributed aggregationtechnique allows each cluster member to individually removethe redundancy existing in its data prior to sending the datato the cluster head, thus significantly reducing the intraclustertransmission cost.

Fig. 9 compares the total amount of data generated in thenetwork using the CSWC and the joint coding, respectively.As expected, the joint coding results in obviously less data,thus leading to better compression performance. This is becausethe joint coding employs CSWC combined with intercluster


Fig. 9. Total amount of data generated with Slepian–Wolf coding and jointcoding.

Fig. 10. Total intercluster communication cost with Slepian–Wolf coding andjoint coding.

explicit entropy coding, which can further strip the data re-dundancy caused by the possible spatial correlation betweendifferent clusters. In addition, it is observed that, in the case ofhigh correlation (i.e., a small value of the correlation parame-ter), joint coding can achieve better performance in terms of thetotal amount of generated data, because higher correlation leadsto more data redundancy between spatially separated clusters,which can further be removed by the joint coding. Meanwhile,more data redundancy removed from the network infers lessenergy consumed for data transmission.

Fig. 10 shows the total intercluster communication cost withSlepian–Wolf coding and joint coding, respectively. The totalintercluster communication cost is defined as the sum of thecommunication costs of all cluster heads for relaying data to theremote sink, where the communication cost is represented by[data volume × transmission distance]. As expected, less com-munication cost is incurred with the joint coding. In addition, it

Fig. 11. Approximate ratio of the total amount of data transmitted with theCSWC to that transmitted with the optimal coding.

is observed that, under moderate correlation (e.g., θ = 0.006),the joint coding leads to 9% less communication cost than thatwith only the CSWC but only 4% less data. This is because eachcluster head employs multihop routing for relaying data fromother cluster heads, and locally removing data redundancy ateach cluster head by joint coding leads to further energy savingfor each cluster head along the multihop routing path.

Fig. 11 shows the approximate ratio of the total amount ofdata transmitted with the CSWC to that transmitted with the op-timal coding in a network of 50 nodes uniformly deployed in thesame region. With the optimal coding, Slepian–Wolf coding isglobally applied in the whole network, with the assumption thateach node has full knowledge of the correlation structure of thenetwork, which can remove all data redundancy in the networkand thus achieve the maximal compression gain. However, thisis costly and usually impossible in a real-world large network.We investigated the total amount of data transmitted in thenetwork, with the cluster diameter ranging from 10 to 20 andthe correlation parameter ranging from 0.005 to 0.01. In Fig. 11,it is seen that, with the increase in the cluster range, the totalamount of data transmitted with CSWC becomes closer to theoptimal result, because increasing the cluster range means thatmore nodes are included in each cluster, thus further reducingthe data redundancy caused by the possible spatial correlationbetween different clusters.

VII. CONCLUSION

In this paper, we have studied the major problems in apply-ing Slepian–Wolf coding for data aggregation in cluster-basedWSNs, including the CSWC problem, the optimal intraclusterrate-allocation problem, and the joint intra-CSWC and inter-cluster explicit entropy coding problem. We have proposed theDOC protocol, which can be used to select a set of disjointpotential clusters that maximize the global compression gainof Slepian–Wolf coding. Under a cluster hierarchy constructed


by the DOC protocol, we have proven that there exists anoptimization algorithm that can find an optimal rate allocationwithin each cluster to minimize the intracluster communica-tion cost and have presented an intracluster coding protocolto locally perform Slepian–Wolf coding within a single clus-ter. Finally, we have proposed a low-complexity joint codingscheme that combines CSWC with intercluster explicit entropycoding to further reduce the data redundancy caused by thepossible spatial correlation between different clusters. The sim-ulation results have shown that the CSWC enabled by the DOCprotocol can significantly reduce the total amount of data inthe whole network, whereas the transmission cost within eachcluster can remarkably be reduced by performing the optimalintracluster rate allocation.

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Jun Zheng (S’99–M’01–SM’09) received the Ph.D.degree in electrical and electronic engineering fromThe University of Hong Kong, Hong Kong, in 2000.

