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Scalable Video Multicast UsingExpanding Window Fountain Codes

Dejan Vukobratovic, Vladimir Stankovic, Dino Sejdinovic, Lina Stankovic, Zixiang Xiong

Abstract—Fountain codes were introduced as an efficient anduniversal forward error correction (FEC) solution for datamulticast over lossy packet networks. They have recently beenproposed for large scale multimedia content delivery in practicalmultimedia distribution systems. However, standard fountaincodes, such as LT or Raptor codes, are not designed to meetunequal error protection (UEP) requirements typical in real-timescalable video multicast applications. In this paper, we proposerecently introduced UEP Expanding Window Fountain (EWF)codes as a flexible and efficient solution for real-time scalablevideo multicast. We demonstrate that the design flexibilityandUEP performance make EWF codes ideally suited for thisscenario, i.e., EWF codes offer a number of design parametersto be “tuned” at the server side to meet the different receptioncriteria of heterogeneous receivers. The performance analysisusing both analytical results and simulation experiments of H.264Scalable Video Coding (SVC) multicast to heterogeneous receiverclasses confirms the flexibility and efficiency of the proposedEWF-based FEC solution.

Index Terms—Fountain Codes, H.264 SVC, Scalable VideoMulticast, Unequal Error Protection

I. I NTRODUCTION

Efficient multicast transmission of scalable video contentover lossy packet networks to heterogeneous receivers isstill a challenge. Scalable video coding techniques enablethe receivers to progressively improve reconstructed videoquality with the amount of the data received. This may enablereceivers with increased capabilities (available bandwidth,screen resolution, processing power, etc.) to experience bettervideo quality, while at the same time providing the basicreconstruction quality for low capability receivers. However,even for high capability receivers, packet losses in scalablevideo transmission may significantly deteriorate the quality ofthe reconstructed data. For example, an early packet loss inthetransmission of a typical scalable coded data segment, where

The material in this paper was presented in part at the 45th Annual Allerton2007 Conference on Communications, Computing and Control,Monticello,IL, USA, 26-28. Sept. 2007, and in part at the IEEE International Conferenceon Multimedia and Expo ICME 2008, Hannover, Germany, 23-26.June 2008.

D. Vukobratovic is with the Dept. of Communications and Signal Process-ing, University of Novi Sad, Trg D. Obradovica 6, 21 000 NoviSad, Serbia,phone: +381214750092, fax: +381214752997, email: dejanv@uns.ns.ac.yu.

V. Stankovic and L. Stankovic are with the Dept. of Electronic andElectrical Engineering, University of Strathclyde, Glasgow, G1 1XW, UK,phone: +441415482704, fax: +441415524968, email:vladimir.stankovic,lina.stankovic@eee.strath.ac.uk.

D. Sejdinovic is with the Centre for Communications Research, De-partment of Electrical and Electronic Engineering, University of Bristol,Bristol, BS8 1UB, UK, phone: +441173315100, fax: +441179545206, email:d.sejdinovic@bristol.ac.uk.

Z. Xiong is with the Dept. of Electrical and Computer Engineering, TexasA&M University, 214 Zachry Engineering Center, College Station, TX 77843,USA, phone: +19798628683, fax: +19798624630, email: zx@ece.tamu.edu.

the data importance decreases along the data segment, maylead to severe error propagation. For this reason, the state-of-the-art real-time scalable video distribution systems rely onpowerful forward error correction (FEC) mechanisms at thevideo server side, optimized with respect to the scalable sourceoutput bitstreams (see [1] for an overview of this topic).

Traditionally, Reed-Solomon (RS) codes [2] are appliedas the FEC solution for error-resilient multimedia multicastover networks with packet erasures. Examples are layeredhybrid automatic repeat request (ARQ) and FEC schemes(HARQ/FEC) investigated in [3][4]. Recently, fountain codes[5], such as LT codes [6] or Raptor codes [7], have been pro-posed as a more flexible and efficient solution for scalable datamulticast over lossy packet networks [8]-[12]. Raptor codesprovide linear encoding/decoding complexity and universalcapacity-approaching behavior for any channel packet lossrateat the price of a small reception overhead, as compared to RScodes. These codes have been proposed as application-layerforward error correcting (AL-FEC) solution for large scalemultimedia content delivery in practical systems. Due to theiradvantages in terms of complexity, performance and flexibilityover RS codes applied at the link layer [13], rateless AL-FEC solutions became part of recent standardization effortsin systems such as Multimedia Broadcast Multicast Services(MBMS) within 3GPP UMTS networks [14] and IP-Datacast(IPDC) within DVB-H networks [15].

For delay-constrained applications, such as real-time videostreaming, the fountain encoder cannot make use of its “rate-less” property as proposed in the original framework [5].Indeed, the encoder can produce “only” a finite amount ofencoded symbols per source block before moving to the nextsource block. In this scenario, many receivers might not beable to collect enough encoded symbols to perform successfuldecoding of the source block. In addition, scalable sourcesdonot require that each receiver recovers the entire source block,but as many input symbols as possible from its beginningonwards, because recovering additional symbols progressivelyincreases reconstruction quality. Therefore, we can identifytwo major drawbacks of standard fountain solutions for scal-able video multicast applications, namely: (i) if a minimumamount of encoded data is not received, the iterative decodercan reconstruct a negligible portion of the transmitted videoblock, (ii) standard fountain codes are equal error protection(EEP) codes, whereas scalable video transmission calls forunequal error protection (UEP) FEC schemes due to theunequal importance of data in the scalable bitstream. We notethat recently proposed rateless solutions for scalable videostreaming address these problems by associating separate

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rateless codes for each layer of scalable coded content, therebyincreasing system complexity and achieving UEP performanceby applying rather complex rate allocation algorithms forconstituent rateless codes [8][9][12].

