Raptor Codes based Unequal Protection for Compressed Video ...

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Raptor Codes based Unequal Protection for Compressed VideoAccording to Packet Priority

Zhengyi Luo, Li Song, Member, IEEE, Shibao Zheng, Member, IEEE, and Nam Ling, Fellow, IEEE

Abstract—Raptor codes are state-of-the-art forward error correction(FEC) solutions for multimedia transmission, which have been applied tounequal error protection (UEP) of multi-layered media such as scalablevideo coding. In this paper, we address the problem of UEP for single-layered video over packet erasure channels. By exploiting the differentpriorities of video packets inside a group of pictures (GOP) and makingfull use of the good characteristics of standardized Raptor codes at largeblock length, we propose an optimized UEP framework for single-layeredvideo and develop an efficient algorithm to solve it. Simulation resultsshow that significant gains can be obtained by our method in case ofpacket losses.

Index Terms—Raptor codes, visual communications, unequal errorprotection.

I. INTRODUCTION

As existing transmission channels, such as wireless channels, oftensuffer from inevitable transmission errors, ways of robust videotransmission have always been explored for many video applications.One effective way of robust transmission is Forward Error Correction(FEC), which requires no feedback but uses channel codes to mitigatetransmission errors. As different parts of video data usually haveunequal importance, FEC is often applied to unequal error protection(UEP) for better performance.

Traditionally, many UEP methods have been proposed based onconventional channel codes like RS codes. Yang et al. [1] proposeda representative RS codes based UEP method, where source videopackets were divided into many blocks and each block got assigneda decent number of repair packets. Zhang et al. [2] proposed a trans-mission distortion-optimized UEP method. Tillo et al. [3] proposedto pilot the UEP allocation by defining an operational rate distortionfunction. Besides, Ha et al. [4] proposed to employ a perceptualweighting scheme in the FEC assignment to improve the subjectivequality. Moreover, RS codes have also been applied to UEP of multi-layered video such as scalable video coding.

Recently, Raptor codes [5], a new kind of fountain channel codes,have been developed. Compared with RS codes, Raptor codes perfor-m well in the case of large block length and have low complexity ofencoding and decoding. Systematic Raptor codes have been standard-ized and adopted as the FEC codes in the latest multimedia standards[6]. Efforts have also been made to provide UEP with Raptor codes.Ahmad et al. [7] proposed an UEP method based on changingthe degree distribution of the original fountain codes by symbolduplication, but they did not explore in depth its application in videotransmission. Vukobratovic et al. [8] proposed an UEP method for

Manuscript received XXXXX XX, 20XX; revised XXXXX XX, 20XXand XXXXX XX, 20XX. This work was supported by the National 863Program (2012AA011703), the National Key Technology R&D Programof China (2013BAH53F04), NSFC (61221001, 61271221), the 111 Project(B07022) and the Shanghai Key Laboratory of Digital Media Processing andTransmissions. This paper was recommended by Associate Editor Z. He.

Z. Luo, L. Song (corresponding author) and S. Zheng are with theInstitute of Image Communication and Information Processing, ShanghaiJiao Tong University, Shanghai, China (e-mail: [email protected];song [email protected]; [email protected]).

N. Ling is with the Department of Computer Engineering, Santa ClaraUniversity, Santa Clara, USA (e-mail: [email protected]).

scalable video multicast based on expanding window fountain codes,which incorporated a window selection procedure in fountain coding.Cataldi et al. [9] applied UEP based on sliding window Raptor codesto scalable video broadcasting, where source block length was variedwith sliding windows in Raptor coding. Both methods adapt to UEPframeworks by modifying the structure of Raptor codes, which isinconvenient for application level protection and may incur extradifficulties in practice compared with the standardized Raptor codes.Hellge et al. [10] implemented UEP by integrating a layer-aware FECapproach into the Raptor coding process, and they targeted to designRaptor FEC across dependent video layers.

In this paper, we explore the UEP method for compressed videotransmission based on the standardized Raptor codes. By exploitingthe different priorities of video packets inside a group of pictures(GOP) and making full use of the good characteristics of standardizedRaptor codes at large block length, we propose an optimized UEPframework for single-layered video and develop an efficient algorithmto solve it. Experimental results show that significant robustness canbe obtained by our method in case of packet losses.

The remainder of this paper is organized as follows. SectionII presents the preliminaries. Section III describes the proposedstandardized Raptor codes based UEP method. Experimental resultsvalidating the effectiveness of our method are shown in Section IV.Section V draws the conclusion.

