POWER-DISTORTION OPTIMIZATION FOR WIRELESS IMAGE/VIDEO SOFTCAST BY TRANSFORM COEFFICIENTS ENERGY MODELING WITH ADAPTIVE CHUNK DIVISION

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1 POWER-DISTORTION OPTIMIZATION FOR WIRELESS IMAGE/VIDEO SOFTCAST BY TRANSFORM COEFFICIENTS ENERGY MODELING WITH ADAPTIVE CHUNK DIVISION Ruqn Xong 1, Feng Wu, Xaopeng Fan 3, Chong Luo, Swe Ma 1, Wen Gao 1 1 Insttute of Dgtal Meda, Pekng Unversty, Bejng 171, Chna Mcrosoft Research Asa, Bejng 1, Chna 3 Department of Computer Scence, Harbn Insttute of Technology, Harbn 1, Chna ABSTRACT Tradtonal communcaton systems usually suffer from the threshold effect when channel sgnal-to-nose rato (CSNR) fluctuates unpredctably n wreless and moble scenaros. The SoftCast scheme, however, provdes graceful qualty transton n wde CSNR range. In SoftCast, nput mage s decorrelated by a transform and modulated drectly to a dense constellaton for transmsson, leavng out the conventonal quantzaton, entropy codng and channel codng. A key pont of SoftCast s that the transmsson power needs to be allocated among the transform coeffcents unequally, accordng to the energy of coeffcents. Importantly, the energy dversty used to gude power allocaton should be shared between the sender and the recever for correct decodng. Ths paper addresses the power dstorton optmzaton problem, ntroducng a new adaptve chunk dvson scheme to descrbe the energy dversty among coeffcents. A concrete algorthm s developed to determne the chunk boundares that acheve optmal transmsson power usage. Expermental results show that the proposed scheme can mprove the performance of the orgnal SoftCast by db usng a smaller number of chunks. Index Terms wreless vsual communcaton, SoftCast, power allocaton, transform coeffcents modelng, optmzaton 1. INTRODUCTION Communcaton system based on source and channel codng generally requres the channel statstcs to be known at the tme of encodng, n order to choose an approprate codng rate. If the actual channel qualty falls below a threshold, the decodng process tends to break down completely; f the channel qualty ncreases beyond that threshold, such system Correspondng author: R. Xong (rqxong@pku.edu.cn). Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna (1733, 13711, 111), Natonal Basc Research Program of Chna (973 Program, 9CB39), Bejng Natural Scence Foundaton (11, 1339) and Research Fund for the Doctoral Program of Hgher Educaton (1117, 11119). cannot provde further mprovement n the qualty of receved sgnal. Ths threshold effect brngs great challenges for the desgn of wreless and moble communcaton system. Recently, a scheme named SoftCast [1,, 3] was proposed for wreless vdeo. Unlke typcal mage or vdeo coders that compress nput sgnal nto a bnary stream, SoftCast transforms the mage sgnal nto a stream of real numbers from whch exact reconstructon s possble, leavng out the conventonal quantzaton and entropy codng. SoftCast also abandons the conventonal channel codng. Instead, t modulates the number stream drectly to a dense constellaton for transmsson. The transmsson n SoftCast s lossy n nature and the nose level n the receved numbers s commensurate wth the channel sgnal-to-nose rato (SNR). The most promnent advantage of SoftCast s that t provdes graceful qualty transton n very wde channel SNR range and can serve varous clents of dfferent channel condtons smultaneously, usng the same transmtted sgnal n the ar. For ths reason, SoftCast has attracted much research attenton n recent years [,,, 7,, 9]. To acheve the best performance, SoftCast allocates transmsson power among the transform coeffcents unequally, by scalng each coeffcent ndvdually accordng to ts energy. Importantly, the energy dversty used to gude power allocaton should be shared between the sender and the recever va meta data for correct decodng. To lmt the overhead, SoftCast dvdes the coeffcents nto a set of chunks of the same sze and perform scalng at chunk level. Ths turns out to be neffcent n terms of power usage. In ths paper, we address the problem by ntroducng an adaptve chunk dvson scheme, explotng the fact that the energy of transform coeffcents decay rapdly from low frequency to hgh frequency. A concrete algorthm s developed to optmze the chunk dvson boundares, based on a mathematcal formulaton of the overall performance of SoftCast. Expermental results ndcate that the proposed approach can mprove the performance of the orgnal SoftCast scheme sgnfcantly. The paper s organzed as follows. Secton revews the SoftCast scheme. Secton 3 and descrbe the proposed chunk dvson scheme and optmzaton algorthm. Secton

