Transmission of Adaptive MPEG Video Over

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005 2777

Transmission of Adaptive MPEG Video OverTime-Varying Wireless Channels: Modeling

and Performance EvaluationLaura Galluccio, Giacomo Morabito, Member, IEEE , and Giovanni Schembra

Abstract—Wireless channels are characterized by high time-varying bit-error rates (BERs). To cope with this problem, severaladaptive forward-error-correction (AFEC) schemes have beenproposed in the literature. They work locally at the wireless link,adding a variable amount of redundancy to the transmitted data inorder to maintain the packet error rate below an acceptable level.However, when such schemes are utilized, the bandwidth offered tothe applications changes when channel conditions change. In thispaper, the effects of these bandwidth variations are investigated

in the case of real-time Motion Picture Experts Group (MPEG)video transmission. The MPEG encoder is controlled in order toadapt its emission rate to the current bandwidth offered by thewireless link. To this end, the encoding quality is diminished bythe source rate controller when the transmission rate has to bedecreased due to an increase in the channel BER, whereas it isimproved when the transmission rate can be increased due to adecrease in the channel BER. A Markov-based model, denoted asSBBP/SBBP/1/ K , has been introduced to model the scenario beingconsidered. The analytical framework allows evaluation of theperformance of the system and can be used to optimize the designof a video transmission system for wireless channels, providing theinstruments to derive the tradeoff between information corruptionin the wireless channel and MPEG video encoding quality.

Index Terms—Forward error correction (FEC), Motion PictureExperts Group (MPEG), quality of service (QoS), switched batch

Bernoulli process (SBBP), wireless channels.

I. INTRODUCTION

THE NEED for supporting multimedia applications in

dynamic environments where users are equipped with

wireless terminals is one of the most challenging research

topics today. In fact, it is known that wireless channels are

characterized by bit-error rates (BERs) that are several orders of

magnitude higher than the corresponding values for terrestrial

networks. Accordingly, data packets may arrive at their desti-

nation corrupted, thus becoming useless.

To overcome this problem, one of the solutions most widely

adopted today is using forward error correction (FEC). FEC

algorithms introduce a chosen amount of redundancy: the

Manuscript received August 15, 2003; revised September 3, 2004; ac-cepted September 13, 2004. The editor coordinating the review of thispaper and approving it for publication is V. K. Bhargava. The work of L. Galluccio and G. Morabito was supported by Ministero dell’Istruzione,dell’Università e della Ricerca (MIUR) under contract VICOM. The work of G. Schembra was supported by MIUR under contract TANGO.

The authors are with the Dipartimento di Ingegneria Informatica e delleTelecomunicazioni (DIIT), University of Catania, 95124 Catania, Italy (e-mail:[email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TWC.2005.858028

higher the BER, the higher the amount of redundancy intro-

duced. However, in wireless channels, the BER is characterized

by high time variability: There are periods when channel

conditions are good, that is, the BER is low, and periods when

channel conditions are bad, that is, the BER is high. In order to

maintain a high level of resource efficiency while guaranteeing

the information accuracy required by applications, several

adaptive FEC (AFEC) schemes have been introduced in the

recent past [1], [2], [6], [7]. According to these schemes, the

amount of redundancy at any time depends on the channel

conditions being low if channel conditions are good, and high

if channel conditions are bad. One consequence is that AFEC

schemes cause variations in the bandwidth offered to user

applications, which therefore have to adapt their output rate

accordingly.

This paper focuses on video applications that are destined

to become very common in wireless-communication scenarios.

More specifically, the target of the paper is the definition of

an analytical framework for the design of a real-time Motion

Picture Experts Group (MPEG) video transmission system over

a wireless link that applies AFEC to keep the packet corrup-tion probability acceptable, i.e., below a given threshold. The

MPEG encoder uses a rate controller that adapts the output

rate by appropriately setting the quantizer scale parameter

(QSP) [8], [12], [29] to follow the bandwidth variations, while

maximizing encoding quality and stability. In order to achieve

this target, the rate controller monitors the activity of the frame

that is being encoded, its encoding mode, and the number of

bytes used to encode the previous frames. Then, it chooses the

appropriate QSP in such a way that the transmission buffer at

the sender site never saturates, even during periods with low

available bandwidth. The whole system can be modeled by an

emission process that feeds the transmission buffer. The serverof this buffer behaves according to the channel conditions

estimated by the adaptive error controller: The serving rate

is higher when channel conditions are good and lower when

channel conditions are bad.

Switched batch Bernoulli processes (SBBPs) are used to

model both the MPEG source [4], [15], [17], and the server

process of the transmission buffer that coincides with the time-

varying bandwidth available in the wireless channel [20], [24]–

[28]. Accordingly, an SBBP/SBBP/1/ K model is introduced to

describe the whole system.