II. PRELIMINARIES

In this paper, we treat the video packets of a GOP as a processingunit and regard every video packet as a Raptor source symbol. Thesource video packets are first divided into several classes. Each classthen gets assigned a decent number of repair symbols. Consideringthe practicality aspect, our method is designed based on the standard-ized systematic Raptor codes [6]. Now the loss probabilities and thedistortion impacts of video packets are first estimated.

A. Source Packet Loss Probability

Let ki and ri denote respectively the number of source and repairpackets of class i. Suppose video packets are transmitted over arandom loss channel, whose packet loss rate is pl. The probabilitythat a video packet of class i gets lost finally can be approximatedby

P (ki, ri)

≈ki+ri∑m=0

Cmki+ri

(1− pl)m pl

ki+ri−m · Pf (m, ki) ·Cm

ki+ri−1

Cmki+ri

,

(1)where Cm

ki+ri(1− pl)

m plki+ri−m is the probability that m out

of ki + ri packets are received, Pf (m, ki) represents the failureprobability of the standardized Raptor code with ki source symbols

if m symbols have been received, andCm

ki+ri−1

Cmki+ri

is the probability

that the video packet is not included in the m received packets dueto systematic Raptor codes. Further, the failure probability of thestandardized Raptor codes can be modeled by [11]

Pf (m, k) =

{1 m < k

0.85× 0.567m−k m ≥ k. (2)

2 MANUSCRIPT SUBMITTED TO IEEE TRANSACTIONS ON MULTIMEDIA

I B B P B B P B B P B B P

I=0 I=1 I=2 I=3 I=4

Fig. 1. Illustration of an example GOP structure.

After substituting it into (1), we have

P (ki, ri) ≈ pl ·ki−1∑m=0

Cmki+ri−1 (1− pl)

m pl(ki+ri−1)−m

+pl ·ki+ri−1∑m=ki

Cmki+ri−1 (1− pl)

m pl(ki+ri−1)−m

·(0.85× 0.567m−ki

) . (3)

B. Distortion Impact

Sum of Squared Errors (SSE) is adopted in this paper as thedistortion metric of video packets. Let M denote the number offrames in a GOP, and let W and H denote respectively the framewidth and height. The distortion impact of the jth packet of class ican be expressed as

D (i, j) =

M∑m=1

W∑x=1

H∑y=1

[f (m,x, y)− f̃i,j (m,x, y)

]2, (4)

where f(m,x, y) and f̃i,j(m,x, y) represent respectively the pixelsof the correctly decoded sequence and those of the decoded sequencewith that packet error concealed. If the proposed method is used fornon-real-time applications, the distortion impacts of video packets canbe calculated directly as (4). Otherwise, the distortion impacts canbe estimated by distortion models [12]–[14]. In this paper, based on[12] the distortion impacts of video packets are estimated as follows.

Generally the distortion impact of a video packet is composed ofthe distortion Dcur in the current frame and the drift distortion Ddri

in other frames. After a simulated error concealment operation Dcur

can be obtained easily. If the packet belongs to a non-reference (B)frame, no drift distortion will be induced and its distortion impact is

DNREF = Dcur. (5)

Thus we focus on the video packets belonging to the reference (Ior P) frames. Let Icur denote the reference frame serial number ofthe current packet’s frame. Take the GOP structure in Figure 1 forexample, the maximum reference frame serial number is Imax = 4.The drift distortion in a later reference frame with serial number Ican be estimated as [12]

Ddri,ref (I) = Dcur1− β (I − Icur)

1 + γ (I − Icur), (6)

where β is the macroblock intra update factor and γ is the leakyfactor accounting for the explicit and implicit filtering effects. As noperiodic macroblock intra update is conducted in this paper, β = 0and the drift distortion in the reference frame can be simplified as

Ddri,ref (I) = Dcur1

1 + γ (I − Icur). (7)

Suppose the number of forward inter-coded macroblocks is equal tothe number of backward inter-coded macroblocks in B frames [15].

1 2 3 4 5 6 7 8 9

1 7 2 3 6 8 54 9

reordering

1 2 3 4

Rk1

7

5

k2descending distortion impacts

8

9

6

k3

k3

replace

Fig. 2. Illustration of the UEP method.

