Wavelet Video with Unequal Error Protection Codes in W-CDMA System and Fading Channels

Transcription

1 Wavelet Vide with Uequal Errr Prtecti Cdes i W-CDMA System ad Fadig Chaels MINH HUNG LE ad RANJITH LIYANA-PATHIRANA Schl f Egieerig ad Idustrial Desig Cllege f Sciece, Techlgy ad Evirmet Uiversity f Wester Sydey Secd Aveue, Kigswd, 747, N.S.W. AUSTRALIA Abstract: - Wavelet-based algrithm fr vide cmpressi with uequal errr prtecti (UEP) cdes i widebad cde divisi multiple access (W-CDMA) system ver additive white Gaussia ise (AWGN) ad Rayleigh fadig chaels are aalysed. The utilizati f Wavelets has cme ut t be a pwerful methd fr cmpress vide sequece. The wavelet trasfrm cmpressi techique has shw t be mre apprpriate t high quality vide applicatis, prducig better quality utput fr the cmpressed frames f vide. A spatially scalable vide cdig framewrk f MPEG i which mti crrespdeces betwee successive vide frames are explited i the wavelet trasfrm dmai. The basic mtivati fr ur cder is that mti fields are typically smth that ca be efficietly captured thrugh a multireslutial framewrk. Wavelet decmpsiti is applied t vide frames ad the cefficiets at each level are predicted frm the carser level thrugh backward mti cmpesati. The prpsed algrithms f the embedded zer-tree wavelet (EZW) cder ad the -D wavelet packet trasfrm (-D WPT) are evaluated. Key-Wrds: - Vide sequece, Uequal errr prtecti cdes, Embedded zer-tree wavelet trasfrm, -D wavelet packet trasfrm, W-CDMA, AWGN, Rayleigh fadig chaels. 1 Itrducti The wavelet fuctis are develped fr harmic aalysis, sigal represetati, speech ad vide badwidth cmpressi, multiresluti sigal prcessig, ad sigal desig i varius cdig ad cmmuicati applicatis. The wavelets i cmmercial applicatis were maily with efficiet cmpressi techiques sigals such as vice ad vide. This was due t the lgarithmic-scale decmpsiti i frequecy, which fits aturally i may f the sud ad vide sequece recstructi studies. Wavelet thery cvers quite a large area. It treats bth the ctiuus ad discrete time cases. The itrducti f the embedded zer-tree ccept fr wavelet-based vide cmpressi has geerated a sigificat imprvemet i perfrmace cmpared t previus vide cdig methds. A refiemet f the EZW apprach, called set partitiig it hierarchical trees (SPIHT) by Said ad Pearlma, is the mst well kw EZW derivative. While SPIHT eys a gd rate-distrti perfrmace fr vide sequeces with cmparatively lw cmplexity, it is quite fragile agaist bit errrs i isy cmmuicati chaels. Direct sequece sigal acquisiti i W-CDMA evirmet is estimated. A digital matched filter is preseted ad ivestigated fr direct sequece spread-spectrum systems [1]. The cdig scheme presets fur levels f errr prtecti fr differet sets f bits i a trasmitted symbl usig W-CDMA system ver AWGN ad Rayleigh fadig chaels. The prpsed scheme accmplishes uequal errr prtecti by ecdig the data accrdig t the sigificace f the ifrmati ad switchig betwee fur cdes. The scheme uses the differet pseud-ise cdes f digital matched filter sychrizer t make up fur levels f uequal errr prtecti cdes. It was shw that fur levels f differet errr prtectis were easily accmplished with the digital matched filter pseud-ise cde sychrizer systems ver AWGN ad Rayleigh fadig chaels by prvidig the cded detecti at the receiver. The scheme prvides the capability f multi-level errr prtecti withut cmplexity as cmpared t regular digital matched filter pseud-ise cde schemes. Wavelet vide with UEP cdes i W-CDMA system btais smaller PSNR tha wavelet vide with UEP cdes fr widebad MC-CDMA ad Rake receiver. Hwever, it requires less cmplex desig ad less cst f acquisiti [].