In this paper, we propose a solution for scalable videomulticast based on UEP fountain codes named ExpandingWindow Fountain (EWF) codes [16][17] that addresses bothof the aforementioned problems. The main advantage of EWF-based approach is that it is a “single code” solution with UEPperformance which is analytically predictable using simpleasymptotic analysis [17]. The design flexibility and UEPperformance make EWF codes ideally suited for this scenarioas they offer a number of design parameters to be “tuned” atthe server side to simultaneously satisfy reception conditionsof heterogeneous receivers by exploiting the scalable featuresof the video codec. Following the introductory section, inSection II we provide a short review of EWF codes and relatedanalytical tools for predicting their performance. In Section III,our scalable EWF multicast system setting and EWF codesdesign methodology are presented, supported by numericalexamples of code design optimization. In Section IV, we focuson EWF code optimization for scalable EWF multicast ofscalable coded video stream encoded by recently introducedextension of H.264 AVC video coding standard [18] calledH.264 Scalable Video Coding (SVC) [19]. Both analyticalresults and simulation study are provided, confirming the flexi-bility and efficiency of the proposed EWF-based FEC solution,and excellent matching between theoretical predictions andsimulation results. The paper is concluded in Section V.

II. EXPANDING WINDOW FOUNTAIN (EWF) CODES

Digital fountain framework [5] is a universal capacity-approaching FEC solution for multicasting data over lossypacket networks. Its enabling component, fountain codes, aredesigned with inherent “rateless” property, that is, fountaincodes may potentially produce an infinite stream of encodedsymbols given the input symbols of a finite source block.The framework became a practical solution upon the in-troduction of LT codes [6]. LT codes provide a completerecovery of the transmitted source block, with high probability,for each receiver collecting any set of encoded symbols ofsize slightly larger than the number of input symbols. Theirencoding/decoding complexity is of the orderO(k log k) fora source block of lengthk, due to the average degree ofrobust soliton degree distribution that scales logarithmicallyin k [6]. Raptor codes [7], an improvement over LT codes,are obtained by precoding LT codes defined by degree distri-bution of constant average value with high-rate Low-DensityParity-Check (LDPC) codes [21]. They represent a state-of-the-art fountain solution with excellent performance and anencoding/decoding complexity of the orderO(k). However,standard LT and Raptor codes are EEP codes, because theyplace equal protection on each input symbol from the sourceblock. Recently, fountain code designs with the UEP propertyhave emerged [16][17][20]. In this section, we shortly reviewEWF codes [16][17] as a basis for the proposed scalablemulticast solution.

. . .

. . .

… … … …

. . .

. . .

1 2 k1 k2 ki k = kr

+ + + + + + + + + + + + + + + +

i-th class ofoutput symbols

innermost window

i-th windowoutermost window

Fig. 1. Expanding Window Fountain (EWF) Codes.

EWF codes are a novel class of UEP fountain codes basedon the idea of “windowing” the source block to be transmitted.We assume that, for video streaming applications, EWF codesare applied on consecutive source blocks ofk symbols (datapackets). The set of expanding windows defined over thesource block determines the set of importance classes associ-ated with different quality layers of scalable coded video.Foreach importance class, asymptotic probability (as the sourceblock length tends to infinity) that a symbol of the class is notrecovered afterl iterations of the iterative Belief Propagation(BP) decoder can be determined analytically using simple setof recursive formulea [17] that we review in this section. Thisanalytical tool is a basis for the optimized EWF code designfor scalable video transmission.

The sequence ofr expanding windows where each windowis contained in the next window in the sequence, is definedover the source block (Fig. 1). The numberr of expandingwindows is equal to the number of importance classes of thesource block. We denote the size of thei-th window aski,wherek1 < · · · < kr = k. The most important symbol classof sizes1 = k1 symbols is defined by the “innermost” window,and is protected by all the other windows in the sequence. Thei-th importance class,i ≥ 2, of sizesi = ki − ki−1, is the setof all input symbols that belong to thei-th window, but do notbelong to the (i−1)-st window. The lastr-th window containsall thek symbols of the source block. We compactly describethe division of the source block into importance classes usingpolynomial notation asΠ(x) =

∑r

i=1 Πixi, whereΠi = si

k.

In addition, it is useful to introduceΘi = ki

k=

∑i

j=1 Πj toour notation. The set of expanding windows is characterizedby a window selection probability distribution described bypolynomial Γ(x) =

∑r

i=1 Γixi, whereΓi is the probability

of selecting thei-th window. Finally, a degree distributionΩ(j)(x) =

∑kj

i=1 Ω(j)i xi is associated with thej-th expanding

window, 1 ≤ j ≤ r, and describes the LT encoding processperformed over the data contained in that window.

EWF encoding proceeds in a slightly different fashion thanthe usual LT encoding. To create a new EWF encoded symbol,one of the windows is randomly selected with respect to thewindow selection probability distributionΓ(x). Upon the win-dow selection, a new encoded symbol is determined with anLT code described by the selected window degree distribution

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0 0.05 0.1 0.15 0.2 0.25 0.310

−12

10−10

10−8

10−6

10−4

10−2

100

Γ1

Asy

mpt

otic

BE

R

LIB

MIB − ΩR

MIB − Ωrs

(100, 0.03, 0.5)

MIB − Ωrs

(500, 0.03, 0.5)

Fig. 2. Asymptotic analysis of MIB and LIB BER performance versusΓ1

for FEW (Π(x) = 0.1x + 0.9x2,Γ(x) = Γ1x + (1 − Γ1)x2,Ω(1),Ω(2))EWF code and reception overheadε = 0.05.

as if encoding were performed only on the input symbols fromthe selected window. This procedure is repeated at the EWFencoder for each encoded symbol. More formally, the EWFcodeFEW (Π, Γ, Ω(1), . . . , Ω(r)) assigns each encoded symbolto thej-th window of sizekj with probabilityΓj and encodesthe data from the selected window using the LT code with thedegree distributionΩ(j)(x) =

∑kj

i=1 Ω(j)i xi. Obviously, EWF

code design generalizes the standard LT code design as LTcodes are EWF codes defined by a single window, i.e., all theinput symbols are of equal importance.