The analytical framework proposed in the paper is used to

evaluate the performance in terms of the distortion introduced

1536-1276/$20.00 © 2005 IEEE


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2778 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 6, NOVEMBER 2005

Fig. 1. Mobile terminal system architecture.

by the quantization mechanism in the encoding process, which

are the loss and mean delay in the transmission buffer, at

different target packet error probabilities (PEPs) achieved usingAFEC. Results obtained in the paper can be used to obtain

the best tradeoff between encoding quality, which requires a

high available bandwidth, and information correctness at the

destination, which requires a high level of redundancy, thus

causing bandwidth reduction.

The rest of the paper is organized as follows. Section II

describes the wireless MPEG transmission system considered

in this paper. Section III proposes an analytical framework of

the whole video transmission system, accounting for both the

video source and the transmission channel. Section IV provides

a derivation of the performance parameters. Section V applies

the analytical framework to a case study in order to demon-

strate the model’s capability of providing performance insights

for the system design. Finally, Section VI concludes the paper.

II. DESCRIPTION OF THE S YSTEM

The architecture of the video transmission system in the

mobile terminal considered in this paper is shown in Fig. 1.

The adaptive rate source is an adaptive-rate MPEG video source

over a User Datagram Protocol (UDP)/IP protocol suite. The

video stream generated by the video source is encoded by

the MPEG encoder according to the MPEG video standard

[30], [31]. In the MPEG encoding standard, the frame, which

corresponds to a single picture in a video sequence, is the basicdisplaying unit. Three encoding modes are available for each

frame: intraframes (I), predictive frames (P), and interpolative

frames (B). The basic idea behind MPEG video compression

is to remove spatial redundancy within a video frame andtemporal redundancy between successive video frames. The

encoder output is a deterministic period sequence in which the

period is a group of pictures (GoPs) realized with three types of

encoded frames.

1) I frames coded using only information present in the

picture itself in order to provide potential random ac-

cess points in the compressed video sequence. The cod-

ing is based on the discrete-cosine transform according

to the joint photographic experts group (JPEG) coding

technique.

2) P frames coded using a coding algorithm similar to the

one used for I frames, but with the addition of motion

compensation with respect to the previous I or P frame

(forward prediction).

3) B frames coded with motion compensation with respect

to the previous I or P frame, and the next I or P frame, or

an interpolation between them (bidirectional prediction).

Typically, I frames require more bits than P frames, while B

frames have the lowest bandwidth requirement.

In encoding each frame, it is possible to tune the number

of bits needed to represent the frame and, thus, its quality, by

appropriately choosing the so-called QSP. Its value can range

within the set [1, 31]: 1 being the value giving the best encodingquality but requiring the maximum number of bits to encode the


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GALLUCCIO et al.: TRANSMISSION OF ADAPTIVE MPEG VIDEO OVER TIME-VARYING WIRELESS CHANNELS 2779

frame, and 31 being the value giving the worst encoding quality,

but requiring the minimum number of bits.

The QSP can be dynamically changed according to the

feedback law implemented by the rate controller in order to

achieve a given target. The MPEG encoder emits one frame

every ∆ seconds, and its output is packetized in the packe-

tizer according to the UDP/IP protocol suite: the packetizerfragments the information flow into blocks of U P bytes

1; these

blocks constitute the payloads for the UDP, which adds a header

of 8 bytes; each UDP packet is then put in the payload field of

an IP packet.

The IP packets are then sent to a transmission buffer whose

service rate is time varying and depends on the channel con-

dition estimated by the adaptive error controller, as will be

explained below. The main target of the rate controller is to

avoid buffer saturation, which causes losses and long delays,

while maximizing the encoding quality and stability. To this

end, it chooses the QSP parameter according to a feedback

law monitoring the activity of the frame being encoded, its

encoding mode (I, P, or B), and the current number of packets

in the transmission buffer. The model introduced in the paper

is so general that it can be applied whatever the feedback law.

The feedback law used in the paper was introduced in [4] and

[17] and, for the sake of completeness, will be reported in

Section V-A. It has been defined in such a way that a controlled

number of packets are present in the transmission buffer at the

end of each GoP, while pursuing a constant distortion level

within the GoP. Packets leaving the transmission buffer enter

the adaptive error controller. Its main target is to use FEC to

partially solve the problem of wireless-link unreliability. The

FEC block creator divides packets into sets of k blocks. These

blocks are given as input to the AFEC encoder and encodedin sets of m blocks, with m ≥ k. If any set of k or moreblocks belonging to the same packet is received correctly, then

the original packet can be reconstructed properly. Obviously,

the larger the value of m, the higher the probability that the

information can be reconstructed at the receiver station, but the

lower the wireless-link bandwidth available at the video source.

