JPEG2000 Images Transmission over Noisy Wireless Channels with Unequal Power Distribution Wavelet Transmultiplexing

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1 JPE2000 Images Transmission over Noisy Wireless Channels with Unequal Power Distriution Wavelet Transmultilexing Luigi Atzori *, Maurizio Murroni * and Vlad Poescu ** * Deartment of Electrical and Electronic Engineering, University of Cagliari, iazza d Armi, Cagliari, Italy ** Deartment of Electronics and Comuters, University of Transilvania, Str. Politehnicii rasov, Romania Astract This aer deals with the roust transmission of JPE2000 (JP2) images over wireless channels. It rooses a comarison among a wavelet transmultilexer ased communication system with a roer unequal distriution of the transmission ower among JP2 coding units, and some state of the art techniques on this toic. In the roosed method, ackets are formed y artitioning the JP2 stream and then transmitted through searate wavelet su-channels. oth acket grouing and ower distriution are driven y the native JP2 rate-distortion function, according to the contriution of each coding unit to the decoded image quality. The major strength of the roosed method is the flexiility on assigning a different rotection level over each transmission suand y selecting the transmission ower from a continuous range of ossile values. This allows comating the influence of fading imairments tyical of wireless channels. The erformance of this technique is evaluated in case of SC and ilert-elliot (E) channels and comared to the state of the art techniques on this toic. I. INTRODUCTION The widesread use of multimedia moile communications for oth ersonal and usiness uroses is exected to significantly intensify, in the near future, the transmission of multimedia data over wireless channels. It is likely that it will e generated a strong demand for wireless devices ale to efficiently transmit data such as images and video contents. In this context, a crucial oint for the overall erformance of the aove devices is the quality of the data delivered to the end user. Within this framework, comression techniques are necessary to reduce the needs in terms of andwidth, while ensuring accetale reconstruction quality. However, due to the extensive use of redictive and variale length codes, a comressed stream is in general more vulnerale to data losses and transmission errors, which can desynchronize the decoder causing satial and temoral error roagation. To comat this rolem, several methods have een roosed to increase the image transmission roustness making use of forward error correction schemes (FEC) ale to rotect the most significant arts in the it-stream. Among the roosed techniques, a major distinction can e made on the asis of the underlying adoted aroach: joint source and channel coding (JSCC) and joint source channel matching (JSCM) coding as named in [1]. While this can e considered the crucial distinguishing features, there are others allowing for additional classifications, such as: use of an equal error rotection (EEP) or an unequal error rotection (UEP) scheme; most of the roosed techniques refer to the transmission of SPHIT [2] coded image while others consider Jeg2000 (JP2) images [3]. It is a matter of fact that the JSCC aroach is more frequently used than the JSCM one. In fact, the roosed techniques are often aimed at otimizing the source coding for a noiseless channel that is given almost noiseless thanks to a searate otimal channel coding. This is a slightly different aroach resect to the JSCC where source and channel coding are jointly otimized. In [1], the roosed UEP JSCM scheme is design for transmission over roadand wireless channels using OFDM systems with satial diversity, that is multile antennas at oth transmitter and receiver sides are deloyed in order to decrease the fading effects. As to the JSCC aroach, a new technique for roust transmission of JP2 images is roosed in [4], making use of the distortion function used during source coding in the JP2 algorithm to assign aroriate imortance to each transmitted acket. Such UEP scheme is tested over SC channels. With reference to the use of the JP2 image codec, [5] rooses the use of the RCPC (rate comatile unctured convolutional) codes to imlement a two level UEP scheme for the transmission over SC and E channels. Indeed, this is not a JSCC aroach since no otimization of the channel use for error rotection and source coding is defined. From the examined works, it arises that the UEP aroach allows for a etter rotection of the visual information than the EEP one. Dissimilar error roustness levels are usually otained y assigning a different channel coding rate R c to each source coding comonent. To this Reed-Solomon (RS) or turo codes are frequently used. Differently, in [6] an alternative aroach is roosed y differentiating the transmission ower level instead of the channel coding rate to achieve an unequal error rotection. It can e oserved that the transmission ower can e selected over a continuous range of values