In [16][17], the asymptotic erasure probabilities (as thesource block lengthk → ∞) of input symbols belonging todifferent importance classes of EWF codes, afterl decodingiterations of the iterative BP decoder [24], are derived. Evo-lution of the erasure probabilies with the iterations of theBPdecoding algorithm are obtained using the generalized and-or-tree analysis which we summarize in the following lemma(c.f., [16][17]):

Lemma 2.1:For an EWF codeFEW (Π, Γ, Ω(1), . . . , Ω(r)),the probabilityyl,j that the input symbol of classj is notrecovered at the receiver upon collecting(1 + ε)k encodedsymbols, whereε is the reception overhead, afterl iterationsof the iterative BP decoder is:

y0,j = 1

yl,j = e

„

−(1+ε)Pr

i=j

ΓiPi

t=1Πt

Ω(i)′„

1−Pi

m=1 Πmyl−1,mPi

t=1Πt

««

.(1)

For a given EWF code, this lemma outputs the set ofasymptotic recovery probabilities for input symbols of differ-ent importance classes. We will use these probabilities in thefollowing sections, when optimizing EWF codes for scalablevideo source output with respect to selected end-to-end videodistortion measures.

In the following, we present a design example for the simplecase of EWF code with two importance classes. The expres-sions for the erasure probabilities of Most Important Bit (MIB)class and Least Important Bit (LIB) class afterl iterations,yl,1 and yl,2, for an EWF codeFEW (Π1x + Π2x

2, Γ1x +

−0.3 −0.2 −0.1 0 0.1 0.2 0.310

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

overhead ε

Asy

mpt

otic

BE

R

EWF MIB BER

EWF LIB BER

EEP BER

Fig. 3. Asymptotic analysis of MIB and LIB BER performance ver-sus overheadε for FEW (Π(x) = 0.1x + 0.9x2,Γ(x) = 0.084x +0.916x2,Ω(1),Ω(2)) EWF code.

Γ2x2, Ω(1), Ω(2)), with the reception overhead fixed toε, can

be easily obtained from the previous lemma (see [16][17]).For the numerical example, let the code under considerationbe the EWF codeFEW (Π(x) = 0.1x + 0.9x2, Γ(x) =Γ1x+(1−Γ1)x

2, ΩR(x), ΩR(x)) and the reception overheadequal toε = 0.05. In other words, one tenth of the source blockis considered more important, and the degree distributionsapplied on both windows are the same and equal to the“Raptor” degree distribution [7]:

ΩR(x) = 0.007969x + 0.493570x2 +

+ 0.166220x3 + 0.072646x4 + 0.082558x5 +

+ 0.056058x8 + 0.037229x9 + 0.055590x19 +

+ 0.025023x64 + 0.003135x66. (2)

Asymptotic erasure probabilities (assumingl → ∞) for MIBclass,y∞,1, and LIB class,y∞,2, as a function of the firstwindow selection probabilityΓ1, are presented in Fig. 2.The figure demonstrates significant Bit Error Rate (BER)improvement of MIB class over the BER of standard EEPLT codes (that corresponds to the pointΓ1 = 0), withnegligible loss in LIB class BER. The trend of MIB BERimprovement continues until the “threshold” value of the firstwindow selection probabilityΓ1, which equalsΓ1 = 0.084 inthis example, upon which LIB BER deteriorates significantly.Also, Fig. 2 presents an important feature of EWF codes: MIBBER performance of EWF codes improves by enhancing thedegree distributionΩ(1)(x) applied on the MIB window. Inour example, when instead of the Raptor distributionΩR(x),we apply “stronger” but computationally more expensive trun-cated Robust Soliton distributionsΩrs(krs, δ, c) [16][17] withthe maximum degrees bounded tokrs = 100 andkrs = 500,we obtain significant MIB BER performance improvements.

In Fig. 3, for EWF codeFEW (Π(x) = 0.1x+0.9x2, Γ(x) =0.084x + 0.916x2, Ωrs(500, 0.5, 0.03), ΩR(x)), we can trackthe asymptotic erasure probabilities of MIB and LIB classesof source symbols as a function of overheadε of encodeddata collected at the receiver. The figure clearly shows that, ascompared to the standard EEP LT codes, EWF codes enable

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earlier and more reliable recovery of MIB class, for the priceof small deterioration of LIB class recovery performance.

III. SCALABLE V IDEO MULTICAST USING EWF CODES

Digital fountain transmission over lossy packet networksis universally capacity approaching for erasure channel as-sociated with any receiver, given that potentially infiniteamount of encoded symbols can be created at the encoder andsent to the receivers. For real-time scalable video streaming,fountain multicast solutions are usually concerned with twoproblems. First, the amount of the encoded symbols sent isfinite, moreover, for many delay-constrained applicationstheamount of encoded data received by a receiver per sourceblock might be severely limited (e.g., due to low receiveraccess bandwidth, or poor channel conditions). With slightlyless amount of received encoded symbols than needed forsuccessful decoding, the iterative decoder is typically able toreconstruct only a negligible part of the data block transmitted,due to the typical “avalanche decoding” behavior. Second,standard fountain codes are EEP codes, whereas scalable videotransmission calls for UEP FEC schemes due to the unequalimportance of data in the source blocks of scalable bitstream.In other words, when scalable video, e.g., H.264 SVC, iscoupled with existing FEC standards (RS, LT, Raptor) theoutput bitstream loses scalable property, resulting in non-efficient video distribution.