2 shows expermental results and Secton concludes the paper.. REVIEW OF SOFTCAST In a typcal conventonal vsual communcaton system, as shown n Fg. 1, nput mage s compressed nto a stream of bts, usng transform, quantzaton and entropy codng. The bt stream s protected by some channel code and mapped to a constellaton usng quadrature ampltude modulaton (QAM) (e.g. BPSK, -QAM, 1-QAM and -QAM) for OFDM transmsson. In the case of 1-QAM, for example, four bts are extracted from the stream each tme and mapped to one of the 1 canddate ponts n the constellaton. T Q VLC FEC QAM bt stream T -1 Q -1 VLC -1 FEC -1 QAM -1 OFDM Channel Fg. 1. Dagram of conventonal vsual communcaton. In SoftCast, as shown n Fg., the compresson stage s solely a transform to decorrelate the mage sgnal, producng a stream of transform coeffcent numbers. The transmsson stage scales each coeffcent ndvdually, apples a Walsh- Hardmard Transform (WHT) to whten the whole stream, and modulates the resulted numbers drectly to a dense constellaton (e.g. k-qam) for OFDM transmsson. A par of real numbers s extracted from the stream each tme and mapped to a pont n the dense QAM constellaton, usng the two numbers as the I- and the Q- components, respectvely. The scalng operaton serves the purposes of power allocaton and unequal protecton aganst channel noses. The scalng factors are determned by a power-dstorton optmzaton (PDO) procedure, and wll be shared by the SoftCast sender and recever va a lmted number of meta data. T Scale WHT k-qam PDO metadata real number stream T -1 LLSE WHT -1 k-qam -1 Fg.. Dagram of the SoftCast scheme [1,, 3]. OFDM Channel 3. POWER-DISTORTION OPTIMIZATION FOR SOFTCAST Suppose x = (x 1,x,...,x N ) R N are the coeffcents to transmt. To acheve effcent power usage, the encoder scales eachx by a factorg and sends outy = g x usng a dense constellaton and OFDM 1. After demodulaton, the recever 1 The Walsh-Hardmard transform can be gnored durng power-dstorton analyss, because the WHT transform of a whte nose s stll a whte nose. gets ŷ = y +n, where n s addtve whte Gaussan nose (AWGN) wth varance σn. The decoder gets an estmaton ofx by ˆx = ŷ /g = x +n /g. In ths process, the expected dstorton n ˆx s D = E[(ˆx x ) ] = σn/g. The expected transmsson power for sendng x s P = E[y ] = g E[x ]. Therefore, D P = σn E[x ]. To acheve optmal performance, the transmsson power s allocated among {x } by (P1): mnmze D s. t. P P total (1) The problem s easly solved by settng D / P to a constant. Ths eventually leads to P E[x ] and g (E[x ]) 1/. Usng the optmal power allocaton, the total dstorton n the reconstructed mage s D total = Equvalently, we have D = σ n P total ( PSNR db = c+csnr db 1log 1 ( E[x ] ) () E[x ] ) (3) wth c = 1log 1 ( N). For a general sgnal x, We defne the actvty of x by H(x) = E[x ].. ADAPTIVE CHUNK DIVISION.1. Why Chunk Dvson n SoftCast? Ideally, to acheve optmal power usage, the scalng factorsg should be selected ndvdually accordng toe[x ]. However, the recever needs to know the scalng factors employed by the sender, for the purpose of correct decodng. Of course, sendng one g for each coeffcent may ntroduce sgnfcant communcaton overhead. Therefore, SoftCast groups the coeffcents nto a set of chunks and perform scalng at chunk level. In other words, all the coeffcents n a chunk choose the same g value, based on the mean coeffcent energy (.e. E[x ]) of that chunk. Fg. 3(a) llustrates the equal-sze chunk dvson approach n the orgnal SoftCast scheme. Typcally, chunks are used so that a total of meta data s sent to the recever va a relable channel, to sgnal the value E[x ] of each chunk... The Proposed Chunk Dvson Scheme In ths secton, we consder the statstcal characterstcs of DCT coeffcents and propose a new chunk dvson approach, for mplementng effcent power allocaton usng a lmted number of metadata. Suppose F(u,v) s the DCT doman representaton of two-dmensonal mage f(, j). For most natural mages, we

