Wireless multicasting of video signals based on distributed compressed sensing

Wireless multicasting of video signals based on distributed compressed sensing

Signal Processing: Image Communication 29 (2014) 599–606 Contents lists available at ScienceDirect Signal Processing: Image Communication journal ho...

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Signal Processing: Image Communication 29 (2014) 599–606

Contents lists available at ScienceDirect

Signal Processing: Image Communication journal homepage: www.elsevier.com/locate/image

Wireless multicasting of video signals based on distributed compressed sensing Anhong Wang a,n, Bing Zeng b,n, Hua Chen a a

Institute of Digital Media and Communications, Taiyuan University of Science and Technology, 66 Waliu Road, Taiyuan, Shanxi, China Institute of Image Processing, University of Electronic Science and Technology of China, 2006 Xiyuan Avenue, Hi-Tech (West) Zone, Chengdu, Sichuan, China b

a r t i c l e i n f o

abstract

Article history: Received 30 September 2013 Received in revised form 14 March 2014 Accepted 14 March 2014 Available online 21 March 2014

Multicasting of video signals over wireless networks has recently become a very popular application. Here, one major challenge is to accommodate heterogeneous users who have different channel characteristics and therefore will receive different noise-corrupted video packets of the same video source that is multicasted over the wireless network. This paper proposes a distributed compressed sensing based multicast scheme (DCS-cast), where a block-wise compressed sensing (BCS) is applied on video frames to obtain measurement data. The measurement data are then packed in an interleaved fashion and transmitted over OFDM channels. At the decoder side, users with different channel characteristics receive a certain number of packets and then reconstruct video frames by exploiting motion-based information. Due to the fact that the CS-measuring and interleaved packing together produce equally-important packets, users with good channel conditions will receive more packets so as to recover a better quality, which guarantees our DCS-cast scheme with a very graceful degradation rather than cliff effects. As compared to the benchmark SoftCast scheme, our DCS-cast is able to provide a better performance when some packets are lost during the transmission. & 2014 Elsevier B.V. All rights reserved.

Keywords: Video multicast Compressed sensing Graceful degradation Distributed video coding

1. Introduction Wireless video multicast services, such as mobile TV, media sharing, broadcasting of sport events, and hot news at airport, have recently increased very rapidly, aiming at simultaneous broadcasting of a video sequence to multiple users through wireless connections. However, since these users have different channel characteristics, including different channel noise, different bit-rate they can support, and packet-loss that is usually unavoidable, they would rarely get the performance that is expected for their individual channels if the video source is not properly coded and/or the transmission is not well arranged.

n

Corresponding authors. E-mail addresses: [email protected] (A. Wang), [email protected] (B. Zeng). http://dx.doi.org/10.1016/j.image.2014.03.002 0923-5965/& 2014 Elsevier B.V. All rights reserved.

In traditional wireless video multicast, scalable video coding (SVC) [1,2] and multiple description coding (MDC) [3,4] have been used for source coding. However, the SVC scheme has the following disadvantages: (1) it sacrifices the compression efficiency to achieve scalability; and (2) it only provides limited choices of base layer and enhancement layer rates so that it may cause severe cliff effects when the channel changes continuously. When applying an MDC scheme to a wireless video multicast, it means transmitting packets through different channels with specific bit-rates, and hence packets would only reach receivers that can support the matched bit-rate. In this sense, MDC is not suitable for broadcasting packets to receivers with highly-diversified channels. Recently, Jakubczak et al. proposed a new multicast method called SoftCast [5,6], featuring one-size-fit-all video multicast over wireless. SoftCast consists of three steps at the sender side: block-wise discrete cosine transform