2 Wavelet Vide Trasmissi with UEP Cdes i W-CDMA System ver AWGN ad Rayleigh Fadig Chaels The fur levels f uequal errr prtecti cdes with wavelet vide trasmissi i W-CDMA system ver AWGN ad Rayleigh fadig chaels are aalyzed. Figure 1 illustrates the blck diagram f wavelet vide trasmissi with UEP cdes i W-CDMA system ver AWGN ad Rayleigh fadig chaels Ecder. Figure shws the blck diagram f wavelet vide trasmissi with UEP cdes i W- CDMA system ver AWGN ad Rayleigh fadig chaels Decder. Fig. Blck Diagram f Wavelet Vide Trasmissi with UEP Cdes i W-CDMA system ver AWGN ad Rayleigh fadig chaels Decder Fig. 1 Blck Diagram f Wavelet Vide Trasmissi with UEP Cdes i W-CDMA system ver AWGN ad Rayleigh fadig chaels Ecder The discrete wavelet trasfrm is described with the geeric sigal g(t) that ca be represeted i terms f traslates ad dilates typically badpass f a sigle prttype wavelet t). + g(t) = α (i, (1) i, = r similarly fr sme W>0 where g(t) + α (i, = W i= η ( α(i, -W i θ( i + i = g ( t ) dt () are detail cefficiets f wavelet. + = g ( t) ( dt η ( θ are apprximati cefficiets r scalig cefficiets, ad θ(t) is a lw-pass scalig fucti. The sigificace is the iterpretati f equati () as a multiresluti aalysis f g(t): i idexes the scale r resluti, the smaller i the higher the resluti, while idexes the spatial lcati f aalysis. If the mther wavelet is cetred at time 0 ad frequecy f c, α(i, measures the ctet f arud time i ad frequecy -i f c, while η( represets the lcal mea arud time W. I this framewrk, we ca thik f g(t) as the fiest scale (W=0) represetati f g(t) itself. The fucti t) has t satisfy sme critical cditis t esure that equati () hlds fr ay square itegrable fucti g(t). I particular, t) has t satisfy the tw scale equatis: θ ( t) = c ( ) θ (t ) (3) β ( t ) = c1( ) θ (t ) (4) where the cefficiets c i () ca be zer ly ver a fiite umber f csecutive values f. Hece, β i, ( t) = β ( ; θ i, ( t) = θ ( The three rthgalities cstraits require * θ i, ( t) θ ( t) dt = δ ( ) i, * β ( t) β ( t) dt = δ ( ) = δ ( i i ) i, i,

3 β * ( t ) θ ( t ) dt = δ ( ) = 0 i, i, The three rthgalities are satisfied by cefficiets c i () thse have the fllwig prperties: c ( ) c ( + k) = δ ( k) c1 ( ) = ( 1) c ( ) where c i () are the cefficiets f a perfect recstructi tw-bad r dyadic filter bak with the quadrature mirrr recstructi prperty. Therefre, the desig f wavelets is equivalet t the desig f filter baks. Observe that the cditis impsed up util w are t sufficiet t cstruct i practice useful wavelets. Certaily, they ca lead t decmpsitis with t eugh regularity. Regularity is impsed requirig a large umber f vaishig mmets. I practice, η( ad α(i, ca be cmputed recursively frm α(i+1, usig the efficiet pyramid algrithm prpsed by Mallat [3]. It is t ecessary t explicitly cmpute the shape f θ(t) ad t). The basic applicatis f wavelets i this paper stems frm a multiresluti decmpsiti f a time-varyig multipath respse ~ ( f the frm h t, τ) at ay τ with respect t t are: ~ h (t, τ ) = + W i= η (, τ ) α(i,, τ ) θ( (5) where α(i,,τ) are wavelet cefficiets ad η(,τ) are scalig cefficiets. If the chael is mdelled as determiistic, wavelet ad scalig cefficiets are csidered determiistic, ad if the chael is mdelled as radm, wavelet ad scalig cefficiets are csidered radm parameters. The waveletbased represetati will exhibit glbal