_ISPRVJl_ IMEN=SE_ 2006 International Symposium on Intelligent Signal_'ER32 rProcessing and Communication Systems (ISPACS2006)L2 0 Db31m Yonago Convention Center, Tottori, Japan

Layered Tree-based Multiple Description CodingJing Chen*, Canhui Cai* and Kai-Kuang Mat

*Institute of Information Science and Engineering, Huaqiao University, Quanzhou, Fujian 362021, ChinatSchool of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798

E-mail: blackmil @vip.sina.com; chcai@hqu.edu.cn; ekkma@ntu.edu.sg

Abstract-In this paper, a layered tree-based multiple descrip- al. [7] explored another zerotree-based MDC scheme, denotedtion coding framework, called the layered spanning multiple de- as MD-SPIHT, by inserting the protection information ofscription coding (LSMDC), is proposed to exploit the advantages one zerotree into more than one packets. Servetto et al.from both multiple description coding and layered coding. With atree-structured codec system, the wavelet coefficients are encoded [8] provided a coding scheme by combnilng MDSQs withto form one base layer and multiple enhancement layers followed subband coders. A JPEG2000 compatible MDC scheme, de-by the use of an X-tree codec individually. Each layer consists of noted as CWJ2000, was proposed in [9] to generate a set ofthe codewords from one or more coding passes. To generate rate-distortion optimized multiple descriptions. Based on themultiple descriptions, codewords are partitioned into several unequal-loss-protected MDC subband coding for the packet-sub-layers according to the importance of related coefficients.The data structure of the proposed LSMDC is organized in a erasure envlronment, another subband MDC scheme, namedlayered spanning tree graphical expression, and each description unequal loss protected packetized MDC, was proposed in [10].is formed by combining codes along a path from the root of the Layered coding provides a convenient way for the hetero-tree to one of its leaves. Simulation results have shown that the geneous client bandwidths and the rate control for dynamicperformance of the proposed LSMDC codec outperforms existing network congestion [ 1]. In order to take the advantages ofstate-of-the-art multiple description codecs in terms of less center both multiple description coding and layered coding, Chou etand side distortions.

al. [12] proposed a layered multiple description coding frame-I. INTRODUCTION work. To provide a better coding efficiency trade-off between

A robust transmission of audio and video streams over noisy the base layer and the enhancement layers, Stankovic et al.communication channels/networks is imperative to many video [13] developed another layered-based MDC by minimizing theapplications. An efficient and error-resilient coding scheme maximum performance loss. To further exploit the advantagesis often highly desirable in the transmission system. As an of both multiple description coding and layered coding, a noveleffective means to combat packet loss and transmission errors, MDC scheme, called the layered spanning multiple descriptionmultiple description coding (MDC) has been proposed for coding (LSMDC), is proposed in this paper. Different fromtransmitting multimedia streams over packet-erasure networks the state-of-the-art [12]-[13], a layer is partitioned into severalin a variety of application scenarios [1]. In the framework of sub-layers, and then, these sub-layers are copied into a singleMDC, source data are coded to form multiple self-decodable or multiple descriptions according to their importance.bitstreams (referred as descriptions in MDC) and then trans- The rest of this paper is organized as follows. Section IImitted to the receiver over diverse channels. The MDC codec describes the proposed MDC framework. Section III showsis designed in such a way that if only one description is some simulation results to demonstrate the performance of theavailable, the decoder is still able to reconstruct the source proposed algorithm. Section IV concludes the paper.data with an acceptable quality. The quality is incrementally II THE LAYERED SPANNING MULTIPLE DESCRIPTIONimproved with the availability of more descriptions. If all the CODINGdescriptions are received correctly, the decoder can achieve ahighest-fidelity reconstruction. A. Bi-layer Bi-description Coding (BBC) - the simplest lay-The first MDC scheme, multiple description scalar quan- ered spanning MDC framework

tizer (MDSQ), was proposed by Vaishampayan [2]. Battlo The simplest framework of the layered spanning MDCand Vaishampayan [3] introduced multiple description trans- is an MDC with two layers and two descriptions, which isform coding (MDTC) with theoretic rate-distortion results for called the bi-layer bi-description coding (BBC) in this paper,sources with memory. Wang et al. [4] proposed a pairwise and shown in Fig. 1 (a), where DWT denotes the discretecorrelating transform to introduce dependencies between two wavelet transform; CQ and FQ represent the coarser quantizerdescriptions transmitted over different channels. Based on the with a larger stepsize and the finer quantizer with a smallerzerotree MDC framework, Jiang and Ortega [5] proposed the stepsize, respectively; CQ-1 stands for the inversed operationpolyphase transform and selective quantization (PTSQ), which of CQ; {2 represents a down-sampling process; Z-1 is a shiftpartitions zerotrees [6] into multiple phases and generates (delay) operator; XT denotes an X-tree encoder; MUX is aindividual description through a combination of the total multiplexer.information of one phase and the redundant information of An X-tree [14], as shown in Fig. 2, is a hierarchical inter-another. To strengthen the error-resilience capability, Miguel et band quadtree, and it is similar to a zerotree [6]. However,

