An Energy Efficient Adaptive Distributed Source Coding Scheme inWireless Sensor Networks

An Energy Efficient Adaptive Distributed Source Coding Scheme in Wireless SensorNetworks∗Caimu Tang Computer Science Department University of Southern California Los Angeles,CA90089caimut@ Cauligi S.Raghavendra and Viktor K.Prasanna Department of EE-Systems and Computer ScienceUniversity of Southern CaliforniaLos Angeles,CA90089raghu,prasanna@Abstract—Sensor networks are used in a variety of applications for event monitoring,environmental sensing and outer space ex-ploration.An important application is detecting a target in the field using sensors gathering acoustic data.In this target detec-tion application(ATR),a cluster of wireless sensors collect acous-tic data and perform signal processing.In the algorithm used for signal processing,acoustic data collected by the sensors need to be communicated to a designated head node for determining the target direction of bearing.The data collected by geometrically closely distributed sensors show high spatial correlation.In this paper,our focus is on energy efficient coding schemes for wire-less sensor networks.First we give an analysis to show why con-ventional compression schemes give poor performance when en-ergy consumption for encoding and decoding processing overheads are considered.We then describe a new coding scheme called EEADSC which minimizes the Lagrangrian cost function,i.e.R+λD D+λE E(R is the bitrate,D is the distortion,E is the energy and λD,λR are the Lagrangrian coefficients).The proposed scheme fully exploits spatial correlation in wireless sensor network and is adaptive according to tracking signal strength.We evaluated the proposed scheme using datasets from an ATR application which achieved up to a factor of8data compression.EEADSC uses TCQ [14]quantization and trellis encoding to represent a16bit data value by as few as2bits.With the scheme,we reduce the over-all energy cost for communication in this application by a factor of 2.53,including the overhead processing cost in encoding/decoding. The scheme alsofits well for general sensor network applications in which some data collection and aggregation are performed.I.I NTRODUCTIONInexpensive sensors capable of significant computations and wireless communication are becoming increasingly available.A variety of modern data sensors are being built including UCLA WINS[2],UC Berkeley SMART DUST[1],Rockwell Scientific Hidra[4],and Jet Propulsion Laboratory SENSOR WEBS[3].All these sensors are light weight,low cost and capable of performing significant amount of computations and communications.Sensor nodes forming a network are highly (*)This research is partially supported by the DARPA under contract F33615-00-C-1633in the Power Aware Computing and Communications Program (PAC/C)and by the DARPA and Air Force Research Laboratory,Air Force Material Command,USAF,under agreement number F30602-01-2-0549.The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied,of the Defense Advanced Research Projects Agency (DARPA),the Air Force Research Laboratory,or the eful in a variety of applications and scenarios.A sensor web can be used to collect information regarding environment,cli-mate,it can be deployed in a battlefield for intelligence gather-ing and for scientific investigations on other planets.Because the nodes in wireless sensor network are powered by battery, energy efficiency has been a focus when devising of new algo-rithms and protocols for wireless sensor networks.Energy effi-cient algorithms and protocols mean longer lifetime of the sys-tem.An application of sensor network is detecting a target using acoustic signal,e.g.ATR.In this type of applications,sensors collect acoustic,seismic or image data.Sensors collaboratively process signal data to detect and classify objects.In one sce-nario,a network consists of a number of clusters,with each cluster having several homogeneous sensors,and each sensor is equipped with a radio card for wireless communications.Sen-sors in a cluster are geometrically close to each other in the range of100meters while inter-cluster distances could be much far-ther(Fig.1shows a cluster with7sensors).One sensor is elected as the head which aggregates the data from the members, e.g,node1in Fig.1,and the head sensor node also observes the same event.SignalSourceFig.1.A cluster with7sensors,with one sensor acting as the cluster head The data collected by sensors in a sensor cluster have high spatial correlation due to the close location proximity.This is shown in Fig.1where the cluster head node1collects acoustic data for5consecutive