2 while this is not true for R c. This is due to the fact that the selection of the ratio etween the numer of information symols k and the total numer of symols n is limited y some constraints: n cannot e taken too ig and it is tyically fixed; the resolution of the rotection level is at code symol level rather than a it level; sometimes, k can e only selected among a set of ossile values. This limits the distriution of the channel andwidth etween source and channel coding. From these considerations, it arises that the roosed aroach should allow for a more flexile assignment of different rotection levels to each source coding comonent than the traditional aroach. ased on this, a new technique was roosed that exloits the recognized otentialities of the wavelet transmultilexing technique to allow suand modulation and ower-ased UEP in image transmission. In this work a study on the influence of the channel coding arameters (n, k) selected for the RS codes is made and a comlete comarison of the method with two state of the art techniques on JP2 transmission over SC and E wireless channel is erformed. The aer is organized as follows. Section II rovides a rief ackground aout the used tools: wavelet transmultilexing, JP2 error resilience features and the E scheme used for wireless channel modeling. Sections III and IV rovide a descrition of the system and ower distriution otimization, resectively. Finally, a enchmark test and the relevant exerimental results are rovided in section V. II. ACKROUND A. Wavelet transmultilexing Recently, alications of orthogonal synthesis/analysis transform configurations (transmultilexer) have ecome very oular in communications. What s more, several common communication alications can e descried in terms of synthesis/analysis configuration of suand transforms. Code division multile access (CDMA), frequency division multile access (FDMA) and time division multile access (TDMA) schemes can e viewed from this ersective. In articular, FDMA (also called orthogonal frequency division multilexing, OFDM for short) or discrete multitone modulation (DMT) ased systems have een more widely used than the others. A articular OFDM technique is the wavelet acketdivision multilexing (WPDM), where a set of self and mutually orthogonal waverforms is used instead of the waveforms that stem from Fourier s theory. The use of wavelets rovides a etter trade-off etween time localization and frequency localization. Additionally, since we do not require guard ands nor guard times to ensure orthogonality in a ractical system, it is ossile to increase the numer of the caacity of a given channel over that of conventional FDM and TDM [7]. To define the wavelet acket asis functions, let g 0 [ n] e a unit-energy real causal fir filter of length L which is orthogonal to its even translates; i.e., g0 [ n] g0[ n 2m] = δ [ m], where δ [ m] is the Knoneker n delta, and let g 1 [ n] e the (conjugate) quadrature mirror n filter, g [ n] = ( ) g [ L 1 n] g 0 n satisfies some If [] mild technical conditions [8], we can use an iterative algorithm to find the function ϕ 01( t) = 2 g [ n] ( t nt ) n 0 ϕ for an aritrary interval T 0. Susequently, we can define the family of l functions ϕ m, l 0, 1 m 2 in the following (inary) tree-structured manner: ϕl+ 1,2m 1 ( t) = g [ n] ϕ ( ) n 0 lm t ntl, (1) ( t) = g [ n] ϕ ( t nt ) ϕl+ 1,2m n 1 lm l, (2) l Where Tl = 2 T0. For any given tree structure, the function at the terminals of the tree form a wavelet acket. They have a finite duration, ( L 1 T, and are self- and mutually-orthogonal at integer multiles of dyadic intervals, and hence they are a natural choice for multilexing alications [7].. Resilience in the JP2 coding In JP2, the image is firstly segmented into rectangular areas called tiles and each tile is indeendently coded. The division of the image in tiles is otional, then, the image is usually regarded as one tile. Each tile is coded y means of the wavelet transform. The wavelet coefficients are quantized using a uniform dead zone scalar quantizer and the quantized coefficients are divided into non-overlaing rectangles called code-locks. A it-lane context ased arithmetic codec is used to comress the quantized coefficients code-lock y codelock and each it-lane is coded with three asses named significance roagation, magnitude refinement, and cleanu. The individual it-streams, one from each code-lock, are organized into ackets and distriuted across a numer of layers. A collation of layers comrises the final JP2 stream. To increase the roustness of the JP2 it-stream a numer of secific features have een included in the standard, as follows: the quantized coefficients relevant to different code-locks are entroy coded indeendently so that errors do not roagate over the affected codelock; the arithmetic coder can e terminated and reset after each ass so it can continue decoding the susequent ass even if an error occurred in the revious one; at the eginning of a acket, a start of acket resynchronization marker can e inserted in order to guarantee decoder resynchronization at acket level; the otional arithmetic coding yass functionality allows the encoder to yass the arithmetic coding in order to revent from error roagation; a segmentation symol is a secial symol that is coded at the end of each it-lane that allows the decoder to detect a correct recetion of such it-lane. ) l