In fountain-based multicast systems proposed in [22], datamulticast transmission proceeds in two phases. In the firstphase, enough encoded packets are sent to facilitate successfuldecoding for most of the receivers. If some receivers cannotcollect enough encoded data to finish decoding, by feedbacksignalling they indicate their participation in the second, repairphase, where only this subset of receivers is fed by a newstream of encoded data. This scheme is suitable for appli-cations that are not delay constrained. In both transmissionphases, the same fountain code is used and all the sourcedata are given the same priority, regardless of the sourcecharacteristics, receiver bandwidths and channel conditions.Alternatively, in [8][9][12], the schemes with independentcodes associated with different enhancement layers of a videostream are proposed. Multiple fountain sources are then allo-cated with different transmission rates providing the overallUEP behavior. However, using multiple fountain codes re-quires rather complex rate allocation optimization and controlof the encoding process. Also, unlike EWF codes which areapplied over the whole source block, separate rateless codesapplied over each enhancement layer are shorter (as each oneis applied over a part of the source block) and therefore lessefficient.

In the following, we describe a scalable EWF-based videomulticast scheme that addresses the aforementioned problemsusing a single-code solution at the transmitter side. The EWFsolution adapts the real-time scalable video stream delayconstraints and unequal data importance to the receptionconditions of heterogeneous receiver classes. Due to UEPand unequal recovery time (URT) properties of EWF codes,reconstruction of the more important parts of the source blockis more reliable and happens earlier.

Sε

1,Rε 2,Rε

rR,ε

Fig. 4. Scalable video multicast to heterogeneous receiverclasses.

A. Scalable EWF Multicast: System Setting

We consider a scenario where a real-time scalable codedvideo stream is transmitted from a video server to a numberof heterogenous receivers over a lossy packet networks, asillustrated in Fig. 4. At the video server side, the scalablecoded video stream is periodically broken into the sourceblocks, and each source block is separately encoded by anEWF encoder. We assume that each source block consists ofan equal number ofk symbols, and that the importance of datadecreases from the beginning towards the end of the block.Typically, each source block contains one group of frames(GOF) of the scalable video information stream. Due to real-time constraints, the video server is able to produce “only”a finite amount of(1 + εS)k EWF encoded symbols beforemoving on to the next source block. The source overhead,εS > 0, is determined by the video server capabilities and/orthe bandwidth of the access link. We assume a setting witha single EWF video streaming server, although by the sameargument as for the standard fountain codes, the system canbe easily implemented with multiple EWF video streamingservers.

EWF encoded symbols are transmitted in a multicast sessionto heterogeneous receivers. We classify receivers intor re-ceiver classes based on their reception capabilities and channelquality. Thei-th receiver class,1 ≤ i ≤ r, is defined by thereception overheadεR,i, where εR,i ≤ εS , i.e., the receiverin the i-th class is able to collect(1 + εR,i)k EWF encodedsymbols for each source block, out of the(1 + εS)k symbolstransmitted. We assume thatεR,i < εR,j if i < j, i.e., thereceiver capabilities increase with the receiver class index i.

The task of the EWF encoder is to supply the receiverswith scalable video source blocks through EWF encoded datastreams. Due to different reception capabilities of differentreceiver classes, our goal is to match the EWF encoded datastream to each receiver class simultaneously, that is, the firstreceiver class (with the worst reception conditions) should beable to recover the first part (the most important part) of thesource block with high probability, the second receiver classshould be able to recover the first two parts of the sourceblock with high probability, etc. To do so, we design EWFcode with r expanding windows by optimizing the set of

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design parametersΠ(x), Γ(x), Ω(1)(x), . . . , Ω(r)(x). EWFencoding with finite source overheadεS is then applied atthe source, across each source block to be transmitted, asdescribed in Section II.

B. Scalable EWF Multicast: System Design

With the described setting, the scalable EWF multicastsystem design reduces to the design of the EWF code suchthat given Quality of Service (QoS) guarantees for different re-ceiver classes are satisfied. In this section, we discuss a generalapproach where, as QoS parameters, we select the probabilitiesof complete reconstruction of different importance classes ofthe source block at the receivers in different receiver classes.In the later sections, the EWF code optimization is furtherextended using more specific video distortion measures.

For a given reception overhead of the receivers belong-ing to the i-th receiver class,εR,i, and the parameters ofselected EWF codeFEW (Π, Γ, Ω(1), . . . , Ω(r)), we can calcu-late (asymptotic) erasure probabilities of input symbols in eachof ther importance classes. Letp

(j)i denote erasure probability

of the input symbol of thei-th importance class at thej-th re-ceiver class. Usingp(j)

i , and under the asymptotic assumptionthat the probabilitiesp(j)

i for different input symbols of thesame class are independent, we can calculate the probabilityP

(j)i that the i-th importance class of the source block is

completely recovered by thej-th receiver class:

P(j)i = (1 − p

(j)i )si , (3)

wheresi is the number of input symbols in thei-th importanceclass of the source block.