The value of m is chosen by the FEC controller in such a

way that the PEP, i.e., the probability that a packet cannot be

reconstructed at the receiver station, is no higher than a target

value P̂ (C )PEP. Given that wireless channel conditions change

dynamically, AFEC encoding is applied, as proposed in [1],

[2], [6], and [7]. This encoding technique requires knowledgeof the current BER on the link. This estimation is performed

by the wireless channel estimator. The estimated BER value

is given as input to the FEC controller, which evaluates m so

that the requirement on the PEP is satisfied. The value of m

therefore changes in time and, as a consequence, the available

link capacity c̃(t) also changes in time as

c̃(t) =

k

m(t)

· c (1)

1

If Real-Time Protocol (RTP)/Real-Time Control Protocol (RTCP) protocolsare also used over the UDP/IP protocol suite, the related overhead should beconsidered.

where c is the capacity (in packets/s) when FEC is not used.

At any time, the service rate of the transmission buffer is set

equal to c̃(t). Accordingly, both the MPEG encoder outputprocess and the transmission-buffer service process are stochas-

tic processes, the first depending on the behavior of the source

and the rate controller, and the second on the BER behavior of

the wireless channel. These processes will be modeled with twodiscrete-time SBBP processes Ỹ (n) and Ñ (n), respectively, asdescribed in detail in Section III.

III. SYSTEM M ODEL

In this section, we derive a discrete-time analytical model of

the system described in the previous section. We will set the

slot duration ∆ equal to the video-frame interval.As a first step, Sections III-B and III-C will describe the mod-

els of the noncontrolled MPEG encoder output and the available

capacity of the channel as SBBPs [9]. Then, the whole system

will be modeled as an SBBP/SBBP/1/ K queueing system in

Section III-D, where K is the maximum number of packets thetransmission buffer can contain. For the sake of completeness,

Section III-A provides a brief outline of SBBP processes.

A. Switched Batch Bernoulli Processes (SBBPs)

An SBBP Y (n) is a discrete-time emission processmodulated by an underlying Markov chain [9], and represents

a special case of the family of the hidden Markov model

processes [19].

Each state of the Markov chain is characterized by an emis-

sion probability density function (pdf): The SBBP emits data

units according to the pdf of the current state of the underlyingMarkov chain. Therefore, the SBBP Y (n) is fully describedby the state space (Y ) of the underlying Markov chain, themaximum number of data units the SBBP can emit in one

slot r(Y )MAX, and the matrix set (Q

(Y ), B(Y ))), where Q(Y )

is the transition probability matrix of the underlying Markov

chain, while B(Y ) is the emission probability matrix whose

rows contain the emission pdfs for each state of the underlying

Markov chain.

If we indicate the state of the underlying Markov chain in the

generic slot n as S (Y )(n), the generic elements of the matricesQ(Y ) and B(Y ) are defined as follows:

Q(Y )[sY ,s

Y ] = ProbS (Y )(n + 1) = sY |S

(Y )(n) = sY

∀sY , sY ∈

(Y ) (2)

B(Y )

[sY ,r] = ProbY (n) = r|S (Y )(n) = sY

∀sY ∈

(Y ), ∀r ∈

0, r(Y )MAX

. (3)

We will introduce an extension to the meaning of the

SBBP to model not only a source emission process, but also

a video-sequence activity process, and an available wireless-

channel-capacity process. In the latter cases, we will indi-

cate them as an activity SBBP and a transmission-channelSBBP, respectively, and their matrices B(Y ) as the activity


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probability matrix and the channel-transmission probability

matrix, respectively.

B. Noncontrolled MPEG Source Model

The noncontrolled MPEG video source is part of the

adaptive-rate source shown in Fig. 1 comprising the videosource, the MPEG encoder, and the packetizer. We denote it as

noncontrolled because we are assuming it works with a constant

QSP q not controlled by the rate controller.

The first step in modeling the whole video transmission

system shown in Fig. 1 is the derivation of the SBBP process

Ỹ q(n), modeling the emission of the noncontrolled MPEGvideo source at the packetizer output for each QSP q .

This model was calculated by the authors in [4] and [17].

