Transcription
Error-resilient Image Transmission System usingCOTCQ and Space-Time Coded FS-OFDMSudheer G. MethukuMartin ReissleinDept. of Electrical Eng.Arizona State UniversityTempe, AZ 85287-5706Email: [email protected]. of Electrical Eng.Arizona State UniversityTempe, AZ 85287-5706Email: [email protected]— We present and evaluate a novel robust imagetransmission system for frequency selective fading channels. Thesystem combines a wavelet image coder and space-time blockcodes (STBC) in conjunction with Fractional Sampling OFDM(FS-OFDM). Specifically, we employ an image coder based onchannel optimized trellis coded quantization (COTCQ), whichhas not been previously studied for frequency selective fadingchannels. We demonstrate that our COTCQ coder based systemboth with (i) (2,2) STBC OFDM without fractional sampling,and (ii) (2,1) STBC with fractional sampling significantly outperforms a system employing trellis coded quantization (TCQ)and set partitioning in hierarchical trees (SPIHT) image codingin conjunction with (2,2) STBC OFDM at low channel signal-tonoise ratios (SNR). The usage of STBC over FS-OFDM systemsimproves the capacity and diversity achievable over the frequencyselective fading channels. For a channel SNR of 9 dB, forinstance, the peak signal-to-noise ratio (PSNR) of the Lennaimage is over 2–4dB higher with our system. Importantly, theresults demonstrate that the diversity gain obtained with a (2,1)STBC FS-OFDM system with low-complexity maximum ratiocombining at the receiver can be translated into significantquality gains (in PSNR) in received images.I. I NTRODUCTIONThe growing demand for multimedia communications overwireless channels creates a need for reliable transmissionof visual data. This challenging task requires a robust andefficient image compression technique along with a errorresilient transmission scheme to deal with frequency selectivefading channels.We use a low bit rate wavelet coding scheme, namelychannel optimized trellis coded quantization (COTCQ) that isdesigned to optimize image coding based on wireless channelcharacteristics. Most of the image coders such as SPIHT donot perform well at low SNRs and in error prone and veryconstrained bandwidth channels. The COTCQ, on the otherhand, is error resilient at low SNRs and performs well inbandwidth constrained channels and also for wide variety ofchannel conditions. Earlier work on COTCQ [1] focuses onthe image transmission over the binary symmetric channel(BSC) which has a constant bit error rate. In this paper,we concentrate on image transmission in wireless frequencyselective fading channels.Space-time coding has gained considerable attention inrecent years as it uses transmit antenna diversity and providescoding gains and increases the channel capacity. In order tocope with the frequency selective fading conditions over wireless channels, space-time coding is used in conjunction withorthogonal frequency division multiplexing (OFDM) for robustdata transmission. In this paper we consider multiple transmitand single receiver antenna systems employing blind schemeswhich do not require feedback or feedforward information.OFDM is a multicarrier transmission scheme that has beenadopted for digital audio/video broadcasting in Europe, andhas been used in local area networks incorporating IEEE802.11a and HIPERLAN/2 standards. In OFDM, a singledatastream is transmitted over a number of lower rate subcarriers which increases the symbol duration thereby reducingthe relative dispersion in time for the symbols. Also due tothe addition of a guard interval, (wherein the OFDM symbolis cyclically extended), there is a reduction in the intersymbolinterference. In addition, OFDM converts a frequency selectivefading