quantized samples shown in the central text box;node5also observes the same event and has very close acoustic data as shown in the box next to it(the differences be-tween the two sequences are small).Sample values change over time,Fig.2illustrates signal sample amplitudefluctuation,in which there are three group sampled at10s,50sand100s with two curves in each group(values in the sequences are quantized) 0-7803-7802-4/03/$17.00 © 2003 IEEEof sensor1and2.From the curves,we can see the dynamic na-ture of the spatial correlations.Fig.2.Changes of Spatial Correlation Over TimeIn this paper,we propose a new energy efficient distributed source coding(EEADSC)scheme to exploit such spatial cor-relation.To achieve this,we devise a novel distributed coding scheme.With this coding,overall energy is saved and the sys-tem lifetime is prolonged significantly.In an ATR scenario with acoustic data from ground vehicles, sensor nodes collect data at the rate of1024samples per frame. With reference to Fig.1,the boundary nodes need to send their collected data to the central node.Here,there is high spatial correlation as all sensors collect data from the same target(s). Therefore,efficient coding scheme that can exploit the spatial correlation can be used to reduce the number of bits transmitted, and hence energy.From thefield data[5],we apply the proposed coding scheme and achieve a factor of8reduction in bits trans-mitted without losing quality in target detection.The proposed approach is different from Directed Diffusion mechanism[11] in that we exploit the correlation at the boundary of the network while data aggregation method in[11]operates inside the net-work.The approach complements directed diffusion approach. Both methods can work jointly on different levels of the network to maximally exploit the spatial correlation of signals in a sensor network and save overall system energy.II.E NERGY E FFICIENCY A NALYSIS ON C ODING S CHEMES There is significant energy consumption in wireless com-munications[9],[10],[12].Energy cost can be reduced by a number of techniques ranging from compression to application based coding.Any approach to reducing the bits communicated should also take into account the overhead cost in processing. Clearly,the overhead cost should not be too high,as otherwise the savings from actual communication will not improve the overall energy cost.In order to quantify the energy efficiency of a coding scheme,we define a simple metric for coding energy gain of a given scheme.Definition1:Coding Energy GainΥ:For a coding scheme with given parameters,denote e t to be the energy saving in com-munication due to the coding and denote e c to be the energy cost of coding/decoding in Joules.The coding energy gain is definedby the ratio e tc.Intuitively,Υgives an energy performance measurement of acoding scheme.However it does not directly give total energysavings for a coding scheme which can be deduced from it usingrelated information.We form an optimization problem using a Lagrangrian costfunction which is defined as follows.Definition2:Lagrangrian Cost Function L(R):For a cod-ing scheme with given parameters,for a given source,the bi-trate generated by the coding scheme is R in bits per sample,therecovered signal distortion is measured as D R dB and the totalenergy dissipation during the transmission of the bitstream,en-coding of the source and decoding the bitstream is E R Joules,the Lagrangrian cost function is defined asL(R)=R+λD D R+λE E R.(1) The cost function takes into account all three factors whileprevious coding scheme only considers the bitrate and distor-tion.We here do not put the delay into the cost function becauseE has incorporated the ing our Lagrangrian cost func-tion,the problem can be stated as follows:minR L(R)subject to D R<D and T R<Twhere,T R is the overall delay,D is the distortion bound andT is the frame interval upper bound.With this cost function,the coding scheme can adjust coding parameters over time to main-tain a low cost value.The two Lagrangrian coefficients are es-timated based on training dataset.The price paid for this is theestimation of the distortion in SNR,computation of the delay atthe end of each iteration and energy cost evaluation.Delay andenergy cost are simple to fetch or compute.To compute SNR,the noise power has to take the mean squared error of the trelliscodes,i.e.1n i(min{s i−l i,u i−s i})2,where l i,u i are the lower bound and upper bound of i-th partition and s i is the sam-pled value at step i and n is the number of samples in a frame.This is because the recovered signal with noise is in the othernode and