Design and Performance Analysis of Network Code Division Multiplexing for Wireless Sensor Networks

Transcription

1 Desgn and Performance Analyss of Network Code Dvson Multplexng for Wreless Sensor Networks Jng Yue, Zhua Ln, Guoqang Mao, and Branka Vucetc School of Electrcal and Informaton Engneerng, he Unversty of Sydney, Sydney, Australa Natonal IC Australa (NICA), Australa School of Computng and Communcatons, Unversty of echnology Sydney, Sydney, Australa E-mal: Astract In ths paper, we nvestgate the performance of a wreless sensor network, n whch multple groups of source nodes communcate wth ther respectve destnaton nodes wth the help of a common relay network A network code dvson multplexng (NCDM) scheme s proposed to remove the ntersesson nterference among multple transmsson sessons at each destnaton We focus on analyzng the soft processng algorthm of the NCDM scheme Based on the analyss results, a new code desgn crtera for the constructon of the generator matrx s proposed Smulaton results show that y followng the proposed code desgn crtera, the t error rato (BER) performance gap etween the scheme we studed and the seral sesson scheme can e managed effectvely In seral sesson scheme, source nodes n a numer of groups communcate wth ther respectve destnatons n a tme dvson manner Index erms Network code dvson multplexng, wreless sensor networks, soft processng algorthm, log-lkelhood rato, t error rato I INRODUCION As a specal channel codng strategy developed for cooperatve communcaton networks [1], dstruted codng has attracted sgnfcant attenton recently Dstruted codng technque has een appled n the desgn of conventonal channel codes, such as dstruted turo codes [], dstruted space-tme codes [3] and dstruted low-densty party-check (LDPC) codes [4] In the aove dstruted codng schemes, transmsson relalty over pont-to-pont wreless communcaton channels has een effcently mproved he dstruted codng schemes dscussed aove are developed for small-scale uncast relay networks owever, many practcal applcatons are n large-scale wreless sensor networks (WSNs) WSNs s the key elements n Internet of hngs (Io) Io s a scenaro n whch oects are provded wth unque dentfers and data transmsson are over a network wthout requrng human-to-human or human-tocomputer nteracton [5] In WSNs, a large numer of sensor nodes gather nformaton from the surroundng envronment and then delver the gathered nformaton to a common destnaton va other sensor nodes, servng as relay nodes he sensor nodes, whch gather nformaton, are referred to as hs work s supported y Australan Research Councl Dscovery Proect DP and the Chna Scholarshp Councl (CSC) source nodes As the source and the relay nodes are n dfferent spatal locatons, the destnaton node receves replcas of the transmtted sgnal va multple nodes, ts sgnal wll have hgher spacal dversty and hence etter performance [6] owever, relay nodes may consume consderale amounts of rado spectrum and energy If not used properly, they may cause further spectrum congeston and nterference Network codng (NC) [7] s a novel approach, n whch the relay nodes are allowed to encode the packets receved from multple source nodes and send the encoded packets nstead Codng operatons enale the relay nodes to compress the nformaton, and whenever possle, to reduce the numer of transmssons and andwdth consumpton and/or maxmzng the transmsson relalty he dea of NC can e appled to WSNs In [8], extrnsc nformaton transfer (EXI) charts are employed to desgn the rregular low-densty generator matrx (LDGM) codes ased on a sngle sesson model In ths paper, we consder a network wth multple sessons We further assume that at each destnaton node, only the nformaton from ts own sesson s requred and the nformaton from other sessons are not allowed to e decoded due to the securty