O-7803-9733-9/06/$20OO©t2006 IEEE947

Description I LL3 HL3Input S E <HL2* _F;_ 3 tM:UX fL:H < \ HL1image <y1

+XLHI2X \H2

k =2

LHI HIDescription 2

(a) (b)

Fig. 1. (a) The encoder block diagram of the bi-layer bi-description coding(BBC), (b) A binary-tree representation of the BBC

Fig. 2. Hierarchical inter-band quadtree

unlike the original zerotree with zero-valued roots, the rootsof an X-tree can be one of the following three cases: a operation.positive number, a negative number, or a zero. The wavelet . Step 6: Let i i + 1, and if i <N go to Step 2.coefficients are first coarsely quantized via CQ and then coded From the above discussion, it is clear that the coefficientsby an X-tree encoder to produce the primary information. after coding, in fact, are the residues between the originalThis primary information is duplicated in both descriptions to wavelet coefficients and the dequantized coarsed coefficients.protect the key information of the source. The original wavelet The selection of To depends on the bit rate used in the basecoefficients are then subtracted by the dequantized coarsed layer. The coding of two enhancement layers is performedcoefficients, and the resulting residues are subsampled through in the similar way. For expression convenience, the codingtwo paths (one with a delay) and requantized by using FQs to process for a given threshold (from Step 2 to Step 6) isform two enhancement layer bitstreams. Finally, the outputs of considered as one coding pass.the FQs are multiplexed with the primary information to form For the ease of follow-up algorithm development, let usmultiple descriptions for being transmitted through different symbolize the above layered coding process (a quantizer andchannels. an XT in Fig. 1) (a) as a node, and denote the subsample

If both channels are available in the receiver, wavelet process (a down-sampler alone or the combination of a shiftcoefficients can be reconstructed from the central decoder operator and a down-sampler in Fig. 1) (a) as a branch. Fig. 1with the base layer information and all the enhancement can be graphically view as a binary tree with one parent node,layer information from both channels. If only one channel is two branches, and two children nodes, which shown in Fig. 1available, the wavelet coefficients can still be reconstructed (b).from one of the side decoders with all information from thebase layer and some enhancement layer information from the B. The Layered Spanning Multiple Description Codingavailable channel. The above-mentioned tree expression for the BBC canFrom the Fig. 1, one can see that the encoder structure of be easily extended for building up multi-layered multiple

the proposed MDC is similar to a SNR scalability encoder, descriptions with k branches from each node, where k denotesexcept that the enhancement layer is now divided into diverse that the next enhancement layer is partitioned into k sub-bitstreams, and the base layer information is duplicated into layers, according to the level of layers and the total number ofboth descriptions. descriptions. To clarify the encoding procedure, the number of

With an X-tree subband codec, the base layer encoding coding passes in the layer is labeled inside the correspondingprocess is as follows: node. Since the framework of the MDC depends on the

* Step 1: [Initialization] For all wavelet coefficients xj, partition of layers, or the layered tree, this MDC scheme isselecting To, such that To/2 < max xj < To. Let i = 1. named the layered spanning MDC (LSMDC).

* Step 2: [Thresholding] Ti =Ti1/2. Fig. 3 illustrates two examples of the four-layer LSMDC* Step 3: [Significance map generation] Compare each schemes. Both MDC schemes generate 16 descriptions. For

coefficient xi with Ti to determine its significance; If notation convenience, LSMDC1 denotes the LSMDC schemexj ) Ti, it is significant (marked by "1"), otherwise, it in Fig. 3 (a), and LSMDC2 denotes that in Fig. 3 (b). Fromis insignificant (marked by "0"). this figure, one can observe the following. First, the base layer

* Step 4: [X-tree generation] Check the zeros in the signif- (BL) of each scheme includes the first two coding passes;icance map to build all the X-trees. the encoding process of the first enhancement layer (EL-1)

* Step 5: [Coefficient encoding] Only the X-tree roots and includes n (or m) coding passes, where n (or m) depends onisolated coefficients (not included in any X-tree) need the total coding pass number (Pass No.), which relies on theto be coded. Set the coded significant coefficients xj as bit rate. Second, the residues of the base layer is divided intoxj MOD TN, where N is the number of coding pass, k1 parts (here, k1 = 4) to form the EL-i layer. All the nodes atTN is the smallest threshold, MOD performs modulus the EL-i are further divided into k2 parts to form the second

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Layer Pass No. Pass No.