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(DCT), power allocation, and whitening. DCT removes intraframe redundancy of a video frame. Then, optimal power allocation is implemented to get the minimum total distortion by scaling the transform coefficients. Finally, whitening generates packets with equal power and importance (on average). SoftCast transmits packets directly over an analog channel without quantization, entropy-coding, and FEC (of any kind); and achieves a graceful degradation because of the power allocation and whitening used in the scheme. More recently, Fan et al. proposed the D-cast scheme [7] that shows a better performance than SoftCast. However, D-cast transmits the middle bins and low significant bit (LSB) in different ways (one in digital transmission and another in analog SoftCast transmission, respectively), which leads to different recovered qualities when users with the same bandwidth receive different packets. Alternatively, motivated by the theory of compressed sensing (CS) [8–10], Markus et al. proposed a new multicast system [11]. It compared different measure matrices Φ and sparse bases Ψ for encoding of multicast, and used the reweighted ℓ1 minimization for decoding. However, it does not make full use of the inter-frame correlation at the decoder. Meanwhile, the distributed compressed sensing (DCS) scheme has been proposed [12–14], which exploits the temporal correlation of video frames at the decoder side. For the same goal, Li et al. proposed a video coding using CS for wireless communications [15]; Xiang et al. proposed a scalable video coding architecture based on compressed sensing (SVCCS) [16]; and Pudlewski et al. presented the design of a sensor network based on the CS theory [17]. However, how to maintain good performance of the CS-based schemes in the wireless video multicast scenario still present us with many challenging problems. In this paper, we extend the DCS idea to the wireless multicasting of video signals to construct our DCS-cast scheme. To keep the encoder simple – an intrinsic requirement in distributed video coding (DVC) systems, we apply the block-wise compressed sensing (BCS) scheme on each video frame to generate the measurement data. These data are then packetized in an interleaved fashion. All packets are sent to the users in a multicast group over a noisy OFDM transmission channel, assuming a certain packet loss ratio during the transmission. Upon receiving certain packets successfully, each user will run the linear least square estimation (LLSE) algorithm [18] for de-modulation and then make use of motion information to help reconstruct video frames with the motion-compensated blockwise compressed sensing combined with the smoothed projected Landweber reconstruction algorithm (MC-BCS– SPL). We present extensive experimental results to show that our DCS-cast scheme achieves a better performance when compared with SoftCast whenever certain packets are lost during the transmission.

2.1. Compressed sensing Suppose that a signal x A RN is K-sparse with respect to an orthogonal basis Ψ A RNN , the CS theory tells us that x can be reconstructed from M measurements by solving an ℓ1 -based convex problem, where M ¼ Οðlog N=KÞ , K o M 5 N. The encoding and decoding of the CS process can be formulated as y ¼ Φ  x ¼ Φ  ðΨ  θÞ

ð1Þ

θ^ ¼ argmin jjθjj 1 s:t: y ¼ Φ  x

ð2Þ

θ

where Φ is the M  N measurement matrix incoherent with the transform matrix Ψ, θ is the transform coefficients, and y denotes the measurement vector with measurement rate r ¼ M=N. Several methods, such as basis pursuit [19] and orthogonal matching pursuit (OMP) [20], have been proposed to ^ Then, x^ can be reconstructed as x^ ¼ Ψ  θ. ^ solve θ. 2.2. BCS–SPL When CS is applied to a whole image or video frame, the resulting requirement for storage and real-time transmission becomes huge. To solve this problem, Gan introduced a block-wise compressed sensing (BCS) [21]. Later on, Mun and James combined BCS with the smoothed projected Landweber reconstruction algorithm (BCS–SPL) [22], which uses a smooth filter and iterative-thresholding to deal with block artifacts in BCS. In the BCS–SPL method, suppose that an original image has N pixels with M measurements taken. The image is first divided into blocks, each of size B  B. Each block is first converted into a vector xj (of length B2 ) and then sampled using the same matrix ΦB to obtain yj ¼ ΦB Uxj ¼ ΦB U ðΨ  θj Þ

where θj and yj are, respectively, the transform coefficient vector and measurement vector of the jth block, yj is with 2

2

2

length M B ¼ jM=N U B2 j, Ψ A RB B , and ΦB A RMB B is chosen to be orthonormal, i.e., ΦB UΦTB ¼ 1. The equivalent measurement matrix Φ for the entire image is a blockwise diagonal one: 2 3 ΦB 6 7 ⋱ Φ¼4 ð4Þ 5 ΦB At the decoder side, given some initial approximation xð0Þ , x^ ¼ WienerðxÞ, then x^ is updated via block-wise successive projection and thresholding operations as follows: ðiÞ

ðiÞ ðiÞ 1 ^ θ^ j ¼ θ^ j þ  Ψ  1  ΦTB  ðyj  ΦB  Ψ  θ^ j Þ γ

2. Background Since our work is largely based on the CS theory, we first review it briefly in this section, and then outline two extensions, namely block-wise compressed sensing (BCS) and distributed compressed sensing (DCS).