reasons hs assumpton s realstc n some applcaton scenaros n Io For example, n smart meter networks, where multple sensors, measurng water, gas and energy consumptons, communcate wth multple utlty control centres [9] he nformaton from varous utltes, such as for water, gas and energy consumptons, cannot e shared We propose to desgn novel network codng mechansms, referred to as network code dvson multplexng (NCDM) he NCDM scheme can provde securty protecton on physcal layer Furthermore, n order to optmze the overall system performance, ncludng mnmzng nterference, and maxmzng the spectral effcency, dversty and codng gans, we analyze the NCDM scheme desgn and ts performance Based on the analyss results, we propose a new code desgn crtera for the NCDM scheme he remander of the paper s organzed as follows: the system model s ntroduced n Secton II Secton III proposes the NCDM scheme for the parallel sesson model Secton IV analyzes the soft processng algorthm of the NCDM scheme and ntroduces a code desgn crtera Secton V presents the /15/$ IEEE 1861 ISI 015

2 smulaton results Fnally, Secton VI concludes the paper II SYSEM MODEL We consder a wreless network contanng L transmsson sessons In each transmsson sesson, a group of source nodes communcate wth ther common destnaton node through a group of relay nodes he th sesson s denoted y ϕ, where {1,,,L} We assume that n the th sesson there are S source nodes he total numer of source nodes n the L sessons s M = L =1 S Denote the destnaton node of sesson ϕ yd Assume that the network conssts of N relay nodes whch are shared among all the L sessons he th relay node s denoted y R, {1,,,N} he system model s shown n Fg 1 Fg 1 A network graph used to descre the system model he data transmsson from the source nodes to ther destnaton nodes s carred out n three phases: a roadcast phase, a relay phase and a data recovery phase In the roadcast phase, all the source nodes roadcast ther data packets to all the relay and the destnaton nodes Each data packet s composed of three parts: an nformaton data part, a Cyclc Redundancy Check (CRC) part and a header he ndces of the source nodes and the sesson to whch the source node elongs are contaned n the header he nformaton data parts of all data packets have the same length, as well as the CRC parts and the headers A certan MAC layer protocol, eg, me-dvson Multple Access (DMA) or Carrer Sense Multple Access (CSMA), s assumed to e employed hs ensures that the source node transmssons do not cause nterference to each other In the relay phase, each relay node lstens to the transmsson from the source nodes, decodes the receved data packets, checks the correctness of the decoded packets y usng CRC and puts the correctly decoded packets nto ts uffer Snce each relay node only performs hard decson decodng and CRC check, the decodng process s very fast and the delay due to the decodng at each relay node can e neglected hen each relay node selects unformly at random a numer of d r data packets from ts uffer to perform network codng y usng lnear comnatons of the packets n the feld of GF() [10] d r s selected wth proalty Ω dr accordng to the degree dstruton Ω(x) = Ω dr x dr Snce the numer d r s much smaller than the total numer of source nodes, e, d r M, the proalty of the event that the numer of data packets n a relay node s uffer s smaller than d r s neglgly small and we can always assume that the network codng process s achevale hen at each relay node, a network-coded data packet s formed he connecton nformaton of the source and the relay nodes s contaned n the header of each networkcoded data packet Fnally, all the relay nodes roadcast ther network-coded data packets to the destnaton nodes usng a DMA or CSMA MAC layer protocol In the data recovery phase, data packets receved