characteristics f the chael dyamics i the lwresluti cefficiets, while retaiig lcal rapid trasitis i ust a few cefficiets at higher reslutis. A practical advatage is that the decmpsiti decuples the variatis i time ad relegates them i t) ad θ(t), s that the wavelets cefficiets are ideed time ivariat fr ay τ. Subsequetly, we will assume discretized respses with reslvable multipath cmpets f the frm ~ Q i 1 i t h( t, τ ) = = g ( ) δ ( τ τ ) [3]..1 Embedded Zer-Tree Wavelet Cdig Embedded zer-tree wavelet algrithm explits the imprtat hypthesis. After the embedded zer-tree wavelet trasfrm f a vide sequece, the imprtat data is ccetrated i the upper left crer that crrespds t the lw frequecy rage f the wavelet cefficiets. The remaiig data i the high frequecy dmai is t as sigificat. A wavelet i cefficiet tree is defied as the set f cefficiets frm differet bads that represet the same spatial regi i the vide sequece. A wavelet vide sequece represetati ca be thught as a tree structured spatial set f cefficiets [1]. Figure 3 illustrates three levels wavelet decmpsiti f the vide sequece. The lwest frequecy bad f the decmpsiti is represeted by the rt des (tp left) f the tree (LL 3 ), the highest frequecy bads by the leaf des (bttm right) f the tree, ad each paret de represets a lwer frequecy cmpet tha its childre. Except fr a rt de, which has ly three childre des, each paret de has fur childre des, the x regi f the same spatial lcati i the immediately higher frequecy bad [4]. Fig. 3 Three Levels Wavelet Decmpsiti. Tw-Dimesial Wavelet Packet Trasfrm Tw-dimesial wavelet packet trasfrm f vide sequece is cmpsed f lw frequecy cmpets ad high frequecy cmpets. Lw frequecy cmpets give a vide sequece its fudati, r character, while high frequecy cmpets give a vide sequece it is fie details r uaces. Figure 4 illustrates the wavelet decmpsiti f the twdimesial wavelet packet trasfrm fr the vide sequece. The utput frm the lw pass filter prduces ad apprximati f the sigal based the lw frequecy detail cefficiets. The utput frm the high pass filter prduces the fie details f the vide sequece, that whe put tgether will frm the rigial vide sequece. Hwever, these values are dw-sampled. This meas that the utput f either filter has every secd cefficiet drpped. This effectively halves the umber f cefficiets frm each filter. Nevertheless, at the recstructi side, this ca prduce sme distrti, but if the filters are chse carefully the perfect recstructi ca ccur. Oe f the aspects that make wavelets s suited t vide cdig is that the filterig prcess ca be iterated repeatedly, allwig us t break up a

4 vide sequece it varius lwer resluti versis r multilevel decmpsiti. Typically, the way i which this is cducted is by filterig the utput f the Lw Frequecy Decmpsig Filter with the same wavelet fucti. The lw frequecy cefficiets f this utput may agai be filtered, extractig mre ifrmati ad s. Nw, because there is a dw samplig rutie de after each filterig prcess, the theretical limit that stps us frm iteratig is util we reach e discrete wavelet trasfrm cefficiet. I geeral, the mre levels f decmpsiti we have, the better the cmpressi, althugh lss f quality []. Fig. 4 Wavelet Decmpsiti f the -D Wavelet Packet Trasfrm fr the Vide Sequece 3 Experimetal Results The QCIF vide sequeces with cmpressi rate f 0.31 bits/pixel are examied. The