ð3Þ

ðiÞ θ^ j ¼

8 < θ^^ ðiÞ ; j

: 0;

^ jθ^ ðiÞ j j else ðiÞ

Z τðiÞ

ð5Þ

ð6Þ

ðiÞ

xðij þ 1Þ ¼ Ψ  θ^ j þ ΦTB  ðyj  ΦB  Ψ  θ^ j Þ

ð7Þ

A. Wang et al. / Signal Processing: Image Communication 29 (2014) 599–606

Here xðij þ 1Þ is the jth reconstructed block at the ði þ1Þth iteration; γ is a scale factor and chosen to be the largest eigenvalue of ΦB U ΦTB and τðiÞ is a threshold used at the ith iteration. In our scheme, ΦB is chosen to be an orthonormal random Gaussian matrix so that the eigenvalue of ΦB UΦTB is 1. Since BCS–SPL is based on block image acquisition, only block measure matrix needs to be stored, which greatly saves the storage space and improves the reconstruction speed. In addition, BCS–SPL combines a Wiener filter to the SPL algorithm, thus offering a much smoothed reconstruction.

2.3. Distributed compressed sensing The distributed compressed sensing (DCS) scheme is proposed according to the principle of a distributed video coding (DVC) system, i.e., keeping a low-complexity at the encoder side but exploiting the inter-frame motion information at the decoder side to improve the decoded quality of individual frames [12–17]. In particular, a motioncompensated BCS–SPL (MC-BCS–SPL) reconstruction algorithm [23] has been developed, which makes use of multi-directional motion estimation and achieves a better performance in the case of a single user. In our present work, we will integrate the idea of MC-BCS–SPL into practical transmission scenarios (i.e., noisy channel and packet loss) and extend it to wireless multicasting of video signals in the environment of multiple users.

3. Proposed DCS-cast scheme The framework of our proposed DCS-cast is shown in Fig. 1, At the encoder side, we partition each frame into blocks of size B  B, denoted as {xj ; j ¼ 1; …; N} after converting them into 1-D vectors, and apply BCS to generate a number of measurements for each block through multiplication with the same measurement matrix ΦB . Measurements over all blocks in a frame are packetized jointly and then transmitted to different receivers over OFDM channels where we will consider different channel noise-levels and packet loss ratios. At the receiver side, each user receives a different number of packets (depending on its channel characteristics) and then reconstructs its own sparsest version according to a chosen basis set. In particular, some motion information among adjacent frames will be utilized at the decoder side to provide an improved reconstruction quality.

x x

xn

It can be seen from Fig. 1 and the above description that the encoder adopted in our scheme is very simple, which obeys the intrinsic requirement of a DVC system. On the other hand, the complexity has been shifted to the decoder side (mainly due to the extraction of motion information among adjacent frames), which is also very common in DVC systems. In the following, we present the details of each step involved in our DCS-cast scheme. 3.1. Preprocessing We propose to do a simple preprocessing – subtraction of 128 – on each original video frame (of 8-bits pixels). The purpose of this subtraction is to reduce the frame's energy (which would otherwise be very big and therefore consumes a large transmission power). After preprocessing, we also denote the blocks of a frame as {xj ; j ¼ 1; …; N} (without ambiguity). 3.2. Encoding To inherit the intrinsic property of a DVC system, i.e., the encoder being made as simple as possible, each frame is divided into non-overlapped blocks of size B  B; each block is then converted into a 1-D vector xj (with length NB ¼ B2 ) and CS-sampled to get the measurement vector yj by Eq. (3), where 1 rj rN and N is the total number of blocks in each frame. Here, in order to provide the best video quality according to the capability of the best user in a multicast group, we use the full CS-rate for each block, i.e., the measurement matrix ΦB is of size N B  NB , and consequently, a total of NB measurements are generated after the CS-sampling. Furthermore, we propose to use the same measurement matrix ΦB for all blocks. Next, packet formation of the CS measurements from all blocks in each frame is also made as simple as an interleaving across blocks, see Fig. 2. It is easy to see that there are totally NB packets for each frame and each packet contains N CS measurements that nevertheless come from different blocks. To our best knowledge, such a packing strategy, though quite simple/straightforward and being adopted quite commonly in other related applications, is proposed for the first time in the framework of CS-based wireless video multicast. One advantageous feature of this packing strategy is that all resulted packets are equally important, which ensures that losing some packets will not erase any single block completely but rather affect all blocks partially and in an even manner.

y

Packet 1

y

Packet 2

y

Packet N B

B B

B

601

Fig. 1. The framework of our proposed DCS-cast.