3 C. Fading Channels In case of wireless communications systems, it is imortant to test the effectiveness and the suitaility for fading channels. A asic channel model incororating the memory associated with fading channels is the ilert-elliot (E) model. The E channel is a two-state channel: OOD and AD. In each state, the channel acts like a SC with a certain it error roaility ( P for the ad state and P for the good state, P < P ), and at each it interval, the channel changes state with roailities governed y the model transition roailities P = Pr( OOD AD) and P = Pr ( AD OOD). Let e α the roaility to e in and kee the AD state, therefore P = 1 α. Analogously, if is the roaility to e in and kee the state OOD, thus P = 1. We called 1 α π =, (3) 1 α + 1 the roaility to e at any instant in the state OOD and 1 π =, (4) 1 α + 1 the roaility to e at any instant in the state AD. A diagram of the channel model is shown in Fig. 1. This same model was used in [5] to model a channel with memory. 1 - α 1 - Fig. 1.The ilert Elliot Channel diagram. D. Reed Solomon codes Reed-Solomon (RS) codes are lock-ased error correcting codes with a wide range of alications in digital communications and storage. RS codes are used to correct errors in many systems including: Storage devices (including tae, Comact Disk, DVD, arcodes, etc), Wireless or moile communications (including cellular telehones, microwave links, etc), Satellite communications, Digital television / DV, High-seed modems such as ADSL, xdsl, etc. The RS encoder takes a lock of digital data and adds extra "redundant" its. Errors occur during transmission or storage for a numer of reasons (for examle noise or interference, scratches on a CD, etc). The Reed-Solomon decoder rocesses each lock and attemts to correct α errors and recover the original data. The numer and tye of errors that can e corrected deends on the characteristics of the RS code. RS codes are a secial case of CH codes. An (n, k) RS code takes a grou of k data symols and generates n-k arity symols; n is the codeword size, measured in symols. In articular, a t error correcting RS code from the alois Field F(2m) has the following arameters. Numer of codeword symols n = 2m 1. Numer of arity symols = n - k = 2 t. Here m is the numer of its er symol and t is the numer of symols, containing one or more it errors, which the code can correct. The RS family of codes rovides a wide range of codes with different code lengths and error correction caailities, from which the most aroriate codes may e selected. The RS codes are simler to decode than turo or convolutional codes. III. SYSTEM DESCRIPTION The roosed image transmission scheme relies on the native JP2 error resilience features and on the advantages of using a wavelet trasmultilexer allowing for assigning different signal ower levels to distinct image sustreams. Accordingly, each coding unit (i.e., JP2 ackets) is transmitted with a ower-ased error roustness that is a function of its contriution to the overall image quality. A sketch of the devised system is deicted in Fig. 2 The image coder outut is slit into N su-streams, each made of a grou j ( j = 1,..., N ) of JP2 coding units. A searate channel coding is alied to each su-stream to rotect source ackets (e.g., RS code or convolutional code). The su-streams are then multilexed y a dyadic wavelet transmultilexer into a signal at higher itrate and transmitted on searate su-channels. The transmission ower is distriuted among the su-channels accordingly to gain factor comuted so as to otimize the exected received quality. The key functions in the devised system are erformed y the Control Unit module, that is devoted to the comutation of the otimal system arameters: average its er ixel s for source coding; numer of sustreams N (this also corresonds to the numer of WPDM su-channels); average its er ixel c for channel coding; and it energy E j ( j = 1,..., N ) for each suchannel j. This should e erformed under the constraint s c of a target overall its er ixel ( = + ) and target average energy er ixel E. To accomlish this task, the Control Unit needs to access the information on the contriution Q i ( i = 1,..., M, where M reresents the numer of JP2 ackets in the stream) of each acket to the overall image quality. Then, it has to drive the rou eneration, the Channel Coder and the Wavelet Transmultilexer modules.

