SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 5, No.2, November 2008, 353-360 Robust Image Transmsson Performed by SPIHT and Turbo-Codes Abdelmounam Moulay Lakhdar, Rachda Mélan 2, Malka Kandouc 2 Abstract: Ths work descrbes the method for provdng robustness to errors from a bnary symmetrc channel for the SPIHT mage compresson. The source rate and channel rate are jontly optmzed by a stream of fxed-sze channel packets. Punctured turbo codes are used for the channel codng, provdng stronger error protecton than prevously avalable codes. We use the most approprate set of puncturng patterns that ensure the best source rate. The presented rate allocaton scheme obtans all necessary nformaton from the SPIHT encoder, wthout requrng mage decompresson. Keywords: SPIHT, Turbo-code, Puncturng, Rate allocaton, Peak sgnal to nose rato (PSNR). Introducton One of the most successful practcal mage coders today for the noseless channel was orgnally developed by Shapro [] and later refned by Sad and Pearlman [2]. Ther schemes acheve a progressve mode of transmsson,.e. the more bts transmtted the better qualty of reconstructed mages produced at the recever. The recever need not wat for all bts to arrve before decodng the mage; n fact, the decoder can use each addtonal receved bt to make slght mprovements on prevously reconstructed mage. These wavelet-based encoders have come out to perform better than almost any other exstng compresson scheme. In addton, they are progressve and computatonally smple. However, for achevng hgh-qualty compresson they use varable-length codng wth sgnfcant amounts of state bult nto the coder. As the result, channel errors can cause non-recoverable loss of synchronzaton between the encoder and decoder. The total collapse of the reconstructed mage often results from the loss of synchronzaton. In fact, vast majorty of mages transmtted by ths progressve wavelet algorthm wll frequently collap- Département de Géne Mécanque, Centre Unverstare de Béchar, Béchar 08000, Algére E-mal: Moulaylakhdar78@yahoo.fr 2 Département d Electronque Faculté des Scences de l Ingéneur Unversté Djllal Labès BP 89, Sd Bel Abbes, Algere 353
A. Moulay Lakhdar, R. Mélan, M. Kandouc se even f a sngle transmtted nformaton bt s ncorrectly decoded at the recever. In order to avod crcumventng loss of synchronzaton on nosy channels the applcaton of fxed-rate mage compresson technques are recommended as well as those not based on fnte state algorthms. However, some of these technques have the dsadvantages of not beng progressve, not performng as well as hgh-qualty channels, or havng extremely hgh computatonal complexty. Two of the most compettve technques for protectng mages from channel nose are found n [3] and [4]. Another approach to protectng mage coders from channel nose s to dvde the transmtted bt stream nto two classes, mportant bts and unmportant ones, based upon the effects of channel errors on these bts. Important bts can then be sent as header nformaton usng good error control codes and the remanng ones can be sent wth weaker channel codes. Ths technque was used n [5] and [6]. A more tradtonal approach to protectng source coder nformaton from the effects of a nosy channel s to cascade the source coder wth a channel coder. The analytcal results have recently been obtaned n [7] as a gude n choosng the optmal trade-off between the source codng and the channel codng. In [8], the progressve nature of the embedded bt stream produced by the set parttonng n herarchcal trees (SPIHT) mage codng algorthm [2] s exploted to provde channel robustness far superor to anythng else avalable n the contemporary lterature. In fact, these results roughly follow those that we use n the present. The work by [8] provdes equal error protecton to all of the mage data. Later work [9 ] extended these results by provdng unequal error protecton. However the desgn of the optmal code rates for each component code s very complcated. In ths paper, we present a low-complexty technque that preserves the encodng power of the progressve wavelet schemes of Shapro Sad Pearlman. Beng easly mplemented n practce, ths technque also ensures the progressve transmsson. In ths paper, we have been focused on bnary symmetrc channels wth large bt error probabltes. The dstnctve feature of the proposed codng s that ts performance for a gven mage remans constant wth probablty near one over all possble receved channel error patterns. Effectvely, no degradaton due to the channel nose can be detected as we use a subset of the puncturng patterns that are well chosen. In fact, the effect of channel nose s to force the transmtter to encode the mage at a lower-source codng resoluton and devote more bts to channel 354
Robust Image Transmsson Performed by SPIHT and Turbo-Codes codng. Thus, on very nosy channels, the reconstructed mage qualty wll be that of the noseless channel encoder, though at a lower source codng rate. The need not be desgned for any partcular transmsson rate, as t actually works qute well over a broad range of transmsson rates. One of the objectves ths paper s to present the state-of-the-art numercal results for the nosy channel mage transmsson s that can be useful for future comparsons. 2 System Descrpton Let us consder the followng model. An embedded (progressve n accuracy) source bt stream s parttoned nto cells denoted as C, C2, C 3, If th the frst k cells are receved wth no errors, whereas the k cell s n error, the decoder performs the decodng usng only the bts from the frst k cells, resultng n a dstorton of. 2 2 Dk Let D 0 = σ x, σ x beng the source varance. In the followng step, let us assume that the length of a packet s fxed, where a packet s comprsed of a cell and redundant bts. If the packet s of length R, and the th cell s of length R then the number of redundant bts, C, s gven by R + C = R, so specfyng R s equvalent to specfyng the channel codng rate for packet. In [0] each cell contans ( R 24 ) bts of data from the J2K bt stream, 8 bts for specfcaton of the next packet s channel codng rate, and 6 bts for a cyclc redundancy check code (CRC). However, n ths work each cell contans ( R 6 ) bts of data from the SPIHT bt stream, no bt for specfcaton of the next packet channel codng rate because R s fxed for gven channel BER, and 6 bts for a CRC. Let Pe( R, P be the probablty of at least one error n the th decoded packet, where P b s the probablty of a bt error from the BSC, and R s the number of nformaton bts n the th cell. The expected dstorton can then be computed as: N + ( ) ( ) 355. () D = DP R, P + D P R, P P( R, P) 0 e b e b e j b = 2 j= N stands for the number of transmtted packets and P ( R P ) rate s R N = e N b, + =. The total R + C = NR. Snce we use an equal error protecton (EEP), = R = const. for every. Thus () can then be smplfed as: N + e(, (, ) = e b. (2) D= P R P D P R P The useful rate of the reconstructon s:
A. Moulay Lakhdar, R. Mélan, M. Kandouc N + e(, (, ) = e b. (3) URR = P R P URR P R P The rate allocaton problem s to mn R D. Fg. System Overvew. Or max R URR such that all N packets are used, assurng the total rate s NR. The advantage of the second method s that we do not use the functons characterzng the performance of the source coder n the case of the mage n queston (functon PSNR () for example), and does not requre mage decompresson. In practce, each packet uses a 6-bt CRC outer code [3] for detecton of packet errors, concatenated wth an nner turbo code for error correcton on the BSC. The turbo code employs the punctured parallel-concatenated recursve convoluton codes (RTCP) of [4], where each of the two 8-state component encoders has feedback/feedforward - generator polynomals 5. (octal). We use a subset of the puncturng patterns recommended n [4] to obtan code rates {8/0, 8/, 8/2, 8/3, 8/4, 8/5, 8/6, 8/7, 8/8, 8/9, 8/20, 8/2, 8/22, 8/23, 8/24}. P (, e R P s ndependent of the source, dependng only upon the BSC, and the selected rate. P (, e R P can then be tabulated, from extensve smulatons, for each permssble channel code rate, r, and for the specfed channel bt error rate, P b. The probablty of a 57 byte block havng a bt error after 20 turbo decoder teratons s presented n Table. The probabltes P (, e R P are ndependent of the source, dependng only upon the BSC bt error rate, P b, and selected channel codng rate, R. P (, e R P can be tabulated, from extensve smulatons, for each permssble channel code rate, R, and for the specfed channel bt error rate, P b. The probablty of a 57 byte block havng a bt error after 20 turbo decoder teratons s presented n Table, based on Monte-Carlo smulatons usng 0000 blocks. 356
Robust Image Transmsson Performed by SPIHT and Turbo-Codes 3 Results Table Probablty of block error vs. channel BER, block length = 57 bytes, 20 turbo decoder teratons. Channel BER Turbo Code Rate 0. 0.08 0.05 0.03 0.0 /3 0 0 0 0 0 8/23 0 0 0 0 0 4/ 0 0 0 0 0 8/2 0 0 0 0 0 2/5.5 0-4 0 0 0 0 8/9 8 0-4 0 0 0 0 4/9 2 0-2 0-4 0 0 0 8/7 4 0-2 0-3 0 0 0 /2 0-2 0-4 0 0 8/5 3 0-2 0-4 0 0 4/7 6 0-5 0-4 0 0 8/3 2 0-3 0-4 0 2/3 6 0-6 0-4 0 8/ 2 0-2 0-4 4/5.5 0-3 All results are based on the packet length of 57 bytes. The packet sze (57 bytes) s typcal for user datagram protocol (UDP) packets sent over the Internet. Paddng s used as needed to assure all packets are of the same length. One excepton s for the channel code rate of /3 where the last party bt from encoder 2 s dropped to ft n 57 bytes. The number of SPIHT bytes used for each channel rate s 394, 357, 326, 299, 276, 257, 240, 225, 2, 99 88, 78, 69, 6, and 54 respectvely for rates of {8/0, 8/, 8/2, 8/3, 8/4, 8/5, 8/6, 8/7, 8/8, 8/9, 8/20, 8/2, 8/22, 8/23, 8/24}. The SPIHT encoder uses default optons, except for the explct specfcaton of the progressve by accuracy btstream. No changes have been made to the functonalty of ether the SPIHT encoder or decoder, hence our protecton scheme s standard complant. Table 2 and Table 3 present codng results (n db PSNR) for Lena and Goldhll (8-bt monochrome) mages respectvely and tree channel bt error rates (BERs). Where possble, our results are compared to those reported n [8, 2], where not possble we put ND n the case. The proposed method provdes about 0.4 db and 0.2dB mprovement over [8] and [2] respectvely at 0.0 BER and an mprovement of.4 db and 0.2 db at 0. BER. For mages Lena and 357