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3.3. Raw OFDM channel

3.4. Decoding

Before packets are transmitted over a raw orthogonal frequency division multiplexing (OFDM) channel [24], the measurements in each packet are rounded and then directly mapped into transmitted symbol, whereas no FEC of any kind is employed. Fig. 3 shows the modulation adopted in our work: P s ½k and P s ½k þ 1 are the kth and ðk þ 1Þth data in the sth packet and such pairs of data are directly mapped as the I and Q components of the transmitted symbol. Finally, the PHY layer directly transmits all symbols over OFDM channels in which we will consider different strengths of channel noise in our experimental results. Fig. 4 shows the overall OFDM channel structure in which the modulation is same as that shown in Fig. 3. At the transmitter side, symbols obtained from modulation are inputted into some sub-bands after the serial-parallel converting. Symbols in each sub-band go through IFFT, guard interval insertion, and the parallel-serial converting to get the OFDM signal. Then, the OFDM signal is transmitted over a wireless channel with additive white Gaussian noise (AWGN). At the receiver side, operations that are opposite to what have been done at the transmitter side are carried out. This whole procedure is the same as in the SoftCast scheme.

3.4.1. Trimming of measurement matrix First of all, the measurement matrix ΦB A R NB  NB used at the encoder side need not to be transmitted, as it can be generated exactly by using the same random seed at the decoder side. However, as different users receiver different numbers of packets in the multicasting scenario, a specific measurement matrix need be composed for each individual user before the CS reconstruction. Based on the indices of all received packets, each user's measurement matrix Φu A R MB  NB , where MB ¼ ð1  pÞ  NB and p is the packet loss ratio (different for different users), can be composed by a simple trimming of ΦB , i.e., all rows of ΦB indexed by the lost packets will be removed. Meanwhile, the received packets are de-interleaved to form vectors {yj;n ; j ¼ 1; …; N}. Note that, as compared to the original yj , yj;n has missed some data due to the packet loss, e.g., all blocks will miss their first CS-measured data if Packet 1 in Fig. 2 is lost. Clearly, this is equivalent to using a reduced CS-sampling rate as compared to the full rate used originally on each xj so that the CS reconstruction can take place in the normal way but the resulted reconstruction quality would decrease as compared to the case of using the full rate. 3.4.2. Linear least square estimator (LLSE) Even without any packet loss, all received data over an OFDM channel will be corrupted by channel noise so that the actual data received at each user are

B

B

y^ ¼ y þn B

ð8Þ

where n is a noise vector whose entries are all assumed to be i.i.d Gaussian. We propose to exploit the linear least square estimator (LLSE) so as to reduce the influence of channel noise. To this end, let us denote the covariance matrix of the measurements and the covariance matrix of the channel noise by Λy and Σ, respectively. Then, LLSE produces the noise-corrected measurement data as

NB

Fig. 2. The interleaving-based strategy used to generate packets in DCS-cast.

^ yLLSE ¼ Λy  ðΛy þ ΣÞ  1  y:

Here, the covariance matrix Λy need be transmitted as metadata. It is easy to understand that the resulted overhead remains at a very minimal level since Λy is of size B2  B2 in each frame. In reality, users will always experience the loss of certain packets. Furthermore, each individual user will end up with losing different packets in the multicasting scenario and the number of lost packets will also be different across different

Fig. 3. Mapping data to I/Q components of transmitted OFDM signals.

+11, -28, ... Real value

Modulation

Serial to parallel

ð9Þ

IFFT

Guard interval insertion

Parallel to serial AWGN channel

+11, -27, ...

Demodulation

Parallel to serial

FFT

Guard interval removal

Fig. 4. Raw OFDM channel structure.

Serial to parallel

A. Wang et al. / Signal Processing: Image Communication 29 (2014) 599–606

users. For the jth block, let us define y^ j;n as y^ j after removing all lost packets; and similarly, nj;n as the noise vector after removing all lost packets. Then, Eq. (9) can be modified as yj;LLSE ¼ Λyj;n  ðΛyj;n þ Σj;n Þ  1  y^ j;n

603

as x^ j ¼ x^ mc;j þ x^ r;j

ð13Þ

ð10Þ

where Λyj;n ¼ E½yj;n  yTj;n  and Σj;n ¼ E½nj;n  nTj;n . Notice that Λyj;n and Σj;n can be derived by trimming Λy and Σ that are both known at the receiver side. Finally, yj;LLSE will be used in the MC-BCS–SPL decoding algorithm as described below.