We will use the set of probabilitiesP (j)i to define QoS

guarantees for each receiver class of the proposed scalableEWF multicast system. It is worth noting thatP

(j)i < P

(k)i

for j < k due to Lemma 2.1 and εR,j < εR,k; that is,a receiver in the better class will be able to satisfy allthe QoS guarantees imposed on the receiver in the worseclass. Therefore, it is convenient to define QoS guaranteesfor the scalable EWF multicast system as the following setof probabilities:P (1)

1 , P(2)2 , . . . , P

(r)r . In other words, for

the i-th receiver class, we define only QoS guaranteeP(i)i

for reconstruction of the input symbols of thei-th class. QoSguarantees for more important classes of input symbols arealready implicitly included in the QoS guaranteesP

(j)j of the

receiver classes indexed withj < i. For input symbols thatbelong to classesj > i, which are of less importance, thei-threceiver class is not provided with any QoS guarantees.

Before proceeding further, we shortly summarize the EWFcode design problem for scalable EWF multicast system.Our goal is to find the set of EWF code design pa-rameters Π, Γ, Ω(1), . . . , Ω(r) such that the correspond-ing EWF code satisfies the performance thresholdPth =

(P(1)1 , P

(2)2 , . . . , P

(r)r ) for the different receiver classes, given

their reception capabilitiesεR = (εR,1, εR,2, . . . , εR,r). Moredetailed exploration on the possible EWF code design scenar-ios for scalable EWF multicast can be found in [23].

C. Scalable EWF Multicast: Numerical Example

In this subsection, we provide a numerical example for thedesign of EWF codeFEW (Π, Γ, Ω(1), . . . , Ω(r)) that meetsthe requested QoS guaranteesPth for a given reception per-formanceεR. For simplicity, we assume a setting withr = 2receiver classes (i.e., EWF code with two expanding windows),the Most Important Bit (MIB) and the Least Important Bit(LIB) class. We simplify the EWF code design by setting thedistribution on the first window as “stronger” truncated RobustSoliton distribution Ω(1)(x) = Ωrs(krs, 0.5, 0.03), wherekrs = k1 = Π1k, and on the second window the “weaker”constant average Raptor degree distributionΩR(x) (2). Withthese simplifications, the design of the EWF codeFEW (Π1x+(1 − Π1)x

2, Γ1x + (1 − Γ1)x2, Ωrs(Π1k, 0.5, 0.03), ΩR(x))

is determined by two independent variables:Π1 and Γ1 (thefirst window selection probability and the fraction of the datacontained in it). In general, as a result of this design process,we obtain a set (region) of possible(Π1, Γ1) pairs that satisfyrequired QoS conditions. Note that, depending on the valuesof εR andPth, this set can be empty, providing no solutionfor the requested scenario.

As an example, we select the following constraints:εR =(0.1, 1) and Pth = (0.95, 0.8) and the source block lengthof k = 3800 symbols. In other words, we have two classesof receivers: the first, worse class, characterized by the 10%reception overhead, and the second, better class, with 100%overhead. The QoS guarantees require that a receiver in theworse class has a probability of reconstruction of the MIBblock of at least 95%, while a receiver in the better classshould, in addition, be able to reconstruct the LIB block withprobability of at least 80%. The reconstruction probabilitiesof the MIB block for the worse class of receivers,P

(1)1 ,

and the LIB block for the better class of receivers,P(2)2 , are

given as functions of two variables(Π1, Γ1) in Fig. 5(a) and5(b), respectively. In both figures, one can track changes ofprobabilitiesP (1)

1 andP(2)2 which are illustratively represented

by differently shaded gray regions. The solution region of(Π1, Γ1) pairs that satisfy given constraintsεR = (0.1, 1) andPth = (0.95, 0.8) is presented in Fig. 5(c).

From the solution of the given design scenario, which is aset of(Π1, Γ1) pairs, we select operational pair(Π1, Γ1) usinga suitable criterion. One way to proceed would be to select asolution that maximizes theΠ1 value, i.e., to place as much aspossible data into the more important class. In this example,such a solution is the point(Π1, Γ1) = (0.365, 0.205) thattreats 36.5% of the transmitted source block as the moreimportant data. However, other optimality considerationsofpoints in the(Π1, Γ1) region are possible, particularly in thecase when the information source is a scalable video coder.We provide some examples in the following section.

IV. D ISTORTION-OPTIMAL SCALABLE EWF VIDEO

MULTICAST

The design methodology described in the previous sectioncan be applied to any kind of data. As a result, the set of(Π1, Γ1) pairs is obtained that provide QoS performance guar-antees for each class of receivers in terms of the reconstruction

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Π1

Γ1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(a) P(1)1 = f(Π1, Γ1)

Π1

Γ1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(b) P(2)2 = f(Π1, Γ1)

Π1

Γ1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(c) Admissible(Π1, Γ1) region

Fig. 5. The region of(Π1,Γ1) that satisfies given constraintsεR andPth .

probabilities of different importance classes. For a specificcase of a scalable video data, different points from the(Π1, Γ1)region will have different performance in terms of the qualityof the reconstructed video.

Scalable video coders are particularly useful in multicastscenarios, due to the fact that they efficiently accommodatereceivers with different data rates and/or channel conditions.The output bitstream of a scalable video encoder is segmentedinto layers of progressively decreasing importance, so thatreceivers with better reception conditions that receive morelayers, will obtain a higher video quality. This makes ascalable video coder together with a scalable EWF multicastsystem a promising combination for multicast multimediadistribution services. Since EWF codes are a UEP fountainsolution flexible to design, they can be easily adapted to amulti-layer scalable coded bitstream offering more protectionto more important layers. Optimizing EWF codes may beperformed jointly with error-resilience mechanisms at lowerlayers, providing a powerful cross-layer optimized multicastfountain solution.