Here, for the sake of brevity, we will refer to those works

in order to define the notation. The model captures two dif-

ferent components: the activity-process behavior and the ac-

tivity/emission relationships. As input, it takes the first- and

second-order statistics of the activity process, and the threefunctions, one for each encoding mode (I, P, or B), charac-

terizing the activity/emission relationships. The state of the

underlying Markov process of Ỹ q(n) is a double variable,

S (Ỹ )(n) = (S (G)(n), S (F )(n)), where S (G)(n) ∈ (G) is thestate of the underlying Markov chain of the activity process

G(n), and S (F )(n) ∈ J is the frame to be encoded in the GoP atthe slot n. The state set (G) represents the set of activity levelsto be captured. For example, according to [5], we have (G) ={Very Low, Low, High, Very High}. Set J , on the other hand,represents the set of frames in GoP and depends on the GoP

structure. For example, if the movie is encoded with the GoP

structure IBBPBB, set J is defined as J = {I,B,B,P,B,B}.As demonstrated in [4] and [17], the underlying Markov

chain of Ỹ q(n) is independent of q . Therefore, we will indicate

its transition probability matrix as Q(Ỹ ) instead of Q(Ỹ q),

and set (Q(Ỹ ), B(Ỹ q)), for each q ∈ [1, 31], defines the SBBPemission process modeling the output flow of the noncontrolled

MPEG encoder, when it uses a constant QSP value q .

C. Service SBBP Model

The target of this section is to derive the SBBP model of

the process Ñ (n), which represents the service process of the

transmission buffer when AFEC is employed. As said so far,it closely depends on the amount of redundancy the AFEC

encoder introduces to achieve the target maximum PEP P̂ (C )PEP

due to the wireless channel.

As usual, (e.g., [14], [24], and [26]), we assume that the

channel behavior can be described by means of an M -states

Markov process. Accordingly, channel statistical behavior can

be described by an M × M transition probability matrix Q(C )

and by BERi, the BERs for each state of the process i ∈ [1,M ].Thus, the service SBBP model is represented by the follow-

ing parameters:

1) the maximum number of packets that can be transmitted

in a time slot r( Ñ )MAX;

2) the state space ( Ñ );

3) the matrix set (Q( Ñ ), B(

Ñ )) containing the transitionprobability matrix and the channel-emission probability

matrix.

Obviously, the transition probability matrix Q( Ñ ) of the un-

derlying Markov chain of the process Ñ (n) coincides withthe channel-transition probability matrix Q(C ), as calculated

in [26]. The state space ( Ñ ) coincides with the channel state

space, i.e., ( Ñ ) = [1,M ]. Instead, in order to derive B(

Ñ ),

we have to calculate the bandwidth reduction due to the AFEC

redundancy for each state i of the channel SBBP. This depends

on the BER characterizing the state BERi.

The FEC redundancy to be introduced to achieve the target

value for the maximum PEP P̂ (C )PEP should be such that the

resulting PEP for any state i of the channel P (C )PEP,i is lower

than or equal to the target one, i.e.,

P (C )PEP,i ≤

P̂ (C )PEP. (4)

According to the notation introduced in Section II, indicating

the size of each block expressed in bits as R, and assuming

that losses introduced by the wireless channel are independent

and uniformly distributed within a block,2 the PEP, when the

channel is in the generic state i, can be calculated as follows:

P (C )PEP,i =

ml=m−k+1

m

l

· (1 − P BEP,i)

m−l · (P BEP,i)l (5)

where P BEP,i represents the probability that a block is cor-

rupted when the channel is in state i, and can be evaluated as

follows:

P BEP,i = 1 − (1 − BERi)R. (6)

Now, substituting (5) in (4), we can numerically find the

minimum value of m verifying the inequality in (4) for each

value i of the channel state. Let us indicate this value as mi.

Accordingly, the capacity Ñ i (in packets/s), which is actuallyavailable for the transmission of data to obtain a PEP lower

than P̂ (C )PEP in the wireless channel when its state is i, can be

calculated as follows:

Ñ i = kmi

· c (7)

where c is the channel capacity when no FEC encoding is

applied (in [packets/s]).

In general, from (7), we obtain a noninteger value for Ñ i.However, we can assume that, when the channel state is i, in

each slot, the channel is able to transmit either Di = Ñ i pack-ets with a probability of pDi = 1 − ( Ñ i − Di), or (Di + 1)packets with a probability of pDi+1 = 1 − pDi , where we haveindicated the largest integer no greater than x as x.

2This assumption is accurate if interleaving is utilized, which is usual inwireless communications [28].