channel into a set of parallel flat fading channels, facilitating low complexity channel estimation and equalization.Sun et al. [2] have proposed a scalable image transmissionsystem over differential space-time coded systems and Songand Liu [3] study progressive image transmission over spacetime coded OFDM systems. Both these works are based onthe SPIHT image coder.In order to exploit the multipath diversity in OFDM, Tepedelenlioğlu and Challagulla [4] propose a low complexity diversity combining scheme through fractional sampling(FS) at the receiver. It is shown that by sampling at a ratehigher than the symbol rate, known as FS, one can improvethe channel capacity and diversity that the wireless channelcan provide in an OFDM system. Also, a low complexitymaximum ratio combining (MRC) scheme is employed toreplace the computationally complex maximum likelihood(ML) receiver. The advantage of using FS at the receiver isthat it converts a single input single output (SISO) channelinto a single input multiple output (SIMO) channel with thehelp of multiple receptions and thus increases the achievablediversity and capacity.As we mentioned, we use COTCQ as an optimal sourcecoder and combine space-time coding with FS-OFDM forerror resilient image transmission in frequency selective fadingchannels. The STBC FS-OFDM combination enhances the
ncoderTx1FS OFDMST EncoderFFTIFFTImageCOTCQChannelFS OFDMReceivedDecoderDecoderST DecoderChannelEstimationFig. 1.System structure for image transmission over FS-OFDM system using (2,1) STBCoutage capacity and the diversity offered by the wirelesschannel and thus reduces the bit error rate. We show that asystem using COTCQ and (2,1) STBC FS-OFDM has betterperformance than a system comprising of TCQ or SPHITencoder in conjunction with (i) (2,1) STBC FS-OFDM and(ii) (2,2) STBC OFDM respectively. Thus with fewer receiveantennas and by employing low complexity MRC, our systemperforms very well at low SNRs, reducing the receiver loadand replacing the computationally complex ML detector usedin [3].This paper is organized as follows. In Section II, we introduce the system structure and describe the COTCQ coder andspace-time coding for FS-OFDM. In Section III we providesimulation results and we conclude in Section IV.II. S YSTEM D ESCRIPTIONThe proposed system structure is shown in Fig. 1. Theimage coding algorithm used is a Channel Optimized TCQ[1] stage that is designed to optimize the image codingbased on wireless channel characteristics. The encoded bitstream from the COTCQ stage thus obtained, s(k ), (k 0, 1, . . . , 2N, . . . , 2M ), is first coded into two sub-streams ofspace-time codes, s1 (k) and s2 (k), (k 0, 1, . . . , N, . . . , M ).These two substreams and pilot symbols are mapped onto thecorresponding OFDM subcarriers resulting in a set of OFDMsymbols each of size N (N is also the number of subcarriers).After performing an inverse fast fourier transform (IFFT), thetwo OFDM symbol substreams (coded as STBC) pass througha pulse shaping filter and are transmitted via two antennasTx0 and Tx1. The receiver consists of a single antenna witha matched filter and fractional sampling is employed and alow complexity maximum ratio combining scheme is used fordecoding the encoded image bits.A. COTCQ Wavelet Image CoderWe have used a wavelet based image coder, a COTCQ stage[1] as shown in Fig. 2, that has been designed to optimize theimage coding based on wireless channel characteristics. TheCOTCQ encoder stage consists of a wavelet decompositionstage which decomposes the image into 22 subbands. Themean and variance of the individual subbands are normalizedand the calculated statistics are used by the rate allocationscheme to choose an optimal and fixed rate