Thus the drift distortion in the B frames immediately before the Ithreference frame can be estimated as

Ddri,nref (I) =

NB (I) · 12

[Dcur

11+γ(I−Icur)

+Dcur1

1+γ(I−Icur+1)

], (8)

where NB(I) is the number of B frames immediately before thereference frame and equals to 2 except for the first reference framein Figure 1. Besides, the drift distortion in the B frames immediatelybefore the current reference frame can be estimated as

Ddri,nref (Icur) = NB (Icur) ·1

2Dcur

1

1 + γ, (9)

where NB(Icur) is the number of B frames immediately before thecurrent reference frame. Therefore, the distortion impact of a videopacket in the Icurth reference frame can be estimated as

DREF = Dcur +Imax∑

I=Icur+1

Ddri,ref (I)

+Imax∑

I=Icur+1

Ddri,nref (I) +Ddri,nref (Icur)

. (10)

III. STANDARDIZED RAPTOR CODES BASED UEP METHOD

RS codes usually prefer small block length. When used for UEPof high resolution video data, large number of blocks will incurmany overheads and complicate the assignment of repair packets. Incontrast, Raptor codes have different error resilience properties andare still practical at large block length, which enables us to reform theconventional UEP methods. As mentioned before, our method worksat the GOP level and builds upon the standardized systematic Raptorcodes for better practicality. Though the video packets of a GOP arealso divided into classes in our method, the number of source andrepair packets in each class can be more freely compared with RScodes.

A. UEP Framework

The good effects UEP has on video transmission can be due tothe fact that video packets of different importance receive differentdegrees of protection. But as repair packets are assigned at the classlevel here, it’s necessary to assemble the video packets with similarimportance during classification for more efficient protection. Thuswe introduce reordering [3], [16] into our Raptor codes based UEPframework. After the evaluation of distortion impacts as in SectionII-B, video packets are first reordered in the order of descendingdistortion impacts as shown in Figure 2. Then video packets aredivided into N classes sequentially, which can be Raptor encodedrespectively based on their number of repair packets. At the receiverside, video packets can be first Raptor decoded and then reorganizedas the original order.

Besides, inspired by the generalized skip mode [17] and theslice dropping option [3], we further allow intentional source packetremoval in the Raptor codes based framework. Since packets havebeen reordered in the order of descending distortion impacts, packetsof the last class, which have the lowest distortion impacts, are

3

excluded from transmission so that a corresponding number of repairpackets can be supplemented to protect more important packets underthe same bandwidth budget as shown in Figure 2.

Let ki and ri still denote respectively the number of source andrepair packets of class i. Assume the distortion impacts of videopackets do not correlate with each other for simplicity. As packetsof the last class are excluded from transmission, based on the lossprobabilities and the distortion impacts of video packets in Section IIthe expected distortion impacts of video packets can be approximatedby

D (k1, · · · , kN , r1, · · · , rN−1)

=N−1∑i=1

ki∑j=1

P (ki, ri) ·D (i, j) +kN∑j=1

D (N, j)

=N−1∑i=1

P (ki, ri) ·ki∑j=1

D (i, j) +kN∑j=1

D (N, j)

, (11)

where the first item denotes the expected distortion impacts of the firstN − 1 classes due to packet losses, and the second item denotes thedistortion impacts of the last class due to intentional packet removal.To obtain good video quality, a reasonable objective is to minimizethe expected distortion impacts. Suppose there are K video packets ina GOP, and R extra packets can be transmitted at the given FEC ratio.The expected distortion impacts can be minimized for the optimaldistribution of both the source and repair packets. Note that R+ kNrepair packets will be available as we deliberately replace kN sourcepackets with repair packets. Thus the optimization of the distributionof source and repair packets can be formulated as{

k̂1, · · · , k̂N , r̂1, · · · , r̂N−1

}= argmin

k1,···,kN ,r1,···,rN−1

D (k1, · · · , kN , r1, · · · , rN−1)

s.t.

N∑i=1

ki = K

ki ≥ 0 (1 ≤ i ≤ N)N−1∑i=1

ri = R+ kN

ri ≥ 0 (1 ≤ i ≤ N − 1)riki

≥ ri+1

ki+1(1 ≤ i ≤ N − 2)

, (12)

where riki

≥ ri+1

ki+1is the descending priority constraint ensuring better

protection for more important packets.Like RS codes, Raptor codes can also be viewed as block codes

[18]. Gallager showed that the probability of decoding error Pe forblock codes is bounded by [19], [20]

Pe ≤ e−L·E(R), (13)

where L is the block length and E(R) > 0 is a function dependingon the way of encoding and decoding. Thus large block length helpsthe error resilience of block codes.