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In summary, the emission probability matrix of the SBBP

modeling the channel is B ( Ñ ) ∈ [M X r

( Ñ )MAX], and its generic

element can be calculated as follows:

B( Ñ )

[i,d] = pDi, if d = Di pDi+1, if d = Di + 1

0, otherwise

(8)

where r( Ñ )MAX is the maximum number of packets that can be

transmitted in one slot, i.e.,

r( Ñ )MAX = maxi

{Di + 1}. (9)

The transition probability matrix and the state space, together

with the channel-emission probability matrix and the maximum

number of packets that can be transmitted in one slot defined in

(8) and (9), completely characterize the channel SBBP model.

D. Video-Transmission-System Model

The adaptive-rate source pursues a given target by imple-

menting a feedback law in the rate controller, which calculates

the value q of the QSP to be used by the MPEG encoder for

each frame. The target of this section is to model the video

transmission system as a whole, indicated here as Σ. To thisaim, we use a discrete-time queueing system model.

Let K represent the maximum number of packets that can

be contained in the queue of the transmission buffer and its

server. The server capacity of this queueing system, that is, the

number of packets that can leave the queue at each time slot,

is a stochastic process that has been modeled with the channelSBBP process Ñ (n).

The input of the queue system is the emission process of

the adaptive-rate source, indicated here as Ỹ (n). Therefore, atslot n, the transmission-buffer queue size is incremented by

Ỹ (n), and decremented by Ñ (n). Both the input and the outputprocesses can be modeled by means of two SBBP processes,

as discussed above, where the slot duration is the frame

duration ∆.To model the queueing system, we assume a late-arrival-

system-with-immediate-access time diagram [3], [11]: Packets

arrive in batches, and can enter the service facility if it is

free, with the possibility of them being ejected almost instan-taneously. Note that in this model, a packet service time is

counted as the number of slot boundaries from the point of entry

to the service facility up to the packet departure time. Therefore,

even though we allow the arriving packet to be ejected almost

instantaneously, its service time is counted as 1, not 0.

A complete description of Σ at the nth slot requires athree-dimensional Markov process, whose state is defined as

S (Σ)(n) = (S (Q)(n), S ( Ñ )(n), S

˜(Y )(n)), where:

1) S (Q)(n) ∈ [0,K ] is the transmission-buffer queue statein the nth slot, i.e., the number of packets in the queue

and in the service facility at the observation instant;

2) S ( Ñ )(n) is the state of the underlying Markov chain of the channel SBBP Ñ (n);

3) S ˜(Y )(n) is the state of the underlying Markov chain of

Ỹ (n), which coincides with that of Ỹ q(n), for any q ∈[1, 31].

According to the late-arrival-system-with-immediate-access

time diagram, the transmission-buffer state in slot (n + 1) canbe obtained through the Lindley equation [13]

sQ = max

minsQ + r,K

− d, 0

(10)

where sQ is the transmission-buffer state in the generic slot n,

while r and d are the server capacity and the number of arrivals

at slot n + 1, respectively.The channel SBBP Ñ (n), modeled in Section III-C, can

be equivalently characterized through the set of transition

probability matrices M ( Ñ )(d), which are transition probability

matrices including the probability that the server capacity is

d (in packets/slot). These matrices can be obtained from the

parameter set (Q

( Ñ )

, B

( Ñ )

) as follows:M (

Ñ )(d)

sÑ

,sÑ

≡ Prob

Ñ (n + 1) = d,S (

Ñ )(n + 1) = sÑ

S ( Ñ )(n) = sÑ

=Q(

Ñ )

sÑ

,sÑ

· B( Ñ )sÑ

,d

∀d ∈

0, r˜(N )

MAX

. (11)

The adaptive-rate source emission process is modeled byan SBBP whose emission probability matrix depends on the

transmission-buffer state. In order to model this process, we

use the SBBP models of the noncontrolled MPEG video source

described in Section III-B, Ỹ q(n), for each q ∈ [1, 31]. So, we

have a parameter set (Q(Ỹ ), B(Ỹ 1), B(Ỹ 2), . . . , B(Ỹ 31)), which

represents an SBBP whose transition matrix is Q(Ỹ ), and

whose emission process is characterized by a set of emission

matrices {B(Ỹ q)}q=1,2,...,31. Consequently, at each time slot,the emission of the MPEG video source is characterized by an

emission probability matrix chosen according to the QSP value

defined by the feedback law q = φ(sQ,a , j).