W-CDMA system btais a badwidth f 5MHz ad will als be i may idr achievemets. The varius sectis f a cmpressed vide sequece btai differet imprtace ad errr sesitivity. The W-CDMA system ver AWGN ad Rayleigh fadig chaels with uequal errr prtecti cdes are csidered with fur levels f sigificace fr peratig with data stream f ifrmati. The prpsed scheme accmplishes uequal errr prtecti by ecdig the data accrdig t the sigificace f the ifrmati ad dividig it fur cdes. The cdig scheme itrduces fur levels f errr prtecti fr differet sets f bits i a trasmitted symbl fuctiig W-CDMA system ver AWGN ad Rayleigh fadig chaels. The prpsed scheme applies the differet pseud-ise cdes f digital matched filter sychrizer t cstruct fur levels f uequal errr prtecti cdes. The fuctiig estimati f fur uequal errr prtecti cdes with W-CDMA system ver AWGN ad Rayleigh fadig chaels are evaluated. Fr the Embedded Zer-Tree Wavelet Cdig, the fur levels f uequal errr prtecti cdes with fur sigificat levels f uequal errr prtecti cdes are prpsed fr this digital matched filter pseud-ise cde sychrizer scheme. Frm figure 3, the first level r the LL 3 is the lwest errr prtecti level with ecdig. The secd level r the HL 3, LH 3, HH 3 is the lwer errr prtecti level with easiest level f digital matched filter pseud-ise cde sychrizer. The third level r the HL, LH, HH is the higher errr prtecti level with easier level f digital matched filter pseudise cde sychrizer. The furth level r the HL 1, LH 1, HH 1 is the highest errr prtecti level with harder level f digital matched filter pseud-ise cde sychrizer. Fr the -D Wavelet Packet Trasfrm, the fur levels f uequal errr prtecti cdes with fur differet levels f uequal errr prtecti cdes are desiged fr this digital matched filter pseud-ise cde sychrizer scheme. Figure 4 illustrates the Wavelet Decmpsiti f the -D Wavelet Packet Trasfrm fr the vide sequece. The first level r the average sigal is the lwest errr prtecti level with easiest level f digital matched filter pseudise cde sychrizer. The secd level r the hriztal vide sequece features is the lwer errr prtecti level with easier level f digital matched filter pseud-ise cde sychrizer. The third level r the vertical vide sequece features is the higher errr prtecti level with harder level f digital matched filter pseud-ise cde sychrizer. The furth level r the diagal vide sequece features is the highest errr prtecti level with hardest level f digital matched filter pseud-ise cde sychrizer. Matlab prgrams are writte t simulate the utcmes f the fur levels f UEP cdes with wavelet vide cmpressi i W-CDMA system ver AWGN ad Rayleigh fadig chaels. The peak sigal t ise rati is calculated. The bective vide sequece quality has bee evaluated usig peak sigal t ise rati, which is defied as fllws: ( PeakSigal Value ) PSNR = 10 lg 10 (6) MeaSquare Errr where, Peak Sigal Value=55 fr a 8 bits/pixel vide sequece. MeaSquare Errr = 1 ( x ) i y i (7) N N ( ) x i -y i =value f pixel (i, i the rigial ad recstructed vide sequeces respectively. NxN=umber f pixels i the vide sequece. i