It should be noted that RS codes are only practical at small blocklength [21], while Raptor codes have fewer constraints on the blocklength. Based on this consideration, we divide the video packetsinto N = 3 classes to make a good tradeoff between the errorresilience and unequal protection. The first class, which contains themost important video packets, are protected by all repair packets,i.e. r1 = R + k3. Packets of the second class are transmittedunprotectedly, i.e. r2 = 0. Packets of the third class are excludedfrom transmission. In this way, (12) can be converted to{

k̂1, k̂2, k̂3

}= argmin

k1,k2,k3

D (k1, k2, k3, R+ k3, 0)

s.t.

{k1 + k2 + k3 = Kki ≥ 0 (i = 1, 2, 3)

. (14)

Algorithm 1. The hybrid hill-climbing algorithm for (14).Step 1

(k1,b, k2,b) = (0,K);Db = MAX;For k1 = 1 : K

k2 = K − k1;If D(k1, k2, 0, R, 0) < Db

(k1,b, k2,b) = (k1, k2);Db = D(k1, k2, 0, R, 0);

Elsebreak;

EndEnd

Step 2(k1, k2, k3)best = (k1,b, k2,b, 0);D

best= D(k1,b, k2,b, 0, R, 0);

(k1, k2, k3)last = (k1,b, k2,b, 0);D

last= D(k1,b, k2,b, 0, R, 0);

For k3 = 1 : k2,bFor k1 = klast1 : min(klast1 + S,K − k3)

k2 = K − k1 − k3;If D(k1, k2, k3, R+ k3, 0) < D

best

(k1, k2, k3)best = (k1, k2, k3);D

best= D(k1, k2, k3, R+ k3, 0);

EndEndIf Dbest

< Dlast

(k1, k2, k3)last = (k1, k2, k3)best;D

last= D

best;

Elsebreak;

EndEnd(k1,e, k2,e, k3,e) = (k1, k2, k3)best ;

We can see that (14) can be solved by two-dimensional search.

B. Parameter Optimization

To constrain the computational complexity we develop a hybridhill-climbing algorithm as shown in Algorithm 1, which can be splitinto two steps. In the first step, the optimal distribution of sourcepackets (k1,b, k2,b, 0) when k3 = 0 is obtained by one-dimensionalsearch. The search will stop once no gains are obtained. In the secondstep, (k1, k2, k3) is initially set to (k1,b, k2,b, 0). Then we examine atmost S distributions to reduce D in each iteration, where S is set to10 empirically in this paper. The iteration process continues until nogains are obtained. If (k1,e, k2,e, k3,e) denotes the finally obtainedoptimal distribution, we can see that the algorithm needs to evaluateD at most (k1,b + 1) + (k3,e + 1) × S times, which obviously hasa much lower computational complexity than exhaustive search.

C. Discussion

If our method is used in real-time applications, the extra delayresults mainly from distortion estimation, packet reordering, param-eter optimization and Raptor coding. As our method works at theGOP level, the above operations have to be conducted after a GOPdelay, which usually is not long. Distortion estimation in Section II-Binvolves only simple calculations and necessitates only limited time.Packet reordering at the sender and receiver side can be implementedby many efficient algorithms and does not cost much time either.Parameter optimization is solved by a hybrid hill-climbing algorithm,which is expected to converge in an affordable number of steps.Besides, as Raptor codes have linear time encoding and decoding[5], the increased delay by Raptor coding with the adopted blocklength is controllable.

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Last but not least, we find that even if video packets are transmittedin the order of classes, extra overhead bits might not be necessaryto indicate their original order. Take the H.264/AVC standard forexample, H.264/AVC slices, which often correspond to video packets,may have “slice type”, “frame num” and “pic order cnt lsb” fields,which can have respective regularity of values and yield differentvalue triples for different frames in a GOP if video streams areproperly configured. Then at the receiver side, the decoding orderof video packets can be restored according to such information,which enables reordering based UEP to be applied without extra orderindication.

IV. EXPERIMENTS AND RESULTS

Our method was evaluated with the first 300 frames of rep-resentative 1280×720 4:2:0 sequences Crew, Raven, Sheriff andSpinCalendar. We used the JM 14.2 software to obtain H.264/AVCvideo packets of 150 bytes. GOPs of IBBPBBP· · · structure of 25frames were considered, with quantization parameter QP=28 andcontext adaptive binary arithmetic coding (CABAC) adopted duringcompression.