More concisely, as in (11), for the channel SBBP, wecharacterize the emission process of the adaptive-rate source

through the set of matrices {M (Ỹ )

sQ

(r)}, ∀r ∈ [0, r(Ỹ )MAX], each

matrix representing the transition probability matrix including

the probability of r packets being emitted when the buffer

state is sQ. Accordingly, the generic element of the ma-

trix M (Ỹ )sQ

(r) can be obtained from the above parameter set

(Q(Ỹ ), B(Ỹ 1), B(Ỹ 2), . . . , B(Ỹ 31)) as follows:M

(Ỹ )sQ

(r)[(i,j),(i,j)]

=

a∈(Act)

Q(Ỹ )[(i,j),(i,j)]

·B(Ỹ q)(r)[(i,j),r]

· f Act(a|i, j) (12)


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where the following hold:

1) q is the QSP chosen when the frame to be encoded is the

j th in the GoP, the activity is a , and the transmission-

buffer state before encoding this frame is sQ. The value

of q is determined by the feedback law = φ(·), i.e.,

q

= φs

Q, a

, j

. (13)

2) f Act(a|i, j ) is the probability that the generic frame j

in the GoP has an activity a when its activity level is i.

This function, as demonstrated in [15], [16], and [21], is a

Gamma pdf, whose mean value and variance characterize

the video trace.

3) (Act) is the set of all the possible activities.

Finally, we can model the video transmission system as a

whole. If we indicate two generic states of the system as sΣ =(sQ, s

Ñ , s

Ỹ ) and sΣ = (s

Q, s

Ñ , s

Ỹ ), the generic element of

the transition matrix of the video transmission system as a

whole Q(Σ) can be calculated, due to (11) and (12), as follows:

Q(Σ)

sQ

,sÑ

,sỸ

,

sQ

,sÑ

,sỸ

≡ Prob

S (Q)(n + 1) = sQ,

S ( Ñ )(n + 1) = s

Ñ ,

S (Ỹ )(n + 1) = sỸ ,

S (Q)(n) = sQ,

S ( Ñ )(n) = s

Ñ ,

S (Ỹ )(n) = sỸ ,

=

d( Ñ )MAXd=0

r(Ỹ )MAXr=0

M (

Ñ )(d)

sÑ

,sÑ

· M (Ỹ )s

Q

(r)s

Ỹ ,s

Ỹ · ψ sQ, sQ, . . . , r , d (14)

where ψ(sQ, sQ, . . . , r , d) is a Boolean condition for the queue

state behavior, and is defined as follows:

ψsQ, s

Q,K,r,d

=

1, if max

minsQ + r,K

− d, 0

= sQ0, otherwise

. (15)

Once the matrix Q(Σ) is known, we can calculate the steady-

state probability array of the system Σ as the solution of thefollowing linear system

π(Σ) · Q(Σ) = π(Σ)

π(Σ) · 1 = 1 (16)

where 1 is a column array whose elements are equal to 1,and π(Σ) is the steady-state probability array, whose generic

element is

π(Σ)

[(sQ,s Ñ ,sỸ )] = ProbS (Q)(n) = sQ, S

( Ñ )(n) = sÑ ,

S (Ỹ )(n) = sỸ

. (17)

A direct solution of the system in (16) may be difficultsince the number of states grows explosively as the maximum

transmission buffer size K increases. Nevertheless, many algo-

rithms, e.g., [10], [18], and [23], enable us to calculate the array

π(Σ), while maintaining a linear dependence on K .

IV. QUANTIZATION-D ISTORTION A NALYSIS

In this section, we evaluate both the static and time-varying

statistics of the quantization distortion, represented by the pro-

cess PSNR(n).More specifically, we will quantize the PSNR process with

a set of L different levels of distortion, {µ1, µ2, . . . , µL},

each representing an interval of distortion values where thequality perceived by the users can be considered constant.

As an example, for the movie Evita, from a subjective

analysis obtained with 300 tests, the following L = 5 lev-els of distortion were envisaged: µ1 = [31.2, 34.2] dB, µ2 =[34.2, 35.0] dB, µ3 = [35.0, 36.2] dB, µ4 = [36.2, 38.4] dB,and µ5 = [38.4, 52.1] dB.

The pdf f PSNR( p) can be easily calculated from the transi-tion probability matrix and the steady-state probability array of

the whole system, which have been derived in (14) and (16),

respectively [see (18) at the bottom of the page], where the

following hold:

1) ψ[s

Q,a

,j

]( p) is a Boolean condition defined as follows

ψ[sQ,a,j]( p) =

1, if F (j

)φsQ, a

, j

= p0, otherwise

.

(19)

2) F (j)(q ) in (19) is the so-called distortion curve [5], [17],

[22] for the generic frame j, which is the curve linking

the average PSNR to the QSP value, q , used to encode

the frame.