from the source and the relay nodes n the roadcast and relay phases, respectvely, are organzed nto a data matrx We consder the quas-statc Raylegh fadng channels Wthout lose of generalty, we focus our analyss on the th row of the receved data matrx At the destnaton noded, the receved sgnal can e expressed asr = α E (J β)+n, wherer s a row vector of sze 1 (M+N) α s the fadng coeffcent vector of sze 1 (M +N) he fadng coeffcents reman constant over the length of one data packet ut change ndependently etween adacent packets hus, we can assume perfect channel state nformaton (CSI) at the destnaton nodes represents the element-wse multplcaton of the vector E s the average transmtted energy per t J s a 1 (M + N) vector wth all elements equal to 1 he nary sequenceβ s a random row of the data matrx[m 1 m m L ] G, where represents the multplcaton operaton over the feld of GF() [m 1 m m L ] represents the nformaton matrx of the L sessons G s the correspondng LDGM generator matrx seen from D of sze M (M + N) he parameter n = [n,1,n,,,n,m+n ] s the addtve whte Gaussan nose wth a zero mean and a doule sded power spectral densty of / Next, each destnaton node mplements the NCDM scheme to remove the nterference from the source nodes of other sessons Note that snce all the connecton nformaton are contaned n the header of each data packet, the destnaton nodes know how the checks at the relay nodes are formed and can correspondngly replcate the code graph and perform message-passng decodng III E NCDM SCEME FOR A PARALLEL SESSION MODEL WI MORE AN WO SESSIONS In ths secton, we wll ntroduce the NCDM scheme for the parallel sesson model, whch can e used to remove the nter-sesson nterference at each destnaton By a parallel sesson model, we refer to source nodes n multple sessons communcatng wth ther respectve destnatons through a common relay network smultaneously he fundamental dea ehnd the NCDM process takes advantage of the property of G = 0 ere G and are the generator matrx and the party check matrx of the LDGM codes, respectvely hroughout the paper, we denote the LDGM generator matrx seen from the th destnaton node D y G and the correspondng party check matrx y G s of sze 186

3 M (M + N) Let G t represent the tth sumatrx of G and of sze S t (M + N), t {1,,,L} S t s the numer of source nodes n the tth sesson Snce G s a systematc matrx, t can e wrtten as G = [I M P ], where I M represents an M M dentty matrx P s an M N party part matrx Let P t e an S t N party part matrx of G t t s the party-check matrx correspondng to the generator matrx G t o otan sesson ϕ s nformaton at the destnatond, {1,,,L}, the nterference ntroduced from other sessons to ϕ needs to e elmnated hs can e done y multplyng the generator matrx G y ( t ) Usng the property that G t (t ) = 0, t {1,,,L}\, the nterference from other sessons can e removed completely owever, the party check matrx ( t ) s also presented to other sumatrces of G, {1,,,L}\t, as an undesrale y-product For example, when t = 1, after carryng out the frst sesson G 1 s nterference cancelaton process, the successve process of G (1 ) ( ) s not equal to zero due to the contruton of ( 1 ) As a result, the nterference from the second sesson s nformaton cannot e elmnated and the nterference cancelaton process stops o solve( ths prolem, ) 1 n ths paper, we delerately ntroduce a term ( 1 ), so that the product of ( 1 1 ) and ( 1 ) approxmately equals to an dentty matrx I he nterference cancelaton process contnues untl ϕ s nformaton at D s otaned Based on the aove dscusson, the equvalent generator matrx for the th sesson seen from destnaton D s gven y ) ) ) ) G t,t {1,,,L 1}\( t 1 ( t, G L = ( f {1,,L 1} ) G t,t {1,,,L }( t, L 1 f = L where ) ) 1 ( t ) 1 ( t s an nverse matrx of ( t ) ) ( t s a matrx otaned y settng the lnear