In the experiments, the error concealment algirithm of I frames wasweighted intra interpolation, while that of P and B frames was directframe copy. Video packets were set to be lost independently duringtransmission. As the experimental results with respect to several FECratios are similar, we only show the experimental results under 10%FEC ratio ( R

K+R= 10%) in this paper.

A. Experimental Configuration

To carry out simulation, we needed to figure out the configurationparameters of our method. For example, by fitting the drift distortionof some representative video packets, the leaky factor γ of thefirst GOP of Crew, Raven, Sheriff and SpinCalendar were estimatedrespectively to be 0.0899, 0.0898, 0.0159 and 0.0064, which werethen used for distortion estimation of video packets.

In our method, video packets were divided into 3 classes with thelast class of packets excluded from transmission. At different packetloss rates, the finally obtained configuration parameters of the firstGOP of the test sequences for our method are shown in Table I forillustration. We can see that as the packet loss rate increases, class1 contains decreasing packets and more packets are excluded fromtransmission.

B. Experimental Results

Based on the optimized configuration parameters, our method wascompared with the no protection case, the representative RS codesbased GRIP method [1], the TD-ULP method [2] and the no loss case.The GRIP method adopted the source block length of 64 similar tothe configuration in [1] and did not use the resynchronization scheme.In the TD-ULP method the source block length was also set to 64 andthe motion reference ratio [14] of fractional pixels was divided amongthe nearest integer pixels that had contributed to the interpolation.

At different packet loss rates, the measured PSNR of the testsequences for all methods is shown in Figure 3, where all the reportedPSNR is averaged over 100 simulations. It can be seen that comparedwith GRIP and TD-ULP, obvious gains can be obtained by ourmethod. This is because in our method, repair packets are assignedto the most important video packets in the sense of distortion impactsand large block length helps better error resilience. Besides, byremoving the least important video packets, more repair packets areavailable at the same bandwidth budget and important video packetscan be better protected. Figure 4 shows respectively a reconstructedframe of Crew for each method when the packet loss rate is 0.3,which validates the effectiveness of our method as well.

TABLE ICONFIGURATION PARAMETERS OF THE FIRST GOP OF THE TEST

SEQUENCES

Sequence pl K R k1 k2 k3

Crew

0.1

1653 184

1586 23 440.125 1533 28 920.15 1483 30 1400.2 1380 40 2330.25 1292 33 3280.3 1203 28 422

Raven

0.1

1305 145

1255 14 360.125 1215 16 740.15 1175 19 1110.2 1093 28 1840.25 1016 32 2570.3 947 27 331

Sheriff

0.1

2249 250

2188 11 500.125 2113 22 1140.15 2051 19 1790.2 1920 22 3070.25 1783 35 4310.3 1664 25 560

SpinCalendar

0.1

2494 278

2431 11 520.125 2354 17 1230.15 2275 26 1930.2 2129 31 3340.25 1977 46 4710.3 1840 43 611

V. CONCLUSION

In this paper, UEP based on the standardized systematic Raptorcodes is explored for robust transmission of compressed video. Wecombine the Raptor codes’ practicality at large block length with thepriorities of video packets to give an easy-to-use Raptor codes basedUEP framework, and develop an efficient algorithm to optimize itsconfiguration as well. Significant robustness of video transmissioncan be obtained by our method. Good practicality is also providedthrough the adoption of standardized Raptor codes.

ACKNOWLEDGMENT

The authors would like to thank Pei Wang for providing the sourcecodes of Raptor encoding and decoding, and thank Jia Wang forhelpful discussion.

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5

0.1 0.15 0.2 0.25 0.322

24

26

28

30

32

34

36

38

40

Packet Loss Rate

PS

NR

(dB

)

No LossOurGRIPNo ProtectionTD−ULP

(a)

0.1 0.15 0.2 0.25 0.3

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No LossOurGRIPNo ProtectionTD−ULP

(b)

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Packet Loss Rate

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No LossOurGRIPNo ProtectionTD−ULP

(c)

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Packet Loss Rate

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No LossOurGRIPNo ProtectionTD−ULP

(d)

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6 MANUSCRIPT SUBMITTED TO IEEE TRANSACTIONS ON MULTIMEDIA

(a) (b)

(c) (d)

(e)

Fig. 4. The 20th reconstructed frame of Crew for (a) no protection, (b) GRIP, (c) TD-ULP, (d) our method when the packet loss rate is 0.3, and (e) no loss.