codebook. Thenormalized subbands are then encoded by the COTCQ encoderthat considers the bit error rate of the channel and rate oftransmission as the input quantities and codes the imagedata and then calculates the transition probability matrix forcorrectly decoding the image bits. The coded bitstream andthe side information consisting of calculated statistics (meanand variance) are given as input to the next stage of the imagetransmission system. The encoder transmits the mean of thelowest frequency subband and the standard deviations of all22 subbands as side information. Since the side informationis small, a simple repetition code is used so that the sideinformation is received without errors. The decoder performsthe inverse operations and consists of a COTCQ decoder anda wavelet reconstruction stage for decoding the image.B. OFDM with STBCIn this paper we use a simple transmit antenna diversityfor FS-OFDM system with two transmit antennas and onereceive antenna, a (2,1) STBC scheme. In order to comparethe performance of the COTCQ image coder with the SPIHTimage coder we also use a (2,2) STBC OFDM system withoutfractional sampling.Here we discuss the system using a (2,1) STBC and OFDMalone and in the next section we discuss fractional samplingin OFDM. We use an information bearing sequence, sn [k]where k 0, 1, . . . , N 1, to denote a single OFDM block.For OFDM transmission we need to take the IFFT of the
COTCQ ENCODERInputImagez0 [k]TS / ( t)OFDMDemodulatorDiversity Combining s[k]andOFDMDemodulatorRateAllocationQNoise Whitening.Equalizationz [k]G 1Fig. 3.Block diagram of FS-OFDM system.COTCQ g. 2.COTCQDecoderChannelC. Fractional Sampling in OFDMDecoderThe information sequence sn , to be transmitted usingOFDM, is converted to a sequence un by using the IFFTand appending a cyclic prefix (CP) as mentioned earlier. Forthe case of a system using fractional sampling (FS) [4], apulse shaping filter is used with an impulse response p(t)toa continuous signal in baseband form, x(t) Pobtain 1u[r]p(t rTs ) with 1/Ts as the symbol rate, to benr 0transmitted in the wireless channel.At the receiver, Pa 1matched filter is used (to capture x(t)) toobtain, y(t) r 0 un [r] · h(t nTs ) v(t), where v(t) isthe additive Gaussian noise. The output of the matched filteris sampled at rate G/Ts to obtain the polyphase components,Block diagram of COTCQ encoder and decoder.information symbols sn and append a cyclic prefix to obtainun ,N 1j2πnk1 un [k] sn [k]e N ,(1)N k 0where n 0, . . . , P 1, and N is the IFFT length, P : N L̄and L̄ is the length of cyclic prefix.Assuming two transmit antennas, two consecutive OFDMcoded blocks un and un 1 are STBC coded. Thus [un u n 1 ] is transmitted through antenna T x0 at time instants tand t 1 respectively, and [un 1 un ] is transmitted throughantenna T x1 at time instants t and t 1.Let H1 and H2 denote the channel coefficient matricesfor the two OFDM blocks transmitted via T x0 and T x1respectively and let v1 ,v2 denote the additive Gaussian noisematrices with zero mean and variance σ 2 associated with thewireless channel. All these matrices H1 ,H2 and v1 ,v2 are ofdimension P 1.At the receiver, the cyclic prefix is removed and an N pt.FFT is performed. Thus, the channel coefficient matrices arediagonalized [5], giving rise to Λ1 and Λ2 of size N Nwhere, Λ1 diag(H1 (0), . . . , H1 (N 1)), and similarily forΛ2 and H2 . Thus the consecutive received signals are,zn Λ1 sn Λ2 sn 1 w1zn 1 Λ1 s n 1 Λ2 s n(2) w2 ,(3)where sn and sn 1 are two consecutive information symbolsof size N 1 and w1 F F T {v1 }, similarily, w2 F F T {v2 }.After combining the outputs of two consecutive receivedsymbols zn and zn 1 via the single receive antenna Rx0, wehave the estimation of transmitted symbols as,ŝn ( Λ1 2 Λ2 2 )sn Λ 1 w1 Λ2 w2 22ŝn 1 ( Λ1 Λ2 )sn 1 Λ 2 w1 Λ1 w2 .