3.4.3. MC-BCS–SPL decoding The original BCS–SPL decoding algorithm is modified in our work to make use of motion information between a current frame x and its reference frame xref . To this end, we first apply BCS-SPL on each yj;LLSE to obtain an initial reconstruction x^ . Next, block-wise motion vectors are obtained through the full-search algorithm between x^ and xref . Finally, motion compensation is applied to obtained x^ mc . More specifically, for block x^ mc;j , we generate a residual measurement yr;j by applying the same block-based measurement matrix Φu as follows: ymc;j ¼ Φu  x^ mc;j ¼ Φu  ðΨ  θ^ mc;j Þ

ð11Þ

yr;j ¼ yj;LLSE  ymc;j ¼ Φu  ðxj  x^ mc;j Þ ¼ Φu  x r;j

ð12Þ

Finally, x^ r;j is recovered by applying the same BCS-SPL algorithm on yr;j and a new reconstruction of xj is obtained

3.4.4. Multi-directional motion estimation Multi-directional (forward, backward, and bi-directional) motion estimation has also been exploited in our work in order to take the best advantage of motion information within a GOP (group of pictures) structure. Suppose that a GOP size is 2lþ 1: frames 1l perform a forward motion estimation; frames lþ2 2lþ1 perform a backward motion estimation; the center frame lþ1 performs a bidirectional motion estimation, see an example shown in Fig. 5 for GOP size¼7 (l¼ 3). 4. Experimental results In order to evaluate the performance of the DCS-cast scheme proposed in this paper, we have done three sets of experiments: The first is to test the effectiveness of LLSE used in our scheme, the second is to test the motion estimation incorporated in our scheme, and the third is to compare our DCS-cast scheme with the benchmark scheme SoftCast. In these experiments, two standard SIF format videos are used: 150-frame tennis and 125-frame football, which are the same as those tested in SoftCast. Block size 8  8 is used in our experiments; whereas the search window size 21  21 is used for the quarter-pixel motion estimation. The CS measurement matrix ΦB used in our tests is chosen to be orthonormal, i.e., ΦB UΦTB ¼ 1, controlled by a random seed that is known at the decoder side so that the same matrix can be generated; and the discrete cosine transform (DCT) is used as the basis set for the CS-reconstruction at the decoder side. Peak signal to noise ratio (PSNR) is used as the quality metric. Both the noiseless channel and additive white Gaussian noise (AWGN) channels (of different noise levels) are tested in our simulations. The lossless channel is used to test the best-effort network. 4.1. Effectiveness of LLSE

Fig. 5. Inter-frame motion estimation in a GOP with size¼ 7.

At the decoder side, suppose that all packets are received but over OFDM channels with different noise-levels. As demonstrated by experimental results shown in Fig. 6, one can see that our DCS-cast scheme with LLSE consistently

Fig. 6. Effectiveness of LLSE: (a) tennis and (b) football.

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achieves a better performance as compared with the case of without LLSE. In particular, when CSNR is low, the achieved improvement can be as large as 4 dB. We can thus conclude that LLSE indeed plays a very effective role in correcting transmission errors so that the MC-BCS–SPL decoding can produce a (much) better reconstruction quality.



4.2. Inter-frame decoding with motion information Fig. 7 shows the improvement for our DCS-cast scheme with multi-directional motion estimation (i.e., the MC-BCS–SPL algorithm), as compared to the intra-frame decoding (i.e., independent processing of each frame by BCS–SPL). It is clear that the inter-frame decoding has achieved a better performance (about 1 dB) in all cases.



4.3. Comparison with SoftCast We compare our DCS-cast scheme with SoftCast under the same conditions (CSNR and packet loss ratio), with some results shown in Fig. 8. A comparison for visual quality of the 34th frame of Football at CSNR¼ 25 dB is shown in Fig. 9. Based on these results, we can see that our DCS-cast scheme shows the following features:



 It achieves a graceful degradation with respect to various



sources of distortion (packet loss and channel noise) so as to avoid the cliff-effect. In fact, our results are actually