A. Moulay Lakhdar, R. Mélan, M. Kandouc Goldhll at 0. BER, the mprovement over [8] s due to superor channel codes and turbo code performances. Table 2 Expected dstorton (PSNR n decbels) for Lena 52 52 mage transmtted over a BSC at total rate 0.252, 0505, 0.994 bpp. 0.252 Overall Rate (bpp) Channel BER 0.0 0.03 0. psnr Rate psnr Rate psnr Rate 32.4 0.72 0.6 0.4 3.64 29.7 8/ 8/3 2/5 [8] 32 0.66 ND ND 28.4 0.28 0.505 0.994 [2] 32.25 0.69 ND ND 29.63 0.38 35.26 0.72 8/ 34.5 0.6 8/3 32.55 0.38 8/2 [8] 35.2 0.66 ND ND 3. 0.28 [2] 35. 0.68 ND ND 32.32 0.36 38.7 0.66 2/3 37.50 0.57 4/7 35.56 0.38 8/2 [8] 38 0.66 ND ND 34.2 0.28 [2] ND ND ND ND ND ND 0.252 0.505 0.994 Table 3 Expected dstorton (PSNR n decbels) for Goldhll 52 52 mage transmtted over a BSC at total rate 0.252, 0505, 0.994 bpp. Overall rate (bpp) Channel BER 0.0 0.03 0. psnr Rate psnr Rate psnr Rate 29.36 0.72 0.6 0.4 28.84 27.64 8/ 8/3 2/5 [8] 29 0.66 ND ND 26.7 0.28 3.5 0.72 8/ 30.92 0.6 8/3 29.42 0.38 8/2 [8] 3.2 0.66 ND ND 28.6 0.28 34.3 0.66 2/3 33.46 0.57 4/7 3.6 0.38 8/2 [8] 34 0.66 ND ND 30.7 0.28 358
Robust Image Transmsson Performed by SPIHT and Turbo-Codes 4 Concluson A novel mage transmsson scheme was proposed for the communcaton of compressed SPIHT mage streams over BSC channels. The proposed scheme employs turbo codes and CRC codes n order to deal effectvely wth errors. A novel methodology for the optmal EEP of compressed streams was also proposed and appled n conjuncton wth an nherently more effcent rate for the RTCP codes. The resultng was tested for the transmsson of mages over BSC channels. Expermental evaluaton showed the superorty of the proposed schemes n comparson to well-known robust codng schemes. 5 References [] J.M. Shapro: Embedded Image Codng usng Zerotrees of Wavelet Coeffcents, IEEE Trans. Sgnal Processng, Vol. 4, No 2, Dec. 993, pp. 3445 3462. [2] A. Sad, W.A. Pearlman: A New, Fast, and Effcent Image Codec Based on Set Parttonng n Herarchcal Trees, IEEE Trans. Crcuts Syst. Vdeo Technol., Vol. 6, No. 3, June 996, pp. 243 250. [3] N. Tanabe, N. Farvardn: Subband Image Codng usng Entropy-coded Quantzaton Over Nosy Channels, IEEE J. Select. Areas. Commun., Vol. 0, No. 5, June 992, pp. 926 943. [4] Q. Chen, T.R. Fscher: Robust Quantzaton for Image Codng and Nosy Dgtal Transmsson, In Proc. DCC 96, Mar/Apr 996, pp. 3 2. [5] T.P. O Rourke, R.L. Stevenson, Y.F. Huang, D.J. Costello Jr.: Improved Decodng of Compressed Images Receved Over Nosy Channels, In Proc. ICIP-95, Vol. 2, Oct. 995, pp. 65 68. [6] D.W. Redmll, N.G. Kngsbury: Stll Image Codng for Nosy Channels, In ICIP-94, Vol., Nov. 994, pp. 95 99. [7] B. Hochwald, K. Zeger: Tradeoff Between Source and Channel Codng, IEEE Trans. Inform. Theory, Vol. 43, No. 5, Sept. 997, pp. 42 424. [8] P.G. Sherwood, K. Zeger: Progressve Image Codng on Nosy Channels, Proceedngs DCC 97. Data Compresson Conference, Mar. 997, pp. 72 8. [9] V. Chande, N. Farvardn: Jont Source-channel Codng for Progressve Transmsson of Embedded Source Coders, In Proc. Data Compresson Conference (DCC 99), Mar. 999, pp. 52 6. [0] B.A. Banster, B. Belzer, T.R. Fscher: Robust Image Transmsson usng JPEG2000 and Turbo Codes, Proceedngs of the Internatonal Conference on Image Processng, Vol., 2000, pp. 375 378. [] N. Thomos, N.V. Boulgours, M.G. Strntzs: Wreless Image Transmsson usng Turbo Codes and Optmal Unequal Error Protecton, IEEE Trans. on Image Processng, Vol. 4, No., Nov. 2005, pp. 890 90. [2] L. Yao, L. Cao: Interleaved Turbo Codes Protecton for Progressve Image Transmsson wth Effcent Rate Allocaton, Proceedngs of the Internatonal Conference On Communcatons And Moble Computng, Honolulu, Hawa, USA, August 2007, pp. 68 622. 359
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