BL: 1 2 1 2

EL-1: 37+4 2n + 2 2 rn+...r3m + 2 4 4 4 4 4 42 = 2 2= 2 2 22 2 2+2 2\222 22222222 2 2 2 =2

fEL-2: n + 3, n + 4 2 i(X td(3 j + 3, mw+ 6 .()()( t()( X1~~~~~~~~~~~~~~~~~~~~~~~~ .k'3 - 2.0. .- -' ... 0'0(a) (b)

Fig. 3. Two spanning tree examples for the proposed LSMDC encoder: (a) LSMDC1; (b) LSMDC2

(a) (b) (c)Fig. 4. Simulation results yielded by the proposed BBC algorithm on "Lena" (bit rate = 0.5 bpp): (a) Only channel I is available (32.43 dB); (b) Only channel2 is available (33.04 dB); (c) Both channels are available (36.15 dB).

enhancement layer (EL-2), which is subject to further partition, spanning tree is only applied to the root of the tree. Moreover,and so on. Note that parameters kl, k2 and k3 are variables, LSMDC intrinsically embodies the advantages of both layeredand their products equals to the total number of descriptions, and multiple description coding.i.e., Hki = 16, in the examples demonstrated in Fig. 3. Third,the codes contributed by all the nodes along a path from the I SIMULATION RESULTS AND DISCUSSIONSroot (the BL) to one of the leaves (a part of the EL-3 in these Experiments were performed on a popular 512 x 512 8-two structures), form a description. bit gray scale image "Lena" to verify the effectiveness of the

Fig. 3 shows the process of generating descriptions: 1) the proposed LSMDC method. In all our experiments, the 9/7information contributed from the base layer is of utmost im- bi-orthogonal wavelet filters [15] is used to conduct a five-portant and duplicated into all descriptions; 2) the information level pyramid wavelet decomposition. Furthermore, the X-treefrom the EL-1 is also critical and heavily protected; 3) the codec incorporates the arithmetic coding [16].rest enhancement layers (i.e., the EL-2 and EL-3) are not so A. Simulation Results by BBCimportant and separated into diverse descriptions. To comparethe error resilient ability between Fig. 3 (a) and Fig. 3 (b), Fig. 4 shows the reconstructed "Lena" images resulted bysuppose coding pass numbers of the two LSMDCs be the using BBC at a bit rate of 0.5 bpp and with about 25%same, i.e., n + 6 = m + 8, the relationship between n and redundancy rate. The redundancy rate p is defined as follows:m in Fig. 3 follows the equation: n = m + 2. For example, let p = (Ri + R2 - RO)IRo (l)the total number of coding pass equals to 10, then n = 4, andm = 2. Hence, the outcomes of coding pass 5 and 6 in Fig. 3 where R1 and R2 stand for the bit rates used in both de-(a) belong to the first enhancement layer, and are exported to 4 scriptions, respectively, Ro is the desired bit rate by a normaldescriptions; whereas, those in Fig. 3 (b) belong to the second (single description) codec with the same distortion as theenhancement layer, and are only exported to 2 descriptions. outcome of the center decoder.As a result, the LSMDC1 possesses stronger error resilient Fig. 5 displays the simulation results obtained by usingability than LSMDC2. PTSQ [5], MDSQ subband coding (MDSQSC) [8], CWJ2000

Since the layer number, the number of coding pass per layer, [9] and the proposed BBC, respectively. The first two areand the partition style are changeable for different application state-of-the-art MDC methods, and CWJ2000 exploits the rate-scenarios, LSMDC is of flexibility. For example, BBC can allocation strategy embedded in the JPEG 2000 encoder, andbe considered as a degenerated case of LSMDC, where the get good results. The comparison with them is worthwhile.

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paper, called the layered spanning multiple description codingm (LSMDC) for image and video transmission over the noisy

channels. In this work, a bi-layer, bi-description codec is first_ 39 ... . . - ........................................z introduced and served as the basic structure to establish multi-

n38.5[ s _ 4 layer, multiple-description codec system, called the layeredo " " spanning MDC. By choosing different spanning tree struc-

o 38 ........... 'm. tures, two examples of LSMDC schemes are presented withan X-tree-based codec. Simulation results have verified theerror-resilient ability of our proposed MDC. Last but not least,

a) 37 -B- C\\J2000 I ....'V the design makes it possible for one to optimize the layer-36 -Ml),QSC tree structure and the total number of descriptions to form an'35 35.5 36 36.5 37 adaptive MDC framework.

Side Distortion PSNR (dB)V. ACKNOWLEDGMENT

Fig. 5. Simulation results by the proposed BBC, PTSQ and MDSQ Subband This work is partially supported by the National Natu-Coding on "Lena" (2 descriptions, bit rate = 1.00 bpp) ral Science Foundation of China under grant 60472106 and

the Fujian Province Natural Science Foundation under GrantA0410018.