5 The table f utcmes f tested Miss America sequeces is tabulated i the table 1. Miss America Sequeces i QCIF with Cmpressi rate f 0.31 (bits/pixel) W-CDMA System ver AWGN chaels W-CDMA System ver Rayleigh fadig chaels PSNR (db) f Fur levels UEP fr EZWT PSNR (db) f Fur levels UEP fr -D WPT Fig. 6 (a) Fig. 6 (b) Table 1: Outcmes f tested Miss America sequeces The rigial tested vide sequeces f Miss America i QCIF (176x144) are illustrated i figure 5. Fig. 6 (c) Fig. 6 (d) Fig. 6 The recstructed Miss America sequece with Fur levels f Embedded Zertree Wavelet trasfrm i W-CDMA system ver AWGN chaels; PSNR=11 db (a) Frame umber 0 (b) Frame umber 0 (c) Frame umber 45 (d) Frame umber 80 Fig. 5 (a) Fig. 5 (b) Fig. 7 (a) Fig. 7 (b) Fig. 5 (c) Fig. 5 (d) Fig. 5 The rigial Miss America sequece i QCIF (a) Frame umber 0 (b) Frame umber 0 (c) Frame umber 45 (d) Frame umber 80 Fig. 7 (c) Fig. 7 (d) The results f Miss America sequeces i QCIF (176x144) are illustrated i figure 6, figure 7, figure 8 ad figure 9. Fig. 7 The recstructed Miss America sequece with Fur levels f Embedded Zertree Wavelet trasfrm i W-CDMA system ver Rayleigh fadig chaels; PSNR=3 db (a) Frame umber 0 (b) Frame umber 0 (c) Frame umber 45 (d) Frame umber 80

6 Fig. 8 (a) Fig. 8 (c) Fig. 8 (b) Fig. 8 (d) Fig. 8 The recstructed Miss America sequece with Fur levels f -D Wavelet Packet Trasfrm i W-CDMA system ver AWGN chaels; PSNR=10 db (a) Frame umber 0 (b) Frame umber 0 (c) Frame umber 45 (d) Frame umber 80 4 Cclusi Wavelet vide cmpressi with fur levels f UEP cdes i W-CDMA system ver AWGN ad Rayleigh fadig chaels are perfrmed ad evaluated. The prpsed scheme achieves uequal errr prtecti by ecdig the data accrdig t the imprtace f the ifrmati ad dividig it fur cdes. The cdig scheme establishes fur levels f errr prtecti fr varius sets f bits i a trasmitted symbl with W-CDMA system ver AWGN ad Rayleigh fadig chaels. The scheme perates the differet pseud-ise cdes f digital matched filter sychrizer t create fur levels f uequal errr prtecti cdes. Wavelet vide cmpressi with fur levels f UEP cdes i W- CDMA system ver AWGN ad Rayleigh fadig chaels are fuctied t icrease the vide sequeces pre-emiece. EZW trasfrm cdig i fur levels f UEP cdes with W-CDMA system ver AWGN ad Rayleigh fadig chaels has advatages cmpared t -D WPT cdig i fur levels f UEP cdes with W-CDMA system ver AWGN ad Rayleigh fadig chaels. The Rayleigh fadig chaels achieve higher PSNR tha the AWGN chaels. The qualities f QCIF vide sequeces imprve with the prgressive icrease f the PSNR. The scheme demstrates desig flexibility s that it is easily mdified t accmmdate differet eeds fr errr prtecti i varius data trasmissi systems. Fig. 9 (a) Fig. 9 (c) Fig. 9 (b) Fig. 9 (d) Fig. 9 The recstructed Miss America sequece with Fur levels f -D Wavelet Packet Trasfrm i W-CDMA system ver Rayleigh fadig chaels; PSNR=31 db (a) Frame umber 0 (b) Frame umber 0 (c) Frame umber 45 (d) Frame umber 80 Refereces: [1] Mih Hug Le ad Raith Liyaa-Pathiraa, Perfrmace Evaluati f Rake Receiver fr Wavelet Vide with UEP Cdes i W-CDMA System ad Fadig Chaels, The 3 rd WSEAS Iteratial Cferece Sigal, Speech ad Image Prcessig, Octber 003. [] Mih Hug Le ad Raith Liyaa-Pathiraa, Wavelet Vide with Uequal Errr Prtecti Cdes fr Widebad Multicarrier CDMA ver Fadig Chaels, The 3 rd WSEAS Iteratial Cferece Sigal, Speech ad Image Prcessig, Octber 003. [3] S. Mallat, A Thery f Multiresluti Sigal Decmpsiti: The Wavelet Represetati, IEEE Tras., PAMI-11: , [4] J. Shapir, Embedded Image Cdig Usig Zer Trees f Wavelet Cefficiets, IEEE Tras. Sigal Prcess. 41, , 1993.