dependent rows n ( t ) to zeros and keepng other rows unchanged ( Let Φ represent the term of ( ) ) ) ) t,t {1,,L 1}\( t 1 ( t L In a matrx form, Φ can e expressed as 0 S1 A 0 S1 S 0 S1 (B S L ) P 1 0 S 1 A 0 S 1 S 0 S 1 (B S L ) P 1 Φ = 0 S A I S 0 S (B S L ) 0 S N 0 S+1 A 0 S+1 S 0 S+1 (B S L ) P +1, (1) 0 SL A 0 SL S 0 SL (B S L ) P L 0 N A 0 N S 0 N (B S L ) I N } {{ } } {{ } (M S L ) columns N columns where A t = t 1 =1 S, when t L and A t = 0, when t = 1 B t = L =t+1 S, when 1 t L 1 and B t = 0,, when t = L (P t ) s the transpose of the matrx P t [11] For the frst M S L columns, all the elements are equal to zero except an dentty sumatrx I S of sze S S, see (1) For the last N columns of Φ, the frst L sumatrces correspond to the party part matrces of G t, t {1,,L}\ he last N rows form an dentty matrx, as shown n (1) Let [m 1 m m L ] represent an artrary row of the data matrx [m 1 m m L ] At destnaton node D, after the NCDM scheme, we can otan the equvalent receved sgnal as r Φ = [ α E ( J [m1 m m L]G ) ] Φ +n Φ, () where α s the fadng coeffcent of sze 1 (M +N) IV PERFORMANCE ANALYSIS OF E SOF PROCESSING ALGORIM AND CODE DESIGN CRIERIA In [1], the performance of the NCDM scheme for the parallel sesson model wth two sessons was analyzed from the perspectve of matrx In ths secton, we analyze the soft processng algorthm of the NCDM scheme hen, ased on the analyss results, a code desgn crtera s summarzed to etter control the BER performance A Soft Processng Algorthm For a nary random varale X {±1}, ( ts log-lkelhood ) rato (LLR) s defned as l(x) = log Pr{X=+1} P r{x= 1} Susequently, the LLR for a transmtted symol x k at the destnaton node s gven y l k = 4α,k r k E, where α,k s thek th element of the fadng coeffcentα, whch s assumed to e known at the recever For addtve whte Gaussan nose (AWGN) channel, α,k = 1 r k s the receved symol correspondng to the transmtted symol x k Once the LLR values are otaned for all the transmtted symols, we then need to fnd the correspondng nput LLR values for each check node hs can e done y multplyng the LLR values wth each column of the matrx Φ he otaned vectors of the LLR values after the multplcaton are then the LLR values of the nput symols for the check nodes Let Ψ e the set of poston ndces of the non-zero elements of the th column of the matrxφ Let z e the output symol of the th check node hen z = k Ψ x k, where represents the addton operaton over the feld of GF() he output LLR values of each check node can e computed y L = tanh 1( Π k Ψ tanh( l k ) ) ere l k, k Ψ, s the LLR value for the k th nput symol of the check node B Analyss of the Soft Processng Algorthm Let Υ t represent the set formed y the ndces of postons of all the non-zero elements n the th column of P t Let z e the output symol of the th check node of the generator matrx, and let x t,k represent the k transmtted symol of the tth sesson, where t {1,,,L} When M < M + N, the output symol of the th check node can e wrtten as z = L t=1 x t t,k he encoded vector correspondng to the generator matrx 1863

4 seen from the th destnaton node can e wrtten as x = [x 1,1,,x 1,S1,,x t,1,,x t,st,,x L,1,,x L,SL, z M+1,,z,,z M+N ] Let l t,k e the LLR value of the k th receved symol correspondng to the transmtted symol from the tth sesson It can e computed y l t,k = 4α t,k r t,k E, (3) where α t,k s the k th element of the fadng coeffcent α t, whch s assumed to e known at the recever for decodng When 0 M, the receved symol correspondng to the transmtted symol x t,k s r t,k = α t,k (1 x t,k ) + n t,k When M < M +N, the receved symol s r = α (1 z )+n After performng the NCDM scheme, the output LLR values of each check node can e represented y L = tanh 1 lt,k tanh (4) t,t {1,,,L} t he values of the frst M output LLR values can e splt nto three regons, e, 0 < 