................................... 'R

[1] V.K. Goyal, "Multiple description coding: compression meets the net-

-a 32qwork," IEEE Signal Processing Magazine, vol. 18, no. 5, pp. 74-93, Sept.t - *> \'^2 t ~~~~~~~~~~~2001.

Z > ~ ) [2] V.A. Vaishampayan, "Design of multiple description scalar quantizers,"CO) . <s .IEEE Trans. Information Theory, vol. 39, no. 3, pp. 821-834, May 1993.

n30 ................ E- -[3] J.-C. Battlo and V. Vaishampayan, "Asymptotic performance of multipledescription transform codes," IEEE Trans. Information Theory, vol. 43,

28 .eo LSMDC2 -. 'no. 2, pp. 703-707, Mar. 1997.-A- MD-SPIHT " [4] Y. Wang, M.T. Orchard and A.R. Reibman, "Multiple description image.-E-PTSQ Ez coding for noisy channels by pairing transform coefficients," The First

IEEE Workshop on Multimedia Signal Processing, Princeton NJ, USA,Number of descriptions lost pp. 419-424, June 1997.

[5] W. Jiang, and A. Ortega, "Multiple description coding via polyphasetransform and selective quantization," Visual Communications and Image

Fig. 6. Simulation results by the PTSQ, MD-SPIHT and two proposed Processing (VCIP), San Jose, CA, USA, pp. 998-1008, Jan. 1999.LSMDCs on "Lena" (16 descriptions, bit rate = 0.50 bpp) [6] J.M. Shapiro, "Embedded image coding using zerotrees of wavelet

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In the coordinates of the side distortion versus the center [7] A.C. Miguel, A.E. Mohr, and E.A. Riskin, "SPIHT for generalized mul-tiple description coding," International Conference on Image Processing

distortion, the upper the performance curve lies, the better (ICIP), Kobe, Japan, pp. 842-846, Oct. 1999.the error-resilience achieves. One can see from Fig. 5 that the [8] S.D. Servetto, "Multiple description wavelet based image coding," IEEE

proposed*BBCalgorith consistently outperformed the other Trans. Image Processing, vol. 9, no. 5, pp. 813-826, 2000.[9] G. Olmo and T. Tillo, "A novel multiple description coding scheme

three for the target rate of 1.0 bpp. compatible with the JPEG2000 decoder," IEEE Signal Processing Letters,no. 11, pp. 908-911, Nov. 2004.

B. Simulation Results by LSMDC [10] J. Chen, and C. Cai, "Unequal loss protected packetized coding," VisualTo evaluate the robustness of the proposed LSMDC scheme, Communications and Image Processing (VCIP), Beijing, China, pp. 1018-

1024, July 2005.some descriptions are randomly removed to emulate the [11] R. Signh, A. Ortega, L. Perret, and W. Jiang, "Comparison of multiplepacket loss. The simulation results of the proposed LSMDC1, description coding and layered coding based on network simulations,"LSMDC~ PTS [5]and MD-SPIHT [7] are shown in Fig. 6. Visual Communication and Image processing (VCIP), San Jose, CA,LSMDC2, PTSQ [5] and MD-SPIHT [7] are shown in Fig. 6. USA, pp. 3974:929-939, June 2000.

The figure shows that 1) both the demonstrated MDC schemes [12] P.A. Chou, H.J. Wang, and V.N. Padmanabhan, "Layered multipleshow a fairly good error-resilience and greatly outperform description coding," In Proc. 13th Int. Packet Video Workshop, Nantes,PTSQ; 2) if only one or two descriptions get lost, LSMDC2 France, Apr. 2003.PTSQ;2'if only one or two descriptions get lost, LSMDC2~ [13] V. Stankovic, R. Hamzaoui, Z. Xiong, "Robust layered multiple descrip-offers the best result; 3) if more than two descriptions get lost, tion coding of scalable media data for multicast," IEEE Signal ProcessingLSMDC1 achieves the best performance. This is in line with Letters, vol. 12, no. 2, pp. 154-157, Feb. 2004.the fact as described earlier that LSMDC1 is more protected [14] C. Cai, S.K. Mitra, and R. Ding, "Smart wavelet image coding: X-treeapproach," Signal Processing, vol. 82, no. 2, pp. 239-249, Feb. 2002.than LSMDC2; thus, possessing stronger error-resilient ability. [15] M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, "Image coding

using wavelet transform," IEEE Trans. Image Processing, vol.1, pp. 205-221, Apr. 1992.

IV. CONCLUSION [16] I.H. Witten, R.M. Neal, and J.G. Cleary, "Arithmetic coding for datacompression," Communun. ACM, vol. 30, pp. 520-540, June 1987.

Based on the methodology of the layered coding, a newmultiple description coding framework is proposed in this

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