To select the “optimal”(Π1, Γ1) point from the regionobtained as an output of the EWF multicast system design, weapply the distortion-based optimization that takes into accountthe expected video distortion at the receiving end [1]. Thisper-formance criterion is based on the fact that the reconstructionprocess at a scalable video decoder deteriorates significantlyafter the first transmission error is encountered, due to an errorpropagation effect. Therefore, we adopt the strategy to stopdecoding after detecting the first uncorrected symbol error,and thus use only error-free layers for reconstruction, thoughdifferent error concealment tools can be applied to enabledecoding after a symbol error occurs. However, in this paper,we focus exclusively on error-correcting capabilities of EWFcodes and do not consider any error concealment tools.

We assume that the source block is divided intor layersof lengths s1, s2, . . . , sr symbols. The importance of datacontained in layers decreases from the first towards the lastlayer in the block. Reconstruction of the source block atthe receiver is based on correctly received consecutive layersuntil the first layer for which a channel transmission error isdetected. We denote a probability of correct reconstruction ofeach ofr data layers asP1, P2, . . . , Pr.

The transmission scheme that minimizes the expected dis-tortion of the video reconstructed at the receiver is consideredto be distortion-based optimal. In case of the expected peaksignal-to-noise ratio (PSNR) measure, it is equal to:

PSNRavg =

r∑

i=0

P (i) · PSNR(i), (4)

whereP (i) is the probability that the firsti consecutive layersare correctly received:

P (i) =

1 − P1 for i = 0∏i

j=1 Pj · (1 − Pi+1) for i = 1, 2, . . . , r − 1∏r

j=1 Pj for i = r,(5)

where PSNR(0) = 0, and for i > 0, PSNR(i) is thePSNR upon the complete recovery ofi layers, averaged overall frames of the video segment. Note thatPSNR(i) can beeither calculated off-line, or different models can be used(see[1]). It is worth noting that the average PSNR is a function ofboth the type of a scalable video coder used and the contentof the data transmitted.

In the multicast scenario, where we are dealing with anumber of receiver classes,PSNRavg have to be averagedover all the classes:

PSNRavg =1

r

r∑

j=1

PSNR(j)avg, (6)

wherePSNR(j)avg is the average PSNR at the receiver of the

j-th receiver class.

A. H.264 SVC EWF Multicast: Numerical Optimization

In this subsection, we present an example of the distortion-based optimized EWF code design where the video server ismulticasting H.264 SVC coded video stream. H.264 SVC [19],standardized recently by the Joint Video Team of the ITU-TVCEG and the ISO/IEC MPEG, is the scalable extension ofH.264/AVC [18]. H.264 SVC outperforms previous scalablevideo coders while providing temporal, spatial, and qualityscalability with backwards compatibility with H.264/AVC.Itmaintains key features of H.264/AVC while introducing new

7

TABLE IMIB W INDOW CONTENT FOR H.264 SVCStefanSEQUENCE.

MIB Window k1 Π1 Bit Rate [kbps] Y-PSNR [dB]ContentBL only 400 0.105 292.37 25.79BL + 1 EL 700 0.185 510.65 27.25BL + 2 ELs 875 0.23 636.56 28.14BL + 3 ELs 1155 0.305 839.82 29BL + 4 ELs 1550 0.41 1127.1 29.51BL + All ELs 3800 1 2764.55 40.28

0.08 0.1 0.12 0.14 0.16 0.18 0.232.2

32.4

32.6

32.8

33

33.2

33.4

33.6

Γ1

PS

NR

avg [d

B]

Π1=0.185

Π1=0.23

Π1=0.305

Fig. 6. Numerical example ofΓ1 optimization for the values ofΠ1 =0.185, 0.23, 0.305.

tools necessary for maximizing scalability, such as new inter-layer prediction of motion and residual, the concept of keypictures, single motion compensation loop decoding providinga decoder complexity close to that of single-layer coding.

We use the CIFStefanvideo sequence (30 fps,352× 288)with the base layer (BL) and fourteen enhancement layers(EL) which gradually improve the overall video quality. Thevideo sequence is segmented into GOFs of size 16 frames,and every16/30 seconds the EWF encoder is supplied by anew GOF data as the source block. The source block sizeis approximately190000 bytes and, assuming symbol sizeof 50 bytes, we obtain the source block size ofk = 3800symbols (as analyzed in Section IIIB). We assume that the baselayer is always placed in the first window, with the minimumwindow size necessary to accommodate the base layer dataset tok1 = 400 symbols. Apart from the base layer, we mayplace additional enhancement layers together with the baselayer inside the first window. Several possible divisions intoMIB and LIB data blocks are presented in Table I, where foreach divison, the corresponding values of the first windowabsolute and relative size (k1 and Π1), MIB data bit rate,and the average PSNR of the Y component upon completerecovery of the first window are presented.

We apply the distortion-based optimization on the systemsetting presented in Section IIIC in order to find the optimal(Π1, Γ1) point in the region given in Fig. 5(c). However, as thedivision of the source block into MIB and LIB class is dictatedby the number of ELs placed in the first window, we performthe distortion-based optimization only for the values ofΠ1 thataccommodate BL and whole number of ELs (for example, the

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.7

0.75

0.8

0.85

0.9

0.95

1

Γ1

P1(1

) , P2(2

)

P1(1)

P2(2)

Fig. 7. The set ofΓ1 values satisfyingPth = (0.95, 0.8) for Π1 = 0.23and scenario A.

values ofΠ1 in Table I). Therefore, our optimization problemreduces to the optimization ofΓ1 for a fixed value ofΠ1,for the interval ofΓ1 values such that the pairs(Π1, Γ1) areinside the region in Fig. 5(c). For each pair(Π1, Γ1) and foreach of the two receiver classes defined by their receptioncapabilitiesεR = (0.1, 1), we can calculate the probabilitiesP

(j)1 and P

(j)2 of complete recovery of the MIB and LIB

blocks at thej-th receiver class. Replacing these probabilitiesas the layer reconstruction probabilitiesP1 andP2 in (5), andusing (4) with the appropriate values of PSNRs from TableI, we can calculate the average PSNR values,PSNR

(1)avg and

PSNR(2)avg, for both receiver classes.

