Estimation of Critical Performance and Optimization of Scalable Joint Source/Channel Coder (SJSCC) For Time Varying Channels

Transcription

1 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 8 Vol II IMECS 8, 9- March, 8, Hong ong Estmaton of Crtcal Performance and Optmzaton of Scalable Jont Source/ Coder (SJSCC) For Tme Varyng s Prof. A. C. Bhagal, Dr. D. D. Shah, Mr. A. L. Wanare Abstract In ths paper, we propose the model of Scalable Jont Source/ Codng for wreless data transmsson where channel s nherently tme varyng and subject to aylegh fadng nature. We consder the problem of stll mage data transmsson over tme varyng channels wth two State Informaton s (CSI) and three bt rates (, ½ and ¼) for effcent transmsson of data. Here, we analyze the effect of CSI avalablty on the optmal performance analyss of proposed scheme. Our source model s based on two level wavelet mage decomposton usng Haar mother wavelet wth Set Partton In Herarchcal Tree (SPIHT) for sgnfcant coeffcents for dynamc thresholdng and channel codng wll be ate-compatble Punctured Convolutonal (CPC) Codes. We smulated the new scheme of SJSCC and tred for optmal performance for wreless channels. Further, we show how our optmzed SJSCC scheme out performs over Optmzed Jont Source/ Coder (OJSCC) for channel states as well for varous bt rates [] [3]. In our optmzaton of SJSCC Scheme, margnal mprovement n PSN of.4db s obtaned for both average and worst channels and sgnfcant mprovements of PSN values n the order of db s also obtaned for all three bt rates over exstng OJSCC system. Fnally, our proposed SJSCC system performance s compared wth CPC and CPT for wde range of SNs and notced margnal s notced wth CPC channel coder or CPT. Index Terms Wavelet, SPIHT, CPC, CPT, OJSCC and SJSCC. I. INTODUCTION The feld of communcatons has developed snce past 6 years based on the separaton prncple. Separaton prncple states that the source codng and channel codng performed ndependently. The block dagram of separaton prncple s shown n Fg.. the separaton approach s to dvde a sngle complex problem n to two smpler problems of desgnng source codng and channel codng ndependently. Ths approach of dvde and conquer prncple has led many advancements n the desgn of source codng and channel codng separately and was popular for tme-nherent channels. In 948, Shannon desgned and developed only source codng concepts for tme-nvarant channels wthout consderng channel codng constrants Modern communcaton. Systems need heterogeneous desgn and development of Jont/Source channel codng for tme-varyng channels Vz. wreless moble communcaton and nternet access. The performance mprovement for moble and nternet access s acheved through jont source/channel codng over conventonal Separaton prncple desgn. Thus, the advance theory s essental for characterzng the Jont Source/ codng and performance analyss through optmzaton of communcaton systems [5] [6] [7] [8]. Prof.A.C.Bhagal Asstt.Prof. & Head, Pryadarshn Insttute of Engneerng and Technology, Nagpur, M.S., Inda (phone no , e-mal-acbhagal@redffmal.com), Dr.D.D.Shah, Prncpal, GH ason College of Engneerng and Management Pune, M.S. Inda (phone no , e-mal.- dlp.d.shah@gmal.com ), Mr.A.L.Wanare, faculty, Pryadarshn Insttute of Engneerng and Technology, Nagpur, (phone no , e-mala.wanare@redffmal.com) Fg..: Separaton Prncple The communcaton systems bult from ndependently desgned source codes and channel codes may requre greater computatonal resources and cause hgher delay of latency than Jont source/channel codng systems. The separaton theorem fals n wde array of practcal applcatons and also gnores the mperfectons n real tme communcatons systems vz. source coder s desgned assumng channel coder corrects all error ntroduced by ISBN: IMECS 8