Now, in order to calculate the statistics of the quantized PSNR

process, let us define the array γ (ζ ) in which the generic

element γ (ζ )l , for each l ∈ [1, L], is the QSP range giving a

distortion belonging to the lth level for a frame encoded withencoding mode ζ ∈ {I, P, B}. Of course, by so doing, weassume that a variation of q within the interval γ

(ζ )l does not

cause any appreciable distortion. From the distortion curves

for the movie Evita, we have calculated the following QSP

f PSNR( p) ≡ Prob {PSNR(n) = p} =K

sQ=0

sÑ

∈( Ñ )

i∈(G)

j∈J

K sQ=0

sÑ

∈( Ñ )

i∈(G)

a∈(Act)

f Act(a|i, j )

· Q(Σ)sQ

,sÑ

,(i,j)

,

sQ

,sÑ

,(i,j) · π(Σ)

sQ

,sÑ

,(i,j) · ψ[sQ,a,j]( p) (18)


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ranges corresponding to the above distortion levels µl, for each

l ∈ [1, 5].

1) For I frames: γ (I) = [[16, 31], [13, 15], [10, 12], [6, 9],[1, 5]].

2) For P frames: γ (P) = [[15, 31], [13, 14], [10, 12], [6, 9],

[1, 5]].3) For B frames: γ (B) = [[17, 31], [14, 16], [11, 13], [7, 10],

[1, 6]].

Let q = φ(sQ, a, j ) be the feedback law, linking the

transmission-buffer state at the beginning of a generic slot

n, sQ ∈ [0,K ], the activity of the frame in the same slot,

a ∈ (G), and the position in the GoP of the frame tobe encoded, j ∈ J , to the QSP to be used to encode the

current frame. Moreover, for each a and j , let θ(a,j)l =

{∀sQ such that φ(sQ, a

, j ) ∈ γ (ζ )

l } be the range of valuesof the transmission-buffer state for which the rate controller

chooses QSP values belonging to the level µl, according to theadopted feedback law. By definition, it follows that a variation

of the transmission-buffer state within θ(a,j)l does not cause

any appreciable distortion variation.

Let us now calculate the probability that the value of the

process PSNR(n) is in the generic interval µl, π(PSNR)[l]

, and

the pdf f δl(m) of the stochastic variable δ l, representing theduration of the time the process PSNR(n) remains in thegeneric interval µl without interruption. They are defined as

π(PSNR)[l]

= Prob {PSNR(n) ∈ µl} (20)

and (21), shown at the bottom of the page. The term π(PSNR)[l] in

(20) can be calculated from the pdf f PSNR( p) obtained in (18)as follows:

π(PSNR)[l] =

p∈µl

f PSNR( p). (22)

In order to calculate the pdf f δl(m) in (21), let us indicatethe matrix containing the one-slot probabilities of transition

towards system states in which the distortion level is µl as

Q(Σ)→µl . It can be obtained from the transition probability matrix

of the system Q(Σ), as in (23), shown at the bottom of the page.

Therefore, the pdf f δl(m) can be calculated as the probability

that the system Σ, starting from a distortion level µl, remains in

the same level for (m − 1) consecutive slots, and leaves thislevel at the mth slot, that is

f δl(m) = π(Σ1,µl) ·Q(Σ)→µl

m−1· Q(Σ)→(=µl) · 1

T

where : π(Σ1,µl) = π(Σ,µl) · Q(Σ)→µl

π(Σ,=µl) · Q(Σ)→µl · 1T

. (24)

The array π(Σ1,µl) in (24) is the steady-state probability array in

the first slot of a period in which the distortion level is µl. The

array π(Σ,=µl), on the other hand, is the steady-state probability

array in a generic slot in which the distortion level is other than

µl, and is defined as

π(Σ,=µl) = π(Σ) · Q(Σ)→µl

π(Σ) · Q(Σ)→µl · 1T . (25)

V. CAS E S TUDY

A. System Characterization

We analyzed the statistical characteristics of 1 hour of MPEG

video sequences of the movie Evita. To encode this movie, we

used a frame rate of F = 25 frames/s, and a frame size of 180macroblocks. The GoP structure IBBPBB was used, selecting a

ratio of total frames to intraframes of GI = 6, and the distancebetween two successive P frames or between the last P frame in

the GoP and the I frame in the next GoP as GP = 3. The sizeof the transmission buffer has been set to K = 60 packets. Thegross link capacity assigned to the video application is 2 Mb/s.

The IP packets at the wireless terminal are divided into 40 bytes

blocks, as usual in the universal mobile telecommunications

system (UMTS) environment. The AFEC module encodes sets

of k = 16 blocks into sets of m.In this case study, we use the eight-state finite-state Markov

channel (FSMC) model introduced in [26] for the wireless

channel and consider two different cases.

1) Pedestrian: The mobile user’s velocity is 5 km/h.

2) Driver: The mobile user’s velocity is 55 km/h.