CSNR=20

45

Intra-frame

PSNR

PSNR

30

30 25

20

20

0.2

0.3 P

0.4

0.5

Intra-frame

35

25

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Inter-frame

40

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45

Inter-frame

40

more graceful as compared to the SoftCast scheme. This is based on the fact that the CS-measuring and packing strategy adopted in our scheme are influencing the whole frame in an absolutely even fashion (i.e., no importance-distinguishing); whereas SoftCast can only reach this goal on average (through its power allocation and whitening). As discussed earlier, SoftCast employs a power allocation by optimally scaling transform coefficient to reduce (to the maximum extent) the overall distortion while our scheme simply applies a random projection matrix. From this aspect, it is clear that our scheme uses a simpler encoder and thus fits more into the framework of distributed video coding. Without any packet loss or when the packet loss ratio is very low, SoftCast's power allocation (by scaling) has played a dominant role (by reducing the channel noise) so that its performance becomes better than our DVCcast. However, when the packet loss ratio gets larger slightly, our DVC-cast consistently outperforms SoftCast. This is mainly because the CS-measuring and packing-strategy adopted in our scheme guarantee an equal important over all packets, which cannot be achieved through SoftCast's power allocation. For noiseless channels, our DVC-cast always outperforms SoftCast. Again, this is due to the ensured equalimportance over all packets generated in our scheme. We have done testing over many more video sequences. All visual results (see Fig. 9 for one example) from our

0.6

0

0.1

0.3 P

0.4

0.5

0.6

Noiseless

45

Inter-frame Intra-frame

40 PSNR

0.2

35 30 25 20

0

0.1

0.2

0.3 P

0.4

0.5

0.6

Fig. 7. Comparison between inter-frame and intra-frame decoding for football under different channel conditions: (a) CSNR ¼20 dB, (b) CSNR ¼25 dB, and (c) noiseless.

A. Wang et al. / Signal Processing: Image Communication 29 (2014) 599–606

SNR=20

45

35 30 25 20

Inter DCS-Cast SoftCast

40 PSNR

PSNR

40

SNR=25

45

Inter DCS-Cast SoftCast

605

35 30 25

0

0.1

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0

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Inter DCS-Cast SoftCast

40 PSNR

0.4

P

35 30 25 20 0

0.1

0.2

0.3 P

0.4

0.5

0.6

Fig. 8. Comparison of DCS-cast with SoftCast under different channel conditions.

P=0.5

PSNR=35.41dB

PSNR=27.67dB

PSNR=36.35dB

PSNR=28.42dB

PSNR=33.99dB

PSNR=25.3dB

Soft Cast

Inter DCS-Cast

Intra DCS-Cast

P=0.11

Fig. 9. Visual quality comparison between DCS-cast and SoftCast: the 34th frame of football with CSNR ¼25 dB.

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A. Wang et al. / Signal Processing: Image Communication 29 (2014) 599–606

DVC-cast scheme are significantly better than those obtained from SoftCast. One final remark is necessary before we conclude the paper: although we did not consider a real multicast scenario that needs to define exactly how many users are included in the multicast group, it has been mimicked closely by allowing different packet loss ratios and channel noise-levels because each ratio/noise combination truly represents a specific user. As these combinations can be many, our DCS-cast becomes fully scalable in serving an arbitrary number of users in a multicast group or even multiple multicast groups, where each individual user receives a number of noise-corrupted packets (depending on its channel conditions) and then runs its own reconstruction independently. 5. Conclusions and future works A distributed compressed sensing based video multicast scheme, DCS-cast, is proposed in this paper. DCS-cast has the following features. First, it utilizes the block-wise compressed sensing (BCS) to generate measurements at full rate and adopts an interleaving-based packing strategy to produce equally-important packets. Both steps are very simple so as to maintain a low complexity at the encoder side – an intrinsic requirement of any DVC system. Second, because of equalimportant packets, DCS-cast offers very graceful degradation with respect to various sources of distortion (e.g., packet loss and channel noise). Third, DCS-cast benefits from the motion estimation performed at the decoder side. As compared to the benchmark SoftCast scheme, the extensive experimental results presented in the paper showed that DCS-cast produces a better performance (2 þ dB) as long as some packets get lost during the transmission channel. For future works, we will focus on several aspects as follows: considering different block sizes at the block-wise CS-measuring stage and further developing an adaptive block-size selection, studying the possibility of performing a transform before the CS-measuring and some associated issues (e.g., the CS-rate allocation for different sub-bands because the full rate is not necessary for all of them, the corresponding packing strategy in the transform domain, etc.), using transforms other than DCT as the basis kernels at the decoder side to do the CS-reconstruction, and testing the DCS-cast scheme under more sophisticated network topologies (e.g., fading channels, relays during the transmission, and cross connections among different users). Acknowledgments This work has been supported in part by the National Natural Science Foundation of China (Nos. 61272262 and 61210006), the Shanxi Provincial Foundation for Leaders of Disciplines in Science (20111022), the Shanxi Province Talent Introduction and Development Fund (2011), the Shanxi Provincial Natural Science Foundation (2012011014-3), and the Program for New Century Excellent Talent in Universities (NCET-12-1037).

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