He is currently a Full Professor with the Na-tional Mobile Communications Research Labora-tory, Southeast University (SEU), Nanjing, China.Before joining SEU, he was with the School of In-formation Technology and Engineering, Universityof Ottawa, Ottawa, ON, Canada. He has coauthored(first author) the book Wireless Sensor Networks:A Networking Perspective (New York: Wiley-IEEE

Press, 2009) and has published more than 80 technical papers in refereed jour-nals and magazines and peer-reviewed conference proceedings. His researchinterests include wireless sensor networks and mobile ad hoc networks, withemphasis on network architectures and protocols.

Dr. Zheng serves as an Associate Technical Editor of IEEE CommunicationsMagazine, an Editor of IEEE Communications Surveys & Tutorials, and aneditorial board member of several other refereed journals, including ElsevierAd Hoc Networks Journal and Wiley Wireless Communications and MobileComputing. He has coedited ten special issues for different refereed journalsand magazines, including a Special Issue of IEEE Network on Wireless SensorNetworking and a Special Issue of Wiley Wireless Communications and MobileComputing on Underwater Sensor Networks, all as Lead Guest Editor. He hasserved as the founding General Chair of AdHocNets’09, General Chair ofAccessNets’07, and Technical Program Committee (TPC) or SymposiumCochair for several international conferences and symposia, including the 2008IEEE Global Communications Conference (GLOBECOM), the 2009 Inter-national Communications Conference (ICC), GLOBECOM’10, and ICC’11.He has also served as a TPC member for a number of international conferencesand symposia.

Pu Wang (S’07) received the B.S. degree in electri-cal engineering from the Beijing Institute of Technol-ogy, Beijing, China, in 2003 and the M.Eng. degreein computer engineering from the Memorial Uni-versity of Newfoundland, St. John’s, NL, Canada,in 2008. He is currently working toward the Ph.D.degree in electrical engineering with the GeorgiaInstitute of Technology, Atlanta.

His research interests include wireless sensor net-works and mobile ad-hoc networks, with emphasison traffic modeling, node clustering, data aggrega-

tion, network coding, and security.


Cheng Li (S’99–M’03–SM’08) received the B.Eng.and M.Eng. degrees from Harbin Institute of Tech-nology, Harbin, China, in 1992 and 1995, re-spectively, and the Ph.D. degree in electrical andcomputer engineering from the Memorial Universityof Newfoundland, St. John’s, NL, Canada, in 2004.

He is currently an Associate Professor with theFaculty of Engineering and Applied Science, Memo-rial University of Newfoundland. He is an EditorialBoard Member of Wiley Wireless Communicationsand Mobile Computing, an Associate Editor for

Wiley Security and Communication Networks, and an Editorial Board Memberof KSII Transactions on Internet and Information Systems and the InternationalJournal of E-Health and Medical Communications. His research interestsinclude mobile ad hoc and wireless sensor networks, wireless communicationsand mobile computing, switching and routing, and broadband communicationnetworks.

Dr. Li is a Senior Member of the IEEE Communications and Com-puter Societies. He is a Registered Professional Engineer of Canada. Hehas served as a Technical Program Committee (TPC) Cochair of Queen’sBiennial Symposium on Communications’10. He has served as a symposiumcochair of the 2011 IEEE International Communications Conference (ICC)Wireless Networking Symposium, the 2010 IEEE Global CommunicationsConference (GLOBECOM) Ad-Hoc and Sensor Networks Symposium, theIEEE GLOBECOM’09 Wireless Communications Symposium, InternationalWireless Communications and Mobile Computing Conference’08–10 WirelessLocal Area Network and Wireless Personal Area Network Symposium, andmany other international conferences. He has served on the organizationcommittees of many international conferences and as a TPC member for manyinternational conferences, including the IEEE ICC; GLOBECOM; the WirelessCommunications and Networking Conference; and the Personal, Indoor, andMobile Radio Conference.

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Distributed Data Aggregation Using Slepian–Wolf Coding in Cluster-Based Wireless Sensor Networks

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