1 =1 S, 1 =1 S < =1 S, and =1 S < M For the regons where 0 < 1 =1 S and =1 S < M, the output LLR values are L = 0 For the regon where 1 =1 S < =1 S, the output LLR value can e wrtten as L = l, For the last N output LLR values, e, M < M +N, we expect that they are n the form of L = l, ere l, represents the LLR value for the th receved symol at the destnaton node D owever, the th output LLR value when M < M +N can e wrtten as (6) For the frst part lt,k n (6), ts expected value s 1 Let x represent the asolute value of x Snce 0 tanh lt,k < 1, the more product terms there are, the smaller the value lt,k s hus, n order to otan etter performance, the column weght of the generator matrx of each user should e as small as possle Also t can e seen that the larger the value of L s, the smaller the value lt,k s It means that as the numer of the parallel sessons ncreases, the value of ths part ecomes smaller Accordngly, the performance of the system ecomes worse α,e For the second part tanh[ α, (1 x,k )) )] x t t,k + n, l, n (6), ts expected form s tanh, e, α,e tanh[ α, (1 )] x,k ))+n, Now, we focus on analyzng the second part of (6) here are four possle cases for the values of the comnaton of x,k and x t t,k he four cases are shown elow 1 : x t t,k = 0, x,k = 0 : x t t,k = 0, x,k = 1 3 : x t t,k = 1, x,k = 0 4 : x t t,k = 1, x,k = 1 For the frst two cases, e, case 1 and case, the second part of (6) ( can e wrtten ( as the expected form, α,e e, tanh[ α, (1 )] x,k ))+n, For case 3, the( second part ( of (6) can e wrtten α,e as tanh[ α, (1 ) x,k ))+n, 4α, E ] And for case 4, the second part can e wrtten α,e as tanh[ α, (1 ) x,k ))+n, + 4α, E ] In order to acheve the expected form of the second part, we should try to avod the case 3 and case 4 herefore, the value of x t t,k s expected to e zero It can e seen that the value of ths part has drect relatonshp wth the numer of the parallel sessons L x t t,k s the sum of the transmtted symols from the L 1 sessons except the th sesson, where x t,k equals to 0 or 1 wth equal proalty, e, P r (x t,k = 0) = P r (x t,k = 1) = 1 C Code Desgn Crtera As mentoned n Secton III,G s the generator matrx seen from the th destnaton node D G t s the tth sumatrx of G Based on the aove analyss, we can summarze the code desgn crtera as When L s an even numer, the column weght of each sumatrx of the generator matrx G, e, G t, where t {1,,,L}, must e an even numer When L s an odd numer, the column weght of each sumatrx of the generator matrx G can e an odd or even numer V SIMULAION RESULS In ths secton, we present smulaton results for the parallel sesson model wth the NCDM scheme We consder a WSN wth L = 3 and 4 transmsson sessons, respectvely Each transmsson sesson has 500 source nodes, sendng data packets to ther correspondng destnaton nodes va a common mult-hop relay network here are 1500 relay nodes when L = 3, and 000 relay nodes when L = 4 We assume that all source nodes have data packets to transmt All the sourcerelay channels n the network are spatally ndependent and have equal transmttng power In the presented fgures, the lael PSM corresponds to the parallel sesson model, and SSM refers to the seral sesson model Fg (a) presents the performance comparson of varous column weghts of G t, (e, ρ = and ρ = 3), for an even numer of sessons (e, L = 4) When the numer of sessons L s an even numer, f the column weght ρ of G t s an even numer, the BER performance gap etween the seral sesson model and parallel sesson model s smaller than the 1864