2 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 8 Vol II IMECS 8, 9- March, 8, Hong ong the channel and channel coder s desgned assumng that all bts generated by the source coder are equally mportant. Unfortunately, these assumptons may not true n modern communcaton systems. II. APPLICATION AEAS. A modern communcaton systems n whch source coder and channel coders are desgned n a dependent fashon and operatng n cooperatve optmzaton of communcaton system components s referred as Jont Source/ Coder (JSCC) [3][4][5]. Advantages of JSCC are as follows Better performance s acheved for the systems wth crtcal resource constrants vz. rate of data transmsson, complexty, power and delay. Potental performance s acheved for hgh mult-user systems And shared channels vz. wreless systems and nternet data. Sgnfcant performance s acheved for mult-user systems wth heterogeneous source, channel and topologes. Source heterogenety: Dfferent data types travelng a sngle communcaton system have dfferent senstvtes to loss, corrupton of data and delay. heterogenety: Dfferent channels wthn sngle network may have dfferent nose characterstcs, rates, packet sze, delay etc. Topology heterogenety: Some networks can be used smultaneously for pont-to-pont, broadcast and multple access communcaton systems. Sgnfcant gans are obtaned for the applcatons characterzed by unknown or tme-varyng sources, channels or networks. III.SPIHT It has been explaned that an alternatve prncple of operaton of the prevous EZW algorthm to better understand the conceptual reasons of ts excellent performance. Accordng to SPIHT, partal orderng by magntude of the transformed coeffcent wth a set parttonng sortng algorthm, ordered bt plane transmsson of refnement bts, and explanaton of self smlarty of the mage wavelet transform across dfferent scales of and mage are the three concepts. In addton, a new and more effectve mplementatons of the modfed algorthm based on SPIHT [] t s explaned that scheme for progressve transmsson of the coeffcent values that ncorporates the concepts of orderng the coeffcents by magntude and transmttng the most sgnfcant bts frst. There s used unform scalar quantzer and clam orderng nformaton made ths smple quantzaton method more effcent than expected. An effcent way to code the orderng nformaton s also proposed accordng to above, result from the SPIHT codng algorthm n most uses surpass those obtaned from prevous algorthm. One mportant fact used n the desgn of the sortng algorthm s that we do not need to sort all coeffcents actually, we need an algorthm that smply select the coeffcents such than n C,j < n+ wth n decremented n each pass. Gven n, f C,j n then we say that a coeffcent s sgnfcant; otherwse s called n sgnfcant To make clear relatonshp between magntude comparsons and message bts, we can be use the functon Max (C,j) n S n (p) Otherwse To ndcate the sgnfcance of a set of coordnates P. smply the notaton of sngle coeffcent sets Sn(,j). Step : calculate the n to select the threshold level :n log (max(,j) (C,j) ) Step : for sortng purpose; followed by the pxel coordnates m(k) and sgn each of the coeffcents such that n Cm (k) < n+ (Sortng Pass) Step 3: output the n th most sgnfcant bt of all the coeffcents wth C,j n+ f requred, those that had ther coordnate transmtted n prevous sortng passes Step 4 : Decrement n by one and to go to step. The above steps that can be mplemented and stop at the desred the rate or dstorton normally, good qualty mages can be recovered after a relatvely small amount of the coeffcents are transmtted. In a practcal mplementaton purpose the sgnfcance nformaton s stored n three-ordered lst as. ) LIS: Lst of nsgnfcant set contans sets of dscrete cosne transform coeffcents whch are defned by tree structures [6][8] and whch had