Assuming that wireless transmission is performed in the 2-GHz

band, which is the value used in UMTS, the maximum Doppler

frequency is f m = 10 Hz in the first case and f m = 100 Hz inthe second.

The values that characterize Q(C ) are given in Table I for the

pedestrian and driver cases. The above matrices were calculated

f δl(m) = Prob

PSNR(n + 1) ∈ µl, . . . ,PSNR(n + m − 1) ∈ µl,PSNR(n + m) ∈ µl

PSNR(n − 1) ∈ µlPSNR(n) ∈ µl

(21)

Q(Σ)→µl

sQ,s

Ñ ,(i,j)

,

sQ,s

Ñ ,(i,j) = a∈(Act) Q

(Σ)

sQ,s˜N

,(i,j),sQ,s˜N

,(i,j)f Act(a|i, j), if sQ ∈ θ(a,j)l

0, otherwise(23)


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TABLE IQ(C ) PARAMETERS IN THE PEDESTRIAN CAS E (f m = 10 Hz) A ND DRIVER CAS E (f m = 100 Hz)

TABLE IIREDUNDANCY BLOCKS AND NET LIN K CAPACITY OFFERED TO THE APPLICATION FOR DIFFERENT CHANNEL STATES AND TARGET ERROR

PROBABILITIES ˆ

P

(C )

PEP IN THE

DRIVER

CAS E

, WHEN THE

GROSS

LIN K

CAPACITY IS

c = 2 Mb/s

assuming that the video-frame rate is 25 frames/s and therefore,

the slot duration is ∆ = 40 ms.The target error-probability values considered are P̂

(C )PEP =

10−5, P̂ (C )PEP = 10

−4, P̂ (C )PEP = 10

−3, and P̂ (C )PEP = 10

−2.

Table II lists, for each state i of the server SBBP model, the

values of mi and the resulting available link capacities c̃i for

these

ˆP

(C )

PEP values in the driver case, taken as an example.In this case study, we will consider a feedback law obtained

from the statistics of the movie Evita, expressed in terms of rate

and distortion curves [5], [17], [23]. The rate curves Ra,j (q )give the expected number of packets which will be emitted

when the j th frame in the GoP has to be encoded, if its activity

value is a, and is encoded with a QSP value q . The distortion

curves F (j)(q ) give the expected encoding PSNR, and havebeen defined in Section IV. The rate and the distortion curves

for the movie Evita are shown in Fig. 2.

The considered feedback law aims to maintain the number

of packets in the transmission-buffer queue lower than a given

threshold K θ at the end of each GoP interval, while maintaining

stable the PSNR during the whole GoP. In this case, both therate curves Ra,j (q ) and the distortion curves F

(j)(q ) are used.

More specifically, if we indicate the transmission-buffer queue

length and the channel available capacity when the jth frame in

the GoP has to be encoded as sQ and sÑ , respectively, and a

being the activity of this frame, the QSP is chosen assuming the

following.

1) The activity will remain constant during the rest of the

GoP, that is, Act(n) = a, for each frame h ∈ [ j + 1, GI ].2) The channel behavior, and therefore the available network

bandwidth Ñ (n), remains constant during the rest of theGoP, that is, for each frame h ∈ [ j + 1,GI ].

Under these assumptions, the QSP is chosen as the minimum

QSP q̄ , such that it is possible to find a set of QSP values for thenext frames of the GoP, [q j+1, . . . , q GI ], so that the followinghold.

1) The PSNR of those frames is constant, and equal to the

value that should be achieved for frame j .

2) The number of emitted packets expected for the next

frames of the GoP, if these QSP values are used, added

to the current queue, minus the number of packets that

will leave the queue until the end of the GoP, results tolower than the given threshold K θ.


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Fig. 2. Rate-distortion curves for I, P, and B frames. Rate curves for (a) frame I, (b) frame B, and (c) frame P. (d) Distortion curves.

In other words, the feedback law works by choosing the QSP

as in (26), shown at the bottom of the page.

B. Numerical Results

Fig. 3 shows the pdfs of the transmission-buffer queuesize for the two values of the Doppler frequency f m and for

a given value of the target error probability among those being

considered. The values shown have been calculated as follows:

ProbS (Q)(n) = sQ

=

s Ñ ∈( Ñ )

sỸ

∈(Ỹ )

π(Σ)

[(sQ,s Ñ ,sỸ )]. (27)

We can observe that the curves are basically Gamma distri-

butions and are very similar to each other independently of

the P̂ (C )PEP value. This is the evidence that the feedback law

works properly. This is further demonstrated in Fig. 4 where

we show the average queue size as well as the mean delay in

the transmission buffer