(4)(5)These combined signals are sent through a maximum likelihood (ML) detector in order to obtain the information symbols.yg [n] P 1 u[l] · hg [n l] vg [n], g 0, . . . , G 1, (6)l 0where yg [n] y(nTs gTs /G), hg [n] h(nTs gTs /G),and vg [n] v(nTs gTs /G).Thus, after the removal of cyclic prefix and performing theFFT at the receiver for each g, we obtain,z[k] H[k] · sn [k] w[k], k 0, . . . , N 1,(7)where z[k] [z0 [k].zG 1 [k]]T with zg [k] F F T {yg [k]},similarly for wg [n] and vg [n] and, Hg [k]{ [H[k]]g } andhg [k].The colored noise covariance matrix at the kth subcarrier isRw [k] E[w[k]wH [k]]. The transmitted bits are estimatedusing a low complexity maximum ratio combining (MRC)scheme assuming perfect channel knowledge at the receiver.Thus ŝn [k], the estimate of sn [k], is given byŝn [k] HH [k]R 1w [k]z[k]. 1HH [k]Rw [k]H[k](8)When transmit antenna diversity is employed for the FSOFDM system, the diversity order achievable is multiplied bythe factor G, due to the multiple receptions made possible byusing FS at the receiver. Thus, for the case of (2,1) STBC andG 2 we obtain a diversity order of 4 using the FS-OFDMsystem as compared to the system with (2,1) STBC OFDMwithout FS which has a diversity order of 2 only.III. R ESULTSIn this paper we have evaluated three different imagetransmission systems namely COTCQ, TCQ, and SPIHT withchannel coding. Also the performance of the COTCQ and TCQimage coders were evaluated for the case of no channel coding
3530PSNR (dB)or forward error correction, and it was found that for SNRvalues ranging from 5–50dB the COTCQ/TCQ algorithmscould not decode the received image data due to large amountsof channel errors. This demonstrates the importance of channelcoding for wireless frequency selective fading channels whenusing the COTCQ/TCQ image coders. Taking into account theadvantages of COTCQ as an optimal source coder, we useda moderate channel coding scheme, such as space time blockcodes, to evaluate the performance at low SNR values.We performed two sets of simulations to evaluate theimage transmission system described in the preceding section.One set of simulations for a 1/2 rate convolutionally coded(2,2) STBC OFDM system without FS and the other set ofsimulations for a (2,1) STBC FS-OFDM system. For both setsof simulations, we used the COTCQ and TCQ image codersto compress the 512 512 Lenna image encoded at 0.5 bppat various SNRs.For the case of the (2,2) STBC scheme, a 128 subcarrierOFDM system is used wherein, a packet of 50 bits of encodeddata obtained from the COTCQ coder is fed into a (5,7)convolutional coder to obtain a block of 100 bits and a 128bit OFDM block is formed with this data using zero padding.In order to simulate the wireless channel we use a three raychannel model with the taps as [0.85 0.15 0.05] to simulatea frequency selective fading channel. The delay spread usedis 20µs and the doppler frequency used is 50Hz. QPSKmodulation and coherent estimation are used, assuming perfectchannel information at the receivers. At the receiver, a Viterbidecoder along with ML decoding is employed to detect theencoded bits.For the case of the (2,1) STBC using the FS-OFDM system,as in [4], we use a fractional sampling factor G 2, a set of64 bit OFDM blocks with cyclic prefix of L̄ 16 were formedfrom the data obtained from the COTCQ coder. Also, a channeldelay spread of τmax 8Ts was employed with Nm 3multipath components. A truncated sinc pulse was assumed forthe pulse shaping filter p2 (t). The image PSNR vs. channelSNR performance curves are shown in Fig. 4 for both thecases. The first set of simulations shows the effectiveness ofCOTCQ as a image coder