Fig. 6 provides an example ofΓ1 optimization for the fol-lowing values ofΠ1 = 0.185, 0.23, 0.305, i.e., when the firstwindow contains BL and one, two or three ELs, respectively(Table I). For each value ofΠ1, we optimizeΓ1 over the rangeof values such that the pairs(Π1, Γ1) satisfy QoS constraintPth = (0.95, 0.8) (Fig. 5(c)). The optimum valuesΓ1 =0.11, 0.135, 0.17 are found that provide maximum averagePSNR values of PSNRavg = 33.036, 33.321, 33.359dB for each MIB window sizeΠ1 = 0.185, 0.23, 0.305,respectively. Average PSNR values for worse and better re-ceiver class arePSNR

(1)avg = 26.982, 27.676, 28.07 and

PSNR(2)avg = 39.09, 38.966, 38.647, respectively. These

values demonstrate the ability of EWF codes to simultaneouslysupport heterogeneous receiver classes, matching the receivedvideo quality with the reception capability of the receiverclass.

B. H.264 SVC EWF Multicast: Simulation Results

The numerical optimization results presented in SectionsIIIC and IVA are derived using asymptotic erasure probabil-ities of input symbols obtained from analytical expressionspresented in Section II. These analytical expressions assumeinfinite source block length (k → ∞), whereas in the designexample, we deal with the finite-length EWF system scenario(k = 3800). To verify that numerical results are a goodapproximation of the “real-world” behavior, we perform simu-lation experiments. We select a simulation setting identical tothe numerical optimization setting presented in Section IIIC

8

0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

Π1

Γ 1

Γ1,min

Γ1,max

(a) Admissible(Π1,Γ1) region: scenario A, simulation results.

Π1

Γ 1

0.1 0.2 0.3 0.4 0.5

0.05

0.1

0.15

0.2

(b) Admissible(Π1,Γ1) region: scenario A, numerical results (5(c)).

0.1 0.2 0.3 0.4 0.5 0

0.1

0.2

0.3

0.4

Π1

Γ 1

Γ1,min

Γ1,max

(c) Admissible(Π1,Γ1) region: scenario B, simulation results.

Π1

Γ 1

0.1 0.2 0.3 0.4 0.5

0.1

0.2

0.3

0.4

(d) Admissible(Π1,Γ1) region: scenario B, numerical results.

Fig. 8. Admissible(Π1,Γ1) region: comparison of numerical and simulation results.

and IVA. We assume a scenario with two receiver classesdescribed by their reception capabilitiesε(A)

R= (0.1, 1),

which corresponds to receiver classes bitrates of 285 Kbpsand 2.85 Mbps, respectively; we also include in our simulationresults the scenario with two receiver classes described byreception capabilitiesε(B)

R= (0.35, 1.5), or roughly 1 Mbps

and 4.275 Mbps. We refer to these scenarios as scenario Aand scenario B, respectively1.

Firstly, we provide the simulation results that correspondtothe setting described in Section IIIC. In other words, we do notspecify the information source, but only request that givenQoSconstraintsPth = (0.95, 0.8) are met at the receivers of bothreceiver classes. Our goal is to find the region of pairs(Π1, Γ1)that satisfy QoS constraintsPth. As the simulation experi-ments are considerably more time consuming than the numer-ical optimization, we simulate the source block transmissiononly for the finite setΠ1 = 0.185, 0.23, 0.305, 0.405 of Π1

values and for each value, we search for the interval ofΓ1

values that satisfyPth. In each simulation run (i.e., for afixed pair of values(Π1, Γ1)), the total number of the source

1In both scenarios, all the receiver classes are defined with positivereception overheadsεR. However, due to URT property of EWF codes,optimization is possible even for negativeεR values. An example of thisscenario is available in [25].

TABLE IISOLUTION INTERVALS OF Γ1 FOR DIFFERENTΠ1 .

MIB Window Size Π1 Scenario A Scenario B[Γ1,min,Γ1,max] [Γ1,min, Γ1,max]

0.185 [0.070, 0.185] [0.027, 0.345]0.230 [0.093, 0.192] [0.037, 0.350]0.305 [0.135, 0.205] [0.055, 0.365]0.405 [0.232, 0.215] [0.087, 0.370]

blocks transmitted is set to 3000. Out of the total numberof transmitted source blocks, we determine the number ofunsuccessfully decoded blocks (both MIB and LIB blocks),the number of blocks with successfully decoded MIB block,and the number of blocks with complete recovery of both MIBand LIB block. These measurements are used to determine thecorrespondingP (1)

1 andP(2)2 values.