been found have magntude smaller than the threshold (nsgnfcant) ) LIP: Lst of nsgnfcant pxels contans ndvdual coeffcents that have magntude smaller than the threshold. ) LSP: Lst of sgnfcant pxels found to have magntude larger that the threshold (sgnfcant accordng to above tree ordered we can be performed for codng purpose for 8х8 block of mage whch s transformed by DCT [7] (Dscrete cosne transform). Accordng to SPIHT, the compresson takes place manly because after the transformaton most of the energy of the mage s concentrated n low frequency coeffcents that s DC coeffcents and rest of the coeffcents have very low values [3]. Ths means that there are many zeros n the most sgnfcant bt planes of the coeffcents, untl the frst sgnfcant bt of a certan coeffcent s found, t contans more nformaton. If largest magntude coeffcent s there, then we get frst non-zero bt. For each coeffcent we call ts frst one bt (non-zero bt) startng from most sgnfcant to less sgnfcant bts (MSB to LSB) as the frst sgnfcant bt (FSB). And the bts of coeffcents pror to the frst sgnfcant bt wll be referred to as the zero bt (ZBS). The sgn nformaton s represented by the sgn bt (SB), whle the rest of the bts after the frst sgnfcant bts are called row bts (BS). Accordng to above defntons, codng startng wth bt plane. In each bt plane the codng wll be form the lowest frequency coeffcent (DC coeffcents) to hghest frequency coeffcents (AC coeffcents).spiht encoder uses these prncples to progressvely transmt DCT (Dscrete cosne transform) coeffcents startng wth the most mportant nformaton. The coeffcents are sorted and the sortng nformaton s contaned n set of elements m (k) contans the (,j) coordnates of a coeffcent (C,j) ISBN: IMECS 8

3 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 8 Vol II IMECS 8, 9- March, 8, Hong ong and such that Cm(k) Cm(k+) for all values of k.[6] The frst coeffcent Cm () C(,3) s s. The second coeffcent Cm () C (3,4) s s.and so on. The sortng nformaton that the encoder has to transmt s the sequence m (k) or (, 3) (3, 4).. In addton. It has to transmt the 8 sgns and 6 coeffcents n order of sgnfcant bts. A drect transmsson would send the 6 numbers. SSSSSS..SS,...; but ths clearly wasteful. Instead of that, t can be performed by technque for teraton a sortng purpose. In the frst teraton t transmts the two coeffcents (whose MSB s one) as shown n fgure, number of coeffcents C,j n fgure that satsfy 7 C,j 8 followed by two pars of coordnates (,3) and (3,4) accordng to our fgure. And by the sgns of the frst two coeffcents. Coeffcents C3 and C3,4 are constructed as 8 bt numbers s.. But t can be recover by transmttng MSB and remanng 4 coeffcents are constructed as all zero. The most sgnfcant bts of the largest coeffcents are transmtted frst accordng to dynamc thresholdng [6]. IV. WOING OF THE SYSTEM. The block dagram of Jont Source/ Coder s shown n Fg. 3.. The proposed scheme of Jont Source/ Codng s developed for transmttng data and mage streams over wreless aylegh channel. The channel state s estmated and optmum bts are allocated to quantzer and channel coder jontly for mprovement n PSN and better vsual qualty of reconstructon of mages. The trade-off between source codng rate and channel codng s acheved through Jont Source/ ate-dstorton functon. The data stream s decorrelated through multlevel and multresoluton dscrete wavelet transform (DWT) usng Haar and Daubeches mother wavelets. Each subband s reshaped to Gaussan dstrbuton by sutable flter. Each sample of subband s then quantzed wth Lloyd max non-lnear quantzer. The output of quantzer s then protected through unequal protecton by channel coder. The recever performs exactly nverse process as per the channel states used for transmsson [4][5][9]. The graphcal representaton of general rate dstorton (-D) functon of Jont Source/ Coder s as shown n Fg.3.. D Jont characterstcs Convex Hull Fg. 3.: Graphcal representaton of Jont Source/ Coder The rate dstorton (-D) functon for memoryless channel s expressed n equaton no-. D S N m E, m + S j A P...