it is too expensive to send over.Since we adaptivelychange the coset size and partitions,the computed SNR shouldbe accurate.Let us denote the average per-bit communication energy costper hop asσ(our analysis is based on unicast messages,for mul-ticast/broadcast messages,it is beyond the scope of this work),which includes the energy costs on both the transmission sideand the receiving side.For clarity of explanation,we assumethe transmission power isfixed,however,extension of our dis-cussion to power controlled radio can be done similarly whilethe transmission energy cost is no longer a constant,rather afunction of form a+r b where a is thefixedcost pertaining to any transmission and r is the farthest the transmitted signal can reach with sustainable SNR,and b is the distance factor in the range of2to7.Letβdenote the average energy cost per arith-metic operation,e.g.addition,multiplication,division.For agiven problemτ,let f:N→N(where N is the set of natural numbers)be the function to output bitrate(bits per sample)for a given number of operations.For a given scheme,let x be the number of operations required for coding(including encoding and decoding)on a dataset.We have the following,Υ=n(f(0)−f(x))σNxβwhere n is the number of hops the coded data will travel,and N is the number of samples.For a proposed scheme in a given setting,it is promising ifΥis greater than1.Just to give an idea,for a Gaussian source,with StrongArm processor and IEEE802.11b WaveLan radio card, the popular gzip scheme turns out to be not promising since Υgzip is approximately0.33.For given number of samples,N,we can rewrite eq.(1)as, L(R)−λD D R(x)=f(x)+λE(N f(x)σn+xβ)(2) Since there is only truncation error,the distortion is negligible (λD is small),and x=0,by eq.(2),we haveL(R)=f(0)+λE N f(x)σnThis is the cost associated with the case where no coding is ap-plied.For some x,when f(x)is significantly smaller then f(0), the coding scheme with x number of operations has a lower La-grangrian cost since we have a rough estimation thatσis about five to twenty times ofβwith the state-of-the-art radio and the SA-1100processor.With lossless entropy coding,we can also ignore the distor-tion component in eq.(2),we haveL(R)=f(x)+λE(N f(x)σn+xβ)For Gaussian source,f(x)is about half of f(0),entropy coding does not give a minimum Lagrangrian cost whenλE xβis too big.We will show that the proposed coding scheme,EEADSC, based on correlated observations by sensors,achieves an im-pressive coding energy gain as high as3.2using the Lagrangrian cost function as the coding selection criterion.It is well suited for distributed signal processing applications in a wireless sen-sor network environment.We have applied this scheme to one type of automatic target recognition(ATR)application.The signal distortion is bounded from above with EEADSC and it has no low bound errorfloor excluding quantization and trunca-tion introduced distortions(it can be as good as that of lossless scheme when the correlation is high).III.P ROPOSED EEADSC S CHEME Proposed coding scheme exploits spatial correlation that exists in sensor network applications.Coding of correlated sources has been studied in[17]and in[19].Later in[7],a prob-lem of distributed sensing of environment to make estimates based on the phenomena sensed is studied.The scheme in[7] uses a two-stage iterative approach with a quantizer followed by an index-reuse which is aimed to make use of the correlation. This scheme has been extended to wireless sensor networks with consideration on the encoding and decoding complexity[15]. In[15]the code construction based on Euclidean distances are studied and trellis based and lattice code can be used for the code design.In[16],joint decoding approach used in DISCUS has good performance on SNR gain,however,the decoding com-plexity is too high.In order to introduce EEADSC,we begin with the following definitions.Definition3:Coset Distance:Given a set(we call it coset)S with cardinality of n as{x1,x2,···,x n}and distance function Φ:Z×Z→R(where Z and R denote a set of integer and realnumbers,respectively),the coset distance between codeword w and coset S is defined as:d w S=nmini=1Φ(w,x i)(3) Definition4:Coset Minimum Distance:The minimum dis-tance for a given coset S is defined as:d S=mins,t∈SΦ(s,t)(4) Note,to extend the above definition for countable set,we sim-ply rewrite(3)asd w S=minx∈SΦ(w,x)It could be of interest for certain applications,however,in wire-less sensor networks,we assume that the coset isfinite.To facil-itate decoding using a reference,we need tofind a coset partition which maximizes the coset minimum distance.For example,given coset S={1,5,7,15},the codeword w=10has d w S=3if we use the Euclidean distance,and d w S=0if we use the Hamming distance.We use the L1norm, i.e.summation of pointwise absolute value of two sequences, as the metric from now on.A.The SchemeIn our application,the decoder can not communicate directly with the encoder to get the reference data either because it is too costly to do so or due to some physical constraints at decoder. The proposed distributed source coding problem can be formu-lated as follows,At Encoder:•Given:1)The pre-constructed cosets D1,D2,···,D m,2)A sequence of quantized samples Y1,Y2,···,Y n.