as compared to the SPHIT coder.The second set of simulations demonstrates the enhancementin performance by using FS along with OFDM at the receiverwith a reduced number of receive antennas.In Figure 4, the plots of the average image PSNR as afunction of the average channel SNR show the performance ofour COTCQ system as compared to the TCQ and SPHIT codersystems for the cases of (2,1) STBC with FS-OFDM and (2,2)STBC with OFDM alone. It can be inferred from the plots thatthe COTCQ algorithm performs extremely well at low SNRvalues of 7dB and 9dB respectively as compared to the TCQalgorithm. This can be intuitively reasoned as COTCQ designsits codebooks based on the channel bit error rate and as aresult the combination of the COTCQ algorithm with the (2,1)STBC FS-OFDM gives rise to a robust image transmissionsystem that adds on to itself the advantage of using FS-OFDMsystem for the frequency selective fading channel. Also the2520COTCQ (2,2) STBC OFDMCOTCQ (2,1) STBC FS OFDMTCQ (2,2) STBC OFDMTCQ (2,1) STBC FS OFDMMDC SPIHT (2,2) STBC OFDMSPIHT (2,2) STBC OFDM151057911Average SNR (dB)1315Fig. 4. Image PSNR as a function of channel SNR for COTCQ and TCQwith (2,1) STBC FS-OFDM and with (2,2) STBC OFDM, compared withMDC-SPIHT and SPHIT with (2,2) STBC OFDM for Lenna image at 0.5bpp.performance of the COTCQ system in the PSNR sense is verygood compared to the SPIHT system.We also tested the (2,1) STBC over FS-OFDM systemwith the 512 512 Goldhill and Peppers images at 0.5 bpp.Table I shows the average received image PSNR (dB) forthe Lenna, Goldhill, and Peppers images which demonstratesthe consistency of performance of the system for differentimages with various intensity levels. Also is shown in Table IIthe lower and upper bounds of the 95% confidence intervalsfor the PSNR values obtained using our system. In order tocompare the performance of the proposed system, a systemwith SPIHT coding and (2,2) STBC-OFDM was simulatedand Tables III and IV show the average image PSNR and the95% confidence intervals for the SPIHT encoded system. Itis evident from the tables that the COTCQ (2,1) STBC FSOFDM system performs very well in the average image PSNRsense as compared to the SPIHT (2,2) STBC OFDM system.Though the confidence intervals for the 5dB and 7dB SNRvalues for the COTCQ system are fairly wide, they becomevery narrow for the SNR values 9dB, 11dB, 13dB, and 15dBrespectively, as compared to the SPIHT system which has amoderate confidence interval gap (about Avg. PSNR 20–25%) for all the SNR values. The PSNR values were tabulatedafter averaging the PSNRs obtained using 25 stochasticallyindependent image transmissions for each of the input SNRvalues of 5dB, 7dB, and 9dB respectively and for the higherSNRs, an average of 6 image transmissions were consideredfor the COTCQ and SPIHT system and an average of 5transmissions were considered for the case of TCQ system.IV. C ONCLUSIONWe have presented an error-resilient image transmissionsystem for frequency selective fading channels employingthe COTCQ coder in conjunction with OFDM (both withand without fractional sampling) and space-time block codes.We have demonstrate that both (i) COTCQ in conjunction