Fig. 7 presents the simulation results for the caseΠ1 =0.230 and the receiver classes of scenario A. The interval ofΓ1 values satisfying the QoS constraintsPth = (0.95, 0.8)is the region approximately located betweenΓ1,min = 0.093andΓ1,max = 0.192 (as determined by vertical dash-dot linesin Fig. 7). Similar procedures are repeated for all the valuesfrom the setΠ1 = 0.185, 0.23, 0.305, 0.405. The results,i.e., the corresponding solution intervals[Γ1,min, Γ1,max], are

9

0.08 0.1 0.12 0.14 0.16 0.18 0.232.2

32.4

32.6

32.8

33

33.2

33.4

33.6

Γ1

PS

NR

avg [d

B]

Numerical OptimizationSimulation Results

Fig. 9. Numerical optimization vs. simulation results ofPSNRavg valuesfor Π1 = 0.23 and scenario A.

tabulated in Table II.The simulation results from Table II are presented in Fig.

8(a) and compared with the results obtained numerically inSection IIIC (Fig. 8(b), which is a zoomed in version of Fig.5(c)). Figs. 8(c) and 8(d) present the numerical solution andsimulation results for scenario B (ε

(B)R

= (0.35, 1.5)), respec-tively. In both scenarios, there is an excellent match betweenthe results predicted by theory (Section IIIC) and the resultsobtained using simulation experiments. This demonstratesthat,although the simulation results are applied on the finite-lengthscenario, the EWF codelengths of several thousands symbolsare already sufficient to confirm the analysis based on theasymptotic probability expressions.

Secondly, we provide simulation results to confirm thedistortion-based optimized EWF code design example, as de-scribed in Section IVA, where the server is multicasting H.264SVC coded video stream. We keep the same assumptions onthe transmitted CIFStefanvideo sequence (Table I) and EWFencoding process as for the numerical optimization. The setof possible MIB window lengths analyzed in simulations isΠ1 = 0.185, 0.23, 0.305. To calculate average PSNR valuefor each Π1, similar experiments are performed using thesame set ofΓ1 values. The results obtained using equations(4) and (5) forΠ1 = 0.23 and scenario A are presented inFig. 9 where they are compared with the results obtainedby numerical optimization in Section IVA. It can be seenthat simulation results correspond to the results obtainedbynumerical optimization. Similar procedures are repeated forother Π1 values which are shown to produce a very goodmatch with the numerical results.

C. H.264 SVC EWF Multicast: Precoded EWF Codes

In this section, we demonstrate how results presented inthis paper can be additionally improved by concatenatingEWF code to a high-rate LDPC precode, in a similar wayto improvement that Raptor codes offer over LT codes [7].We have seen that the linear encoding/decoding complexity ofan EWF code is achieved by applying the constant averagedegree distributions over its windows. However, this results in

. . .

. . .

. . .

… … … …

…

…

. . .

. . .

1 2 k1 k2 kik = kr

+ + + + + + + + + + + + + + + +

i-th window containingprecoded information symbols

high-rate LDPCprecoding

EWFencoding

i-th class of EWFencoded symbols

Fig. 10. Precoded EWF codes.

0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

Π1

Γ 1

Γ1,max

Γ1,min

Fig. 11. Admissible(Π1,Γ1) region for precoded EWF codes.

an increase of error floors in the asymptotic recovery prob-abilities, especially for the low importance symbols. Highererror floors combined with the assumption (3) that each inputsymbol of thei-th importance class at thej-th receiver classis decoded independently with probabilityp(j)

i , gives modestvalues of the probabilityP (j)

i of the complete reconstructionof the i-th importance class source block at thej-th receiverclass. Thus, even at the overheads as high asεR,2 = 1in the example setting explored in the previous subsections,the QoS constraint ofP (2)

2 = 0.8 is obtained. In order toincrease QoS guarantees, we add redundancy within each ofthe importance class prior to the EWF encoding process byprecoding each of the importance class source blocks by ahigh-rate LDPC code (Fig. 10). This way, once the decodingof an EWF code allows recovery of a sufficientfraction of theimportance class source block, the LDPC precode should beable to “finish off” decoding with a vanishing probability oferror, resulting in dramatically increased probabilityP

(j)i of

complete importance class reconstruction.We performed simulation experiments to determine the

performance of a precoded EWF code with degree distributionΩR(x) over both windows and the source block of lengthk = 3800 symbols. Each of the importance class source blockswas encoded by a systematic hybrid LDPC-Half code [14].

10

The admissible(Π1, Γ1) region for significantly restrictedreception capabilitiesεR = (0.05, 0.2), and at the same timemore demanding QoS guaranteesPth = (0.99, 0.95), ascompared to the previous sections, is presented in Fig. 10.We note that this preliminary investigation does indicate thatadditional improvement of the robust scalable H.264 multicastis possible by combining low block-error-rates achieved byprecoding with the flexibility of the EWF design.

V. CONCLUSIONS

A novel scalable multicast system based on EWF codesis proposed as an efficient and flexible solution for real-time multimedia delivery to various classes of receivers withdifferent reception conditions. In this scenario, classical EEPfountain codes would perform poorly due to a potentially largenumber of receivers not being able to collect enough encodedsymbols to perform successful decoding. EWF code designis shown to offer simple “single-code” solution, where theapplied EWF code can be optimized to adapt the encodeddata stream to satisfy QoS guarantees offered to each receiverclass. We demonstrated that, in the case of a scalable videosource, further distortion-based optimization of EWF codesis possible for improved video reception quality. A detailedanalysis of EWF multicast system design for H.264 SVCvideo streaming is presented both using analytical tools andsimulation experiments. Numerical examples of EWF codeperformance obtained using analytical tools match extremelywell with the corresponding simulation analysis. The obtainedresults illustrate promising flexibility and efficiency of EWFcodes in adapting the code at the video server side to receiverswith heterogeneous reception capabilities. Finally, potentialimprovements of EWF-based scheme by applying Raptor-likeprecoding is a promising direction for further investigation.

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