∀Y i,∃D j,such that,Y i∈D j.3)Distortion bound D.4)Time bound T.•Find:A bit sequence conveying information about coset sequence D v1,D v2,···,D vnwhich minimizes the La-grangrian cost L(R)subject to the time bound T andthefollowing distortion bound,ni=1d Y i D v i<DAt Decoder:•Given:1)The pre-constructed cosets D1,D2,···,D m.2)A codeword sequence from encoder w1,w2,···,w n,3)A sequence of quantized reference samplesY 1,Y 2,···,Y n.•Reconstruction:The coset sequence D˜v1,D˜v2,···,D˜v n and therefore the quantized samples˜Y1,˜Y2,···,˜Y n,and ˜Yi∈D˜v i such that n i=1Φ(Y i,˜Y i)is minimized.A distributed scheme consists of two parts:(1)the coset par-tition and(2)the code design.For a given coset partition,one feasible solution of(2)is to select a coset for each sample so that the distance is minimized individually and encode the coset in-dex corresponding to each sample into the bitstream.It is a fea-sible solution since,in this case, n i=1d Y i D v i equals to0.D is a measure of the distortion.Perfect reconstruction is possible when the reference samples are correlated with the samples col-lected at the source.For certain applications,when perfect re-construction is not required,D is greater than0and high com-pression ratio is possible by exploiting spatial correlation.Due to noise,it is not practical,and also not necessary to require per-fect reconstruction in sensor network applications.For our ATR application,it is certainly the case that perfect reconstruction is not required as we are only interested in accurate event detec-tion.The encoding scheme consists of the following steps from a higher level point of view:1)Search the best coset partition and trellis constraint lengthaccording to the Lagrangrian cost function(The La-grangrian coefficients are pre-computed.).2)Quantize the sample sequence using TCQ[14]using anadaptive scalar amplitude interval.3)For a given quantized sample s,reduce it by a predictedmodulus M.4)Compute coset index using s mod(M)via looking up a pre-defined table.5)Use V A[8]tofind a bit sequence to denote the most prob-able path constraint by the trellis diagram.6)Code the parameters,start state using Fibonacci code be-fore coding of the V A bit sequence and the coset indices. For easy implementation,we use uniform coset partition,i.e. using modulo of a number for the coset index.Note that the se-lection of modulus M is based on application and prediction al-gorithm.For high correlated frame,this modulus should be set to a smaller number,otherwise,larger modulus.The decoder performs the following steps once the encoding parameters and Fibonacci code of the start state is received, 1)Use Convolutional code table to reconstruct the coset in-dex.2)Use quantized reference sample to search the closestmatch in the coset which is an approximation of the quan-tized sample from the source.3)Use TCQ to recover the original sample.B.An Illustrative ExampleWe use an example to get across the main idea of EEADSC. Figure3shows a sensor node(encoder)which performs encod-ing and a receiving sensor node(decoder)that also observes the same event.The data samples collected by the decoder on ob-serving the event is shown at the bottom of Fig.3designated with label“R”.The decoder uses these values as reference val-ues in decoding the received values.The two tables on the right of thisfigure give the distance mapping(top table)from code-word to coset and the decoding mapping(bottom one).There are two trellis diagrams,the top trellis diagram shows trellis it-eration states and transitions,and the bottom diagram shows the actual coded trellis path and the initial state is1(index starts from0)as computed.The decoded results designated with la-bel“D”are the coset index.Thefinal reconstructed values can be deduced by the decoding mapping table and the reference values.For example,at time0,the decoded result should be7 which is closer to reference value6since the computed coset index is3which can be reconstructed as either2or7.At time 