3 v log F(u, v) 1 3 u 1 v log F(u, v) 1 3 (a) (b) Fg. 3. Chunk dvson for SoftCast power allocaton. (a) The scheme n orgnal SoftCast. (b) The proposed scheme. have the followng observatons (as shown n Fg. 3): (1) The ampltude of F(u,v) decays rapdly from low frequency regon to hgh frequency regon, as the value of (u,v) = u +v ncreases; () The ampltude off(u,v) vares wth the angle of frequency (.e. θ = arctan(u/v)) only slghtly. Based on these observatons, we propose a chunk dvson scheme as llustrated by Fg. 3(b). To be precse, for dentfyng the chunk boundares, we ntroduce a vector r = (r 1,r,...,r M ), satsfyng = r < r 1 < < r M 1 < r M = 1. For an H W mage, the vector r defnes a set of smlar rectangles R(r ) n the(u,v)-plane: R(r) = {(u,v) u r H, v r W} () Based on these rectangles, we construct a set of chunks C, lettng chunk C contan the coeffcents n R(r ) but not n R(r 1 ). The proposed strategy allows chunks wth nonequal szes. For typcal natural mages, we prefer dense dvson at the up-left corner and sparse dvson at the bottomrght corner of the transform coeffcent plane..3. Chunk Dvson Optmzaton Gven the total number (denoted by M) of chunks to use, the parametersr, = 1,,...,M 1 should be optmzed n order to acheve the best possble transmsson performance. In ths secton, we propose an optmzaton algorthm for solvng the parameters {r }. Accordng to Secton 3, the problem s equvalent to fndng the optmal values of {r } that mnmze the data actvty H(F) assocated wth the chunk dvson result constructed from {r }. To facltate the optmzaton, we defne T E (r) as the total energy of the coeffcents nr(r): T E (r) = (u,v) R(r) u F(u,v) () and T N (r) as the total number of the coeffcents nr(r): T N (r) = #{(u,v) (u,v) R(r)} () Wth the ad of T E (r) and T N (r), the mean energy of coeffcents n chunk C can be formulated by T E (r ) T E (r 1 ) E[F(u,v) (u,v) C ] = T N (r ) T N (r 1 ). (7) Therefore, the data actvty assocated wth the chunk dvson becomes: H(F,{r }) M = {T N (r ) T N (r 1 )} E[F(u,v) (u,v) C ] = =1 M (TN (r ) T N (r 1 ))(T E (r ) T E (r 1 )) =1 Here we explctly nclude {r } as arguments of H( ) n () to reveal ts dependence on the chunk dvson result. Note that T E (r) and T N (r) can be calculated beforehand. For the specal case r =, we have T E (r ) = and T N (r ) =. Before presentng our algorthm, we note that the coeffcents F(u,v) locate only at nteger postons n the (u,v)- plane. Therefore, we only need to consder a fnte set of values V for parameter r. Snce an exhaustve full search for jont optmzaton of all them 1 parameters can be computatonally prohbtve, we employ a more practcal teratve algorthm. In ths algorthm, each parameter s frstly ntalzed by r = /M (and rounded to the nearest value n V), whch corresponds to equal dvson n each drecton. Then, the algorthm teratvely updates the parameters r 1,r,...,r M 1 one by one, wth only one of them beng optmzed whle the others beng fxed each tme. Ths teraton process s termnated when a maxmum number of teratons s reached or when the changes nh(f,{r }) s small enough. Now we consder the sub-problem of choosng the optmalr k for a partculark, wth all the other parameters{r } k beng fxed. Ths s to select a rectangle boundary that dvdes the regon R(r k+1 ) \ R(r k 1 ) nto two chunks (.e. C k and C k+1 ) so that H(F,{r }) s mnmzed. Snce all the other chunks are unchanged, the optmzaton problem s reduced to choosng a value r V, subject to r k 1 < r < r k+1, that mnmzes H (k) sub (r) = (T N (r k+1 ) T N (r))(t E (r k+1 ) T E (r)) () + (T N (r) T N (r k 1 ))(T E (r) T E (r k 1 )). (9) Ths problem can be easly solved.. EXPERIMENTAL RESULTS In ths secton, we conduct some experments to evaluate the performance of the proposed chunk dvson scheme and compare t wth the equal-sze chunk dvson scheme n the orgnal SoftCast. Lena, Peppers, Elane, Barbara, Baboon and Fshngboat (1 1, gray) are used as test mages.