4 Control Unit Inut Image JP2 Coder rou eneration N... Channel Coding... Fig. 2. Sketch of the roosed ower-ased UEP system. N Wavelet Transmultilexer Outut Stream A. The Control Unit The Control Unit is aimed at oth alancing source coding versus channel coding and otimizing transmission ower distriution among JP2 ackets. To this urose, such module makes use of several inut and outut arameters that are groued in default, inut and system arameters. The former ones reresent those that are usually left unchanged. The use of default values is motivated y the fact that the comutation of image secific otimal values is quite comlex and doesn t ring to significant imrovements. These are: the dimension of the JP2 code-lock, the numer of JP2 resolution levels, the maximum numer of WPDM tree levels, and the default vector that hels in assigning source and channel coding its whose meaning is descried in the following. The second grou is related to settings that drive the image coding and transmission oerations. These are rovided y the oerator or arise from the image characteristics, such as: the image dimension, the numer of JP2 ackets, the target overall its er ixel, the target average energy er transmitted it, the channel state (exected channel conditions), and the vector. The latter grou includes all the settings that are automatically erformed y the system on the asis of the values assigned to the first two grous arameters: the numer of su-channels (that corresonds also to the numer of acket grous), the source and channel coding its er ixel, the acket quality contriution, the transmultilexing tree structure, the it energy er su-channel, the acket error sensiility, the acket error roaility, and the it error roaility. These are comuted so as to maximize the exectation of the image quality at the receiver. Assuming that the quality contriution of a acket i can e exloited y the decoder only if the revious i-1 ackets have een correctly received, the exectation of the image quality EQ can e written as follows: M i i Q ( P ) EQ = k 1 l Pi + 1 (5) i= 1 k= 1 l= 1 where P i reresents the roaility to have at least one error in acket i after channel decoding and PM + 1 is considered equal to 1 for notation convenience. This exression is quite similar to that used in [9] aart from considering the acket quality instead of the distortion in case of incorrect acket recetion. Maximizing (3) is quite comlex since EQ deends on several arameters together (the named system arameters). Additionally, not all the relations etween EQ and these arameters may have an analytical reresentation. In articular, the deendence of the image quality from the source coding and from the acket grouing is of difficult reresentation. ased on this, the roosed solution relies on an emirical aroach. In articular, the otimal (actually, su-otimal) numer of s source coding its er ixel is ed in a set of ossile values reresented y the vector : dim h = h, with h = 1,...,. is a default vector whose elements reresent ercentage values of the overall to e used for source coding. dim For h = 1,...,, the following stes are erformed: - The JP2 coding of the inut image is erformed at h its er ixel. The acket quality contriution vector Q h is then extracted making use of the otimum rate allocation algorithm used in the it lane coding in JP2 [3]. - The JP2 ackets are divided into searate grous y analyzing their error sensiility that should drive the rotection level to e rovided to each acket. The sensiility factor for a acket I is estimated as follows: EQ α I = PI I 1 I 1 M i i (6) = Qk ( 1 Pl ) Qi ( 1 Pl ) Pi + 1 k= 1 l= 1 i= I k= 1 l= 1 l i While the acket quality contriution is availale at this stage this is not true for the acket error roaility. In fact, this can e otained only after the acket grouing and the transmission ower distriution rolems have een solved. Then, it has een necessary to introduce a simlification: the acket error roaility P i is sustituted with an average acket error roaility P that is otained assuming a uniform distriution of channel coding its and ower among the ackets. In case of transmission on a E channel:

5 P = π P + π P (7) The ackets are then groued so as to maximize the uniformity of error sensiility of ackets in a grou hj ( j = 1,..., N h ). This roerty allows for otimizing the use of transmission ower that is assigned to each su-stream hj on the asis of the average error sensiility. A grou with ackets with too dissimilar sensiility would cause assigning too much ower to its with low imortance or vice versa. As already stated, each su-stream (ackets elonging to a given grou) has to e sent through a searate suchannel in the WPDM tree. Let then reresent the WPDM tree structure with a vector T h where each element T hj codes the levels of the tree leafs in lexicograhic order, with the root level set to 1 and T h = N h. The solution T h is found y maximizing the error sensiility under two constraints: a maximum numer of tree levels L t cannot e exceeded and the difference etween the longest su-channel and the shortest one cannot exceed 1/10 of the average length. The length of su-channel transmitting the data of a s Thj grou hj is equal to hj 2. At the end of this ste, we get