TABLE IAVG . IMAGE PSNR(dB) USING COTCQ AND (2,1) STBC FS-OFDMSCHEME FOR VARIOUS CHANNEL SNR VALUESImage5 dB7 dB9 dB11 dB13 dB15 3432.9135.81TABLE II95% C ONFIDENCE INTERVALS (L OWER AND U PPER BOUNDS ) FOR IMAGEPSNR(dB) FOR COTCQ AND (2,1) STBC FS-OFDMImageLennaGoldhillPeppers5 dB12.623.3512.4723.5510.9224.27 dB18.2429.7616.6830.1318.7232.789 dB31.3832.5130.7632.3324.0735.3611 dB31.7933.0529.3633.2632.3035.9713 dB33.0333.1430.4233.5735.3935.65TABLE IIIAVG . IMAGE PSNR(dB) USING SPIHT AND (2,2) STBC OFDM SCHEMEFOR VARIOUS CHANNEL SNR VALUESImage5 dB7 dB9 dB11 dB13 dB15 1226.2824.47TABLE IV95% C ONFIDENCE INTERVALS FOR IMAGE PSNR(dB) FOR SPIHT AND(2,2) STBC OFDMLennaGoldhillPeppers5 dB9.0914.6012.2218.679.8213.987 dB11.6916.6012.9319.9710.9117.019 dB12.3219.2116.0621.9512.3120.1811 dB16.5523.1016.4023.3316.1524.3613 dB20.0326.1518.9724.2519.0827.47(b) PSNR 31.84 dB.(c) PSNR 27.00 dB.(d) PSNR 29.52 dB.15 dB33.2433.4331.7034.1235.6935.93with (2,2) STBC OFDM without fractional sampling, and(ii) COTCQ in conjunction with (2,1) STBC FS-OFDMsignificantly outperform TCQ and SPIHT in conjunction with(2,2) STBC OFDM at low SNR levels. For an SNR of 9dB, forinstance, using a single receive antenna our COTCQ systemgives over 2dB and 4dB larger image PSNR than the TCQand SPIHT systems with two receive antennas, respectively.The COTCQ image transmission system with (2,1) STBCFS-OFDM combines the advantages of the COTCQ imagecoder as optimal image coder for wireless channels and thefractional sampling at the receiver to reduce the complexity byusing a low complexity MRC scheme and a single receiver.Thus, the resulting system gives rise to a very robust imagetransmission scheme with lower bit errors and with increasedoutage capacity and diversity gain. The results show thatthe diversity gain obtained using our (2,1) STBC FS-OFDMsystem can be translated into quality gains (in PSNR) in theImage(a) PSNR 31.95 dB.15 dB21.8732.3723.6628.9019.8029.14Fig. 5. Received Lenna images at avg. channel SNR 9dB with (a) COTCQwith (2,1) STBC and FS-OFDM, (b) COTCQ with (2,2) STBC and OFDMalone, (c) TCQ with (2,1) STBC FS-OFDM (d) TCQ with (2,2) STBC andOFDM at 0.5bpp.transmitted images.ACKNOWLEDGEMENTSupported in part by the National Science Foundationthrough grant Career ANI-0133252R EFERENCES[1] T.-T. Lam, G. Abousleman, and L. Karam, “Image coding with robustchannel-optimized trellis-coded quantization,” IEEE Journal on SelectedAreas in Communications, vol. 18, pp. 940–951, June 2000.[2] Y. Sun, Z. Xiong, and X. Wang, “Scalable image transmission over differentially space-time coded OFDM systems,” IEEE Journal on SelectedAreas in Communications, vol. 16, pp. 1451–1458, Oct. 1998.[3] J. Song and K. Liu, “Robust progressive image transmission over OFDMsystems using space-time block code,” IEEE Trans. on Multimedia, vol. 4,pp. 394–406, Sept. 2002.[4] C. Tepedelenlioglu and R. Challagulla, “Low complexity multipath diversity through fractional sampling in OFDM,” Asilomar Conference onSignals Systems and Computers, vol. 2, pp. 1813–1817, May 2000.[5] Z. Wang and G. Giannakis, “Wireless multicarrier communications:Where fourier meets shannon,” IEEE Signal Processing Magazine,vol. 17, pp. 29–48, May 2000.[6] L. Gao, L. Karam, M.Reisslein, and G. Abousleman, “Error-resilient image coding and transmission over wireless channels,” IEEE InternationalSymposium on Circuits and Systems, vol. 5, pp. 629–632, May 2002.[7] V. Tarokh, N. Seshadri, and R. Calderbank, “Space-time codes forhigh data rate wireless communication: performance criterion and codeconstruction,” IEEE Trans. Inform. Theory, vol. 44, pp. 744–765, Mar.1998.[8] S. Alamouti, “A simple transmit antenna diversity technique for wirelesscommunications,” IEEE Journal on Selected Areas in Communications,vol. 16, pp. 1451–1458, Oct. 1998.[9] J. Yue and J. Gibson, “Performance of OFDM systems with space-timecoding,” Wireless Communications and Networking Conference, vol. 1,pp. 280–284, Mar. 2002.
Sun et al. [2] have proposed a scalable image transmission system over differential space-time coded systems and Song and Liu [3] study progressive image transmission over space-time coded OFDM systems. Both these works are based on the SPIHT image coder. In order to exploit the multipath diversity in OFDM, Te-