4 Lena (1 1, gray) Elane (1 1, gray) Barbara (1 1, gray) Peppers (1 1, gray) Baboon (1 1, gray) Fshngboat (1 1, gray) Fg.. Performance comparson between the proposed approach and the equal-chunk approach. We frst evaluate the beneft of employng chunk dvson schemes, based on the formulaton (3). The beneft s measured by the performance gan n the reconstructon qualty, compared wth the case that all coeffcents are transmtted wthout chunk dvson (.e. usng the same scalng factor), subject to the same channel SNR condton and the same channel usage. The results are shown n Fg.. We frst check the results of the equal-sze chunk dvson scheme n orgnal SoftCast. We can see that, as the number of chunks ncreases, a maxmum chunk dvson gan of db can be acheved. The actual number of maxmum chunk dvson gan s mage dependent and reflects the strength of correlaton n the mage sgnal. We also note that, wth equal-sze chunk dvson, only about % and 7% of the whole gan can be acheved by usng 1 and 1 chunks, respectvely. To realze 9% of the whole gan, t requres more than 1 equal chunks. Such huge number of chunks (and meta data) s of course undesred. Wth the proposed adaptve chunk dvson scheme, however, employng only, or 1 chunks can acheve a performance comparable to the orgnal SoftCast usng 1, 1 3 or 1 equal-sze chunks. Therefore, the proposed chunk dvson approach s very effcent n dfferentatng the transform coeffcents wth dfferent energes. Fg. 7 llustrates the chunk dvson results, produced by the proposed chunk dvson optmzaton algorthm. Fg. summarzes the smulated performance of SoftCast transmsson usng the proposed approach and the equal-sze chunk approach. These smulaton results confrm the results n Fg. obtaned from theoretcal analyss n (3). Usng as few as 1 chunks, the proposed strategy can acheve much better performance than the equal-sze chunk approach usng chunks. The reconstructed mages are shown n Fg. to provde a subjectve performance comparson between the proposed approach and the equal-sze chunk approach. Snce the pro-

5 Fg.. Reconstructed mages by the proposed chunk dvson and the equal-sze chunk dvson at CSNR= db. In ths experment, whole-frame DCT s used for decorrelaton. The columns from left to rght: equal-sze chunk dvson wth 1 chunks, equal-sze chunk dvson wth chunks, equal-sze chunk dvson wth chunks, and the proposed chunk dvson approach wth 1 chunks. posed approach works much better than the equal-sze chunk approach, we consder a relatvely low channel qualty,.e. CSNR= db. In such case, the reconstructon mages produced by the equal-sze chunk approach are far from satsfactory. They contans very annoyng artfacts and noses, especally for the case of usng chunks or less. The reconstructon mages by the proposed approach usng 1 chunks only, on the other hand, are much better. The noses remaned n the decoded mages are almost nvsble.. CONCLUSIONS AND DISCUSSIONS SoftCast s a flexble scheme for vsual communcaton n wreless and moble envronment. It provdes graceful qualty degradaton