5 { } L = tanh 1 lt,k anh α,e α, 1 x t N t,k + n, 0 t,t {1,,L} k Υ t { = tanh 1 lt,k anh α,e t α, 1 } x,k x t,k + n, (6) t,t {1,,L}\ k Υ t one for the case when ρ s an odd numer Note that when the column weght ρ s an odd numer, the BER performance of the parallel sesson model gets worse Fg () presents the performance comparson of varous column weghts ofg t, (e, ρ = and ρ = 3), wth an odd numer of sessons (e, L = 3) he smaller the column weght ρ of G t s, the closer the BER performance of parallel sesson model wth NCDM to that of the seral sesson model From Fg () we can see that when ρ =, the BER performance of the parallel sesson model s very close to the one for the seral sesson model he oservaton s consstent wth the theoretcal results BER BER AWGN,ρ=,SSM AWGN,ρ=,PSM AWGN,ρ=3,SSM AWGN,ρ=3,PSM Fadng,ρ=,SSM Fadng,ρ=,PSM Fadng,ρ=3,SSM Fadng,ρ=3,PSM AWGN,Rep Codes,d=4 Fadng,Rep Codes,d= E /N (db) (a) he numer of sessons s L = 4 AWGN,ρ=,SSM AWGN,ρ=,PSM AWGN,ρ=3,SSM AWGN,ρ=3,PSM Fadng,ρ=,SSM Fadng,ρ=,PSM Fadng,ρ=3,SSM Fadng,ρ=3,PSM AWGN,Rep Codes,d=3 Fadng,Rep Codes,d= E / (db) () he numer of sessons s L = 3 Fg he BER performance comparson etween two dfferent column weghts of generator matrx, e, ρ = and ρ = 3, over AWGN and Raylegh fadng channels, respectvely he numer of sessons s L = 3 and 4 For the Raylegh fadng channel, the BER performance gap etween the seral sesson and parallel sesson model s much larger than that of the AWGN channel hat s ecause the effect of the resdual nterference from other sessons to the performance s relatvely large for fadng channel For comparson, the BER performance for repetton codes s also plotted After usng the NCDM scheme at each dest- 1 naton node, the code rate ecomes L+1 hus we compare the performance of our proposed scheme wth the repetton code wth parameter d = L, e, the messages are repeated L tmes From Fg, t can e seen that the proposed system acheves a sgnfcantly BER performance gan compared wth the system wth the repetton codes n a hgh sgnal to nose rato (SNR) regon VI CONCLUSION In ths work, we proposed a novel network code dvson multplexng scheme for the parallel sesson model We analyzed the soft processng algorthm of the NCDM scheme Based on the analytcal results, a code desgn crtera for the generator matrx constructon method was proposed Smulaton results showed that the prolems caused y the NCDM scheme can e managed effectvely and the BER performance can e mproved sgnfcantly y followng the desgn crtera REFERENCES [1] unter and A Nosratna, Dversty through coded cooperaton, IEEE rans Wreless Commun, vol 5, no, pp 83 89, Fe 006 [] B Zhao and M Valent, Dstruted turo codes: owards the capacty of the relay channel, IEEE VC 03-Fall, vol 1, pp 3 36, Oct 003 [3] S Yu, R Schoer, and L Lampe, Dstruted space-tme lock codng, IEEE rans Commun, vol 54, no 7, pp , Jul 006 [4] A Chakraart, A Baynast, A Saharwal, and B Aazhang, Low densty party check codes for the relay channel, IEEE J Sel Areas Commun, vol 5, no, pp 80 91, Fe 007 [5] L Atzor, A Iera, and G Morato, he nternet of thngs: a survey, Computer Networks, vol 54, no 15, pp , Oct 010 [6] M Dohler, Y L, B Vucetc, A Aghvam, M Arndt, and D Barthel, Performance analyss of dstruted space-tme lock-encoded sensor networks, IEEE rans Veh echnol, vol 55, no 6, pp , Nov 006 [7] R Ahlswede, N Ca, S L, and R Yeung, Network nformaton flow, IEEE rans Inf heory, vol 46, no 4, pp , Jul 000 [8] K Pang, Z Ln, Y L, and B Vucetc, Desgn of dstruted networkchannel codes for wreless sensor networks, n Proc of IEEE ICC 11, Kyoto, Japan, Jun 011, pp 1 5 [9] (011) Newngton smart vllage [Onlne] Avalale: proects/smart-grd-proects/smart-grd-smart-cty/newngton-smart- Vllageaspx [10] S Ln and D Costello, Error Control Codng: Fundamentals and Applcatons, nd ed New Jersey: Prentce all, 004 [11] J Gentle, Matrx Algera: heory, Computatons, and Applcatons n Statstcs, 1st ed New York: Sprnger, 007 [1] J Yue, K Pang, Z Ln, Y L, B Ba, and B Vucetc, Dstruted network channel codng for multple access relay nterference channels, n Proc IEEE Gloecom 1, Anahem, CA, USA, Dec 01, pp