() Where, N s the number of sub bands, S s the total number of pxels n the orgnal mage, S s the number of pxels n the th subband, E,m, s the dstorton caused by m bt quantzaton for the th subband and A, P are bt error senstvty and channel bt error rate after channel codng for the jth bt of the th subband. V. ATE COMPATIBLE PUNCTUED CONVOLUTIONAL CODES (CPC) For wreless communcaton n real world dfferent channel code rates are essental for provdng dfferent channel error protecton. Hence dfferent code wll certanly allow dfferent channel rates. We selected dfferent channel rates smply by selectng dfferent punctured bts to facltate varous rates e. CPC. The channel code CPC wll allow very precse and accurate predcton of the expected s for specfed channel condtons and gven channel code rates [] [] [5] [6]. CPC codes wll provde reasonably accurate Vs PSN values whch wll certanly provde the overall analyss of Scalable Source/ coder performance. The channel coder rate s expressed for j th poston and selected th Subband of the mage decomposton wll be expressed as; c, n j n /. j Where j s bt poston of th subband of decomposton. The overall channel rate can be expressed as: c [( n. s ) / n. s c, n s. j n. s (/, j. ) r Where s S /, S s total number of pxels n the orgnal mage, s s the number of samples per subband, r representng the resoluton of th subband and s number of dfferent sub bands and n s the codeword of th subband. Jont Source/ rate: The combned rate of source/channel s denoted as and expressed by ( / ).(/ log M s c )...3 Where M s modulaton order as, 4,8,6. n s+ c. log M s. (/, j ) S j n. s s+ c.log M s. s+ c,... S c, S we are concerned to allocate the bts for overall rate of jont source/channel coder for mnmum dstorton and hence the MSE ISBN: IMECS 8

4 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 8 Vol II IMECS 8, 9- March, 8, Hong ong VI. ESULTS. esults obtaned by our Scalable Jont Source/ Coder are shown n Table- for two channel states and three s. JSCC 3 5 x - scheme AVG worst avg worst avg worst (PSN) OJSCC SJSCC Table-:PSN esult of SJSCC Graphcal representaton as shown n fg 6. are results of SJSCC and wll be clearly ndcatng margnal mprovement by SJSCC over other optmzed JSCC schemes for wreless channels esults of SJSCC for three channel SNs s ndcated n Table-3. The optmal source and channel rates notced for four bands. Optmal varatons of source and channel rates as shown n fgure 6.3. Sub bands SN db SN 4dB SN 8 db S c S c S c Band Band Band Band Table-3: Sub bands wth varous source channel ates PSN Vs PSN AVG WOST AVG WOST AVG WOST X Fg 6.: esult of SJSCC vs PSN over OJSCC. OJSCC SJSCC Bt ates wth Varous condtons S c S c S c Band Band Band Band 3 SN db SN 4dB SN 8 db ates and s Fg 6.3: Sub bands wth varous source channel ates ate.5.5 Schemes 3-5 X - SJSCC OJSCC SJSCC OJSCC SJSCC OJSCC Table- : esult of SJSCC Over OJSCC for varous Bt ates esults obtaned for three bt rates,.5 and.5 by the proposed Scalable Jont Source/ Coder s shown n Table- for varous values. Graphcal representaton of results n table s as shown n fg 6.. esults of SJSCC for three bt rates are clearly ndcatng margnal mprovement by SJSCC over other optmzed JSCC Schemes for wreless channels. PSN PSN Vs SJSCC OJSCC SJSCC OJSCC SJSCC OJSCC.5.5 Bt rate Bt rate.5 Bt rate.5 aylegh AWGN SN n db CPC CPT CPC CPT (D) (D) (D) (D) Table-4: Comparson of SJSCC esults of SJSCC for wde range of SNs are obtaned for both alegh & AWGN channels. The dstrbutons for both CPC & CPT are plotted n fg 6.4 for all SNs. The results of CPC s proved to be better than CPT results. Dstrubuton Comparson of SJSCC wth CPC and CPT over AWGN and aylegh s ISBN: IMECS SN n db CPC (D) CPT(D) CPC(D) CPT(D)