for very wde channel SNR range. A key ssue n SoftCast s that the transmsson power should be allocated among the coeffcents unequally, accordng to the dversty n the energy of coeffcents. Ths paper proposed a new chunk dvson scheme for SoftCast. Compared wth the prevous approach n the orgnal SoftCast, the proposed scheme can descrbe the dversty n the energy of transform coeffcents more accurately, usng very lmted number of meta data. Therefore, t facltates effcent power allocaton n SoftCast transmsson. Expermental results show that the proposed method can mprove both the objectve and subjectve qualty sgnfcantly. 7. REFERENCES [1] Szymon Jakubczak, Harharan Rahul, and Dna Katab, Softcast: One vdeo to serve all wreless recevers, n MIT Techncal Report, MIT-CSAIL-TR-9-, 9. [] Szymon Jakubczak, Harharan Rahul, and Dna Katab, One-

6 Peppers 1 1 Lena FDCT+EqualChunk (1 chunks) FDCT+EqualChunk ( chunks) FDCT+EqualChunk ( chunks) FDCT+Proposed (1chunks) FDCT+EqualChunk (1 chunks) FDCT+EqualChunk ( chunks) FDCT+EqualChunk ( chunks) FDCT+Proposed (1chunks) FDCT+EqualChunk (1 chunks) FDCT+EqualChunk ( chunks) FDCT+EqualChunk ( chunks) FDCT+Proposed (1chunks) 1 Baboon 1 1 Elane FDCT+EqualChunk (1 chunks) FDCT+EqualChunk ( chunks) FDCT+EqualChunk ( chunks) FDCT+Proposed (1chunks) 1 1 Fg.. Performance comparson between the proposed approach and the equal-chunk approach. Frame-DCT s consdered here for decorrelaton. Lena (1 1, gray) Lena (1 1, gray) Lena (1 1, gray) Lena (1 1, gray) Lena (1 1, gray) Lena (1 1, gray) Lena (1 1, gray) Fg. 7. Examples of chunk dvson results by the proposed scheme. sze-fts-all wreless vdeo, n The egth ACM SIGCOMM HotNets Workshop, New York, NY, USA, 9. [3] Szymon Jakubczak and Dna Katab, A cross-layer desgn for scalable moble vdeo, n Internatonal conference on Moble computng and networkng (MobCom 11), New York, NY, USA, 11, pp [] Xaopeng Fan, Feng Wu, Debn Zhao, C. Oscar Au, and Wen Gao, Dsrbuted soft vdeo broadcast (dcast) wth explct moton, n IEEE Data Compresson Conference, 1, pp [] Xaoln Lu, Wenjun Hu, Qfan Pu, Feng Wu, and Yongguang Zhang, Parcast: soft vdeo delvery n mmo-ofdm wlans, n Internaton Conference on Moble Computng and Networkng (Mobcom), 1, pp. 33. [] Xaopeng Fan, Ruqn Xong, Feng Wu, and Debn Zhao, Wavecast: Wavelet based wreless vdeo broadcast usng lossy transmsson, n IEEE Vsual Communcatons and Image Processng (VCIP), 1, pp. 1. [7] Ruqn Xong, Xaopeng Fan, Feng Wu, and Wen Gao, Analy- ss of uncoded mage communcaton over nosy channels wth unequal protecton, n SPIE Electronc Imagng 13, Vsual Informaton Processng and Communcaton IV, Feb. 13, p. 3. [] Ruqn Xong, Feng Wu, Jzheng Xu, and Wen Gao, Performance analyss of transform n uncoded wreless vsual communcaton, n IEEE Internatonal Symposum on Crcuts and Systems (ISCAS), 13, pp [9] Xaopeng Fan, Feng Wu, Debn Zhao, and C. Oscar Au, Dstrbuted wreless vsual communcaton wth power dstorton optmzaton, IEEE Transactons on Crcuts and Systems for Vdeo Technology, vol. 3, no., pp. 1 3, 13.