the otimal numer of transmission suchannels N h, the wavelet trasmultilexing tree T h, s and the source its er su-channel h. - Channel coding its hj c are assigned to each suchannel hj so as to rovide a error rotection level uniformity etween the su-channels. The total amount of channel coding its is equal to ( ) L W. - The last ste is reresented y the distriution of transmission ower among the su-channels. The used algorithm for ower distriution otimization is resented in the following section. At the end, this rocedure rovides the h EQ h associated to each h. The final image coding configuration, reresented y the system arameters T, c, c, E, is then selected y looking for that roviding the maximum exected quality: T = T j s s = j c c = j E = E j : EQ j = max h dim ( 1, ) EQh IV. POWER DISTRIUTION OPTIMIZATION ALORITHM When looking for the ower otimal distriution among the su-channels, the only free arameter is (8) reresented y the matrix E [ E,..., E ] 1 N, that is the ower er it er su-channel. Let then write now EQ as a function of the only error roaility: EQ = EQ( P1,..., PN ) (9) where P j is it error roaility for the su-channel j. P j deends directly on N E j, with: E = j = E 1 j (10) Indeed we consider the rolem of maximizing (8) with the constraint of (10). It is worth noting that in general it is difficult to find a suitale analytical exression for EQ, consequently the solution has een given y using a numerical aroach. V. EXPERIMENTS An evaluation study of the ehavior of the roosed method in case of AWN and Rayleigh slow fading channels was roosed in [6]. The aim of this work is to comare the erformance of the roosed scheme, imlemented in a unequal ower distriution (UPD) scheme in conjunction with a EEP channel coding, with those otained under the same constraints y two state of the art techniques [4, 5] in use for the transmission of JP2 images over noisy channels. The transmission has een simulated across an SC and E asic channel model incororating the memory associated with wireless channels according to the technique of equivalent aseand simulation. The exeriments have een conducted using a software latform ased on the simulator Simulink and the scientific software Matla. The signal and across the channel is aout 1 MHz. As a test images we considered Lena and oldhill, 512x512 ixel, coded at The erformance of the roosed system has een evaluated with different channel rotection, in articular we used RS codes (15,9) and (31,19). A comarison with the results resented in [4] have een conducted over the SC channel, whereas a comarative test rocedure have een set u using the E channel model, for the comarison with the RCPC- UEP method roosed in [5]. Tale I and II illustrates for the two test images the difference in received PSNR over SC etween the aforesaid coding strategy in case of use of (15,9) and (31,19) RS codes. In fact, it is noticeale that a dee overhead roduces etter results only for range values etween 4 and 6 d. Aove this interval the UPD is redominant and an increase of the overhead is useless. eyond 2 d the redominance of the noise ower at revelation stage is too high making irrelevant any channel coding action. Instead tales III and IV show the comarison etween the roosed system and the algorithm resented in [4] over a SC channel. Tale V reorts the results relevant to the comarison etween the results otained y the roosed system and the one achieved y the RCPC-UEP channel coding scheme resented in [5] over a E channel.

6 Tale I RS (15,9) vs RS (31,19) over SC PSNR (d) for Lena (512 x 512, 0.25 ) (d) (15,9) (31,19) Tale II RS (15,9) vs RS (31,19) over SC PSNR (d) for oldhill (512 x 512, 0.25 ) (d) (15,9) (31,19) Tale III UPD+EEP vs Turo Codes over SC PSNR (d) for Lena (512 x 512, 0.25 ) (d) UPD+EEP Turo Codes Tale IV UPD+EEP vs Turo Codes over SC PSNR (d) for oldhill (512 x 512, 0.25 ) (d) UPD+EEP Turo Codes Tale V UPD+EEP vs RCPC-UEP over E channel PSNR (d) for Lena (512 x 512, 0.25 ) (d) UPD+EEP RCPC-UEP REFERENCES [1] J. Song and K. J.R. Liu, Roust Progressive Image transmission over OFDM Systems using sace-time lock code, IEEE Trans. Multimedia, vol. 4, , Set [2] A. Said and W.A. Pearlman, A new, fast, and efficient image codec ased on set artitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Technol., vol. 6, , June [3] D. S. Tauman and M. W. Marcellin, JPE2000: Image comression fundamentals, standards and ractice, Norwell, MA: Kluwer Academic Pulishers, [4].A. anister,. elzer, and T.R. Fisher, Roust Image transmission using Jeg2000 and turo-codes, IEEE Signal Processing Lett., vol. 9, no. 4, , Aril [5] V.S. Sanchez and M.K. Mandal, Roust transmission of Jeg2000 images over noisy channels, IEEE Trans. Cons. Electr., vol. 48, no. 3, , August [6] L. Atzori, Transmission of JPE2000 images over wireless channels with unequal ower distriution IEEE Transactions on Consumer Electronics, Vol 49, no. 4, , Novemer 2003 [7] K.M. Wong, J. Wu, T.N. Davidson, and Q. Jin, Wavelet acket division multilexing and wavelet acket desing under timing error effects, IEEE Trans. Signal Processing, vol. 45, , Dec [8] I. Dauechies, Ten Lectures on wavelets, Philadelhia, [9] J.. Proakis, Digital Communications, Mcraw-Hill, 4th edition, 2001.