5 Proceedngs of the Internatonal MultConference of Engneers and Computer Scentsts 8 Vol II IMECS 8, 9- March, 8, Hong ong VI. CONCLUSIONS. We have modeled the Scalable Jont Source/ Coder (SJSCC) for wreless channels and extensve smulatons are carred out for varous channel states and bt rate. The results obtaned are margnally mproved wth CPC Coder over exstng Optmzed Jont Source/ Coder (OJSCC). Overall mprovement of PSN n the order of.4db s notced n our developed model of SJSCC for two channel states and three values. esults of SJSCC for three channel SNs obtaned for source and channel rates are seems to be optmal and analyzed for four subbands. esults are obtaned for dstrbutons of CPC and CPT for channel SNs rangng from 5dB to 45dB and are margnally mproved over CPT for low bt rates and for both aylegh and AWGN channels. Fnally, we clam the mprovement n PSN and SN values rangng from.4db to db for varous combnatons of source and channel coder and also for varous bt rates. Codng of Images. IEEE Transactons on Image Processng. Vol. 8, No-3, pp 35-3, March [5] J.ogers and P. Cosman, Wavelet Zerotree mage compresson wth packetzaton. IEEE Sgnal Processng Lett. Vol. 5, pp 5-7, May [6] S.G. Mallat, A theory for multresoluton sgnal decomposton : The wavelet epresentaton. IEEE Trans. Pattern Analyss and Machne Intellgence. Vol., pp , July [7] A. Sad and W. Pearlman, A new, fast and effcent mage codec based on set parttonng n herarchcal trees," IEEE Trans. Crcuts Syst. Vdeo Technol., vol. 6, no. 3, pp , 996. [8] J. Burg and Y. L. Wong JPEG Compresson Sprng 3 Avalable: 4/CSC36-66/course-materals/JPEGCompresson.ppt [9] A. Sad and W. A. Pearlman, "Image compresson usng the spatal orentaton tree", IEEE Internatonal Symposum on Crcuts and Systems 993, No., pp [] Dr. D.D.Shah, A.C.Bhagal, Sgnals and Systems 3Ed.- chapte-9, pp EFEENCES [] J. Hugenauer, Source-Controlled Decodng. IEEE Transacton Communcaton. Vol. 43, pp , Sept [] J. W. Modestno and D.G.Daut, Combned Source/ Codng of Images. IEEE Transacton Communcaton. Vol. COMM-7, pp , Nov [3] M. J. uf., Combned Source/ Codng for Image Transmsson. In Proc. 6 th Jont Conference Communcaton and Codng, Selva, Italy, March 994. [4] G. Cheung and A. Zakhor, Jont Source/ Codng of Scalable Vdeo Over Nosy s. In Proc. Int. Conf. Image Processng, Lausanne, Swtzerland, Vol.3, pp , Sept [5] M. Srnvasan and. Chellappa, Jont Source/ Codng of Images. In Proc. IEEE Conf. On Acc. & Speech Sgnal Processng, Munch, ermony, 997. [6] Jll. Boldschneder and Eve A. skn, Jont Optmal Bt Allocaton and Best Bass Selecton for Wavelet Packet Trees. Proc. Of IEEE Int. Conf., pp , June [7] Srnvasan, Chellappa and Vurlna, Adaptve Source/ Subband Vdeo Codng for Wreless s. IEEE Sgnal Processng Socety Workshop on Multmeda Sgnal Processng, pp -4, June. 3-5, 997. [8] A. C. Bhagal Dgtal Sgnal Processng wth MATLAB Programs 3Ed. Chapter-3. [9] H. Jafarkhan, P. Lgdas, and N. arvardn, Adaptver rate allocaton n a Jont Source/ Codng framework for wreless channel. In IEEE Trans. On Vehcular Technology, Sept [] G. Sherwood and. Zeger, Progressve mage codng for nosy channels. IEEE Sgnal Processng Lett. Vol. 4, pp 89-9, July [] A. C. Bhagal Dgtal Communcaton chapte-6, pp [] G. Sherwood and. Zeger, Progressve mage codng for nosy channels. IEEE Sgnal Processng Lett. Vol. 4, pp 89-9, July [3] Gene Ceung, and Avdeh Zakhor, Bt allocaton for Jont Source/ Codng of Scalable Vdeo IEEE Transactons on Image Processng. Vol.9, No-3, pp , March.. [4] Mchael J. uf. And James W. Modestno, Operatonal ate-dstorton Performance for Jont Source/ ISBN: IMECS 8