1,the coset is again3,but this time,the reconstructed value is 2as this is close to the reference value3.Likewise,the next three samples will be decoded as1,0,and6.The decoded val-ues in this example are the same as the original coded values, i.e.a perfect reconstruction.However,it is not the case in gen-eral.There will be some distortion on the reconstructed signal as discussed in Section IV.The Lagrangrian cost is computed for the selection of the coset partitioning and constraint length. The Lagrangrian coefficients are pre-computed based on train-ing dataset.In this example,the distortion is105=2.The La-grangrian cost is3.888whereλD=0.01D when D is less than 8andλD=1.01D−1,otherwise,andλE=2.2.3320263015D:R:Fig.3.An example of EEADSC using V A with4state Ungerb¨o ck trellis dia-gramIV.E XPERIMENTAL E VALUATIONSOur implementation of the encoder consists of two parts: TCQ quantization and DSC encoding.Similarly,the imple-mentation of the decoder consists of two parts:DSC decodingand TCQ value reconstruction.The decoder implementation is straightforward(timing calibration with the encoder needs to be addresses here).For encoding,we use the TBA for the traver-sal of the trellis.So there are a total of two passes of the trel-lis,namely,forward with the end state and backward with the start state.In TCQ,the same algorithm is used.In thefinal bit-stream,two states have to be coded,one start state from the TCQ and one start state from DSC.Both states are coded usingfirst degree Fibonacci code.We coded the start state in the begin-ning of the bit sequence so that the decoder can start to decode once thefirst bit is received after the start state is received.This can significantly reduce the decoder buffer requirement.In ATR application,decoder normally decodes many bitstreams,and in our experiment it decodes6bitstreams every second.For trellis with small constraint length,we use one pre-computed table for look-up operations and eliminate the Add-Compare-Select pro-cedure.In order to maintain a small table,a simple trellis nor-malization[18]is used.Initialization includes the construction of the TCQ partitioning tables and DSC state and accumulative value tables.The initialization energy cost is incurred once. A.Experimental Results of EEADSCIn order for the proposed scheme to be practical,thefidelity of reconstructed signal should be viable for signal processing application.In ATR application,the reconstructed signals will be used to detect the moving object,its direction,and velocity. Fig.4shows two curves,the original frame labeled as“Source Signal”and the noise curve drawn in the middle.The decoder on sensor4uses sensor1as the reference to decode the100th frame.The SNR is24.19dB.The SNR is defined asSNR=10log10 1024i=1s2i SSE,where SSE is the sum of squared errors of1024samples for the noise power as explained before and s i is the signal ampli-tude at step i.The SNR performance is given at100-th frame and it is close to the worst case,all other frames have better per-formances than that of100th frame since the spatial correlation is the worst at100th second(spatial correlation plot across all frames is omitted here).We measured the energy costs for transmitting and receiv-ing large number of frames of data with and without EEADSC scheme.Figure5shows the experiment setting.In our ex-periments,we used234frames offield data available in the CDROM[5]and they are loaded into the iPAQ(we skip the sensing steps).The Lagrangrian coefficients used in the coding scheme are the same as these explained in III.B.It is not neces-sary to have an exact number of the Lagrangrian cost.To esti-mate the energy cost,we use the formula as following,E= T V(δ¯A+A)whereδis1or0based if radio is on transmission/reception or idle/sleep,¯A is the average current when radio is on and A is theFig.4.Signal distortion of sensor1at the100-th secondTABLE IE NERGY P ROFILE OF U NCODED V ERSIONSending ReceivingComp.0.00.0Comm.969.2mJ840.8mJTotal1810mJaverage current when node is on and radio current is excluded, T is the estimated time for each activity.The whole calculation on Lagrangrian cost is based on a baseline which is computed offline based on the platform used,the cost on this optimal pro-cedure is just a few table lookup operations based on different selected quantization and coding parameters.To compute the rought energy dissipation,we used SourceMeter[6]as the power source for iPAQs and de-veloped a program to fetch the current values from it via a RS-232serial link while encoding,decoding,transmitting, and receiving proceed.Fig.6and Fig.7show two such current curve on encoding and transmission as one of4plots (others are omitted due to space limitation).In Fig.6,there are two current peaks,thefirst peak is due to energy drawn by processor on encoding and the other is due to energy drawn by radio on transmission.The unit of x axis is the time in second and that of y axis is the current in mA,the single durations of encoding and transmission are much short,we repeated the same many times so that we can have better meter readings and we average out the readings.The voltage isfixed at5V.When CPU arithmetic and memory access energy dissipation drops or the data have to travel more than1hop,more gain is expected. The energy consumption for EEADSC scheme is compared with uncompressed version where each sample value requires transmission of2bytes.Table I&II show our measurement results.We achieve an overall improvement by a factor of2.53 including overhead.Since we use the IEEE802.11b Wireless LAN for the experiment,and the per bit transmission energyis very low due to high data speed.To apply the proposed scheme in real sensorfield,the gain is expected to be much better than what we reported here.TABLE IIE NERGY P ROFILE OF EEADSC C ODED V ERSIONSending Receiving Comp.331.5mJ 177.29mJ Comm.107.99mJ 93.86mJTotal710.65mJFig.5.Experiment Settingputationand Communication Current (Encoding and Transmis-sion,in this plot,the radio is on while encoding.)putation and Communication Current (Receiving and no Decod-ing)V.C ONCLUSIONSIn this paper,we proposed a novel distributed coding scheme to exploit the spatial signal correlation observed by independent sensors based on a Lagrangrian cost function.We used experi-ments to identify such correlation in field data acquired from an ATR application.We implemented the proposed coding scheme to investigate the energy profile of the scheme and it shows sig-nificant energy reduction for communication including process-ing overhead.We will work on further reduction via adding more exploring space of the Lagrangrian minimization,includ-ing exploitation of the temporal correlation intra-frame using 1-D wavelets transformation,and extend our results for 2-D sig-nals.R EFERENCES[1]“COTS Dust”,/∼shollar/macro motes/macromotes.html.[2]“The WINS Project”,/WINS.[3]“Wireless Sensor Networks”,/∼grimace/re-search/sensorsimii/wireless sensor networks.ppt.[4]“Hidra sensor node”,http://wins.rockwellscientifi.[5]ATR Field Data,DARPA and ISI,University of Southern California,2000.[6]“SourceMeter 2400Manual”,/products/2400.[7]T.J.Flynn,and R.M.Gray.“Encoding of Correlated Observations”,IEEE Transactions on Information Theory,vol.IT-33,no.6,pp.773-787,Nov.1987.[8]G.Forney.“The Viterbi Algorithm”,Proceedings of the IEEE,vol.61,no.3,pp.268-278,March 1973.[9]L.M.Feeney,M.Nilsson,“Investigating the Energy Consumption of a Wireless Network Interface in an Ad Hoc Networking Environment,”Pro-ceedings INFOCOM,2001.[10]W.Heinzelman,A.Chandrakasan,H.Balakrishnan,“En ergy efficient Communication Protocol for Wireless Microsensor Networks,”Proce ed-ings of the Hawaii Conference on System Sciences,Jan.2000.[11]C.Intanagonwiwat,indan,and Deborah Estrin.“Directed Diffu-sion:A Scalable and Robust Communication Paradigm for Sensor Net-works”,In Proc.Sixth Annual International Conference on Mobile Com-puting and Networks (MobiCom 2000),Aug.2000.[12] C.E.Jones,K.M.Sivalingam,P.Agrawal,J.C.Chen,“A Survey of En-ergy Efficient Network Protocols for Wireless Networks,”Wireless Net-works,V ol.7,pp.343-358,2001.[13]J.H.Kasner,M.W.Marcellin,and B.R.Hunt.“Universal Trellis Coded Quantization”,IEEE Transactions on Image Processing,vol.8,no.12,pp.1677-1687,Dec.1999.[14]M.W.Marcellin,and T.R.Fischer.“Trellis Coded Quantiz ation of Mem-oryless and Gauss-Markov Sources”,IEEE Transactions of Communicati ons,vol.38,no.1,pp.82-92,Jan.1990.[15]S.S.Pradhan,and K.Ramchandran.“Distributed source coding:Sym-metric rates and applications to sensor networks”,Proc.IEEE Data Com-pression conference (DCC),March 2000.[16]S.S.Pradhan,and K.Ramchandran.“Distributed source coding Using Syndromes (DISCUS):Design and Construction”,Proc.IEEE Data Com-pression Conference (DCC),1999.[17] D.Slepian,and J.K.Wolf.“Noiseless Coding of Correlated Information Sources”,IEEE Transactions on Information Theory,vol.IT-19,no.4,pp.471-480,July 1973.[18]G.Ungerb¨o ck.“Adaptive Maximum-likelihood Re ceiver for Carrier-Modulated Data-transmission Systems”,IEEE Transactions on C ommu-nications,22(5):626-636,May 1974.[19]A.D.Wyner,and J.Ziv.“The Rate-Distortion Function for Source Coding with Side Information at the Decoder”,IEEE Transactions on Information Theory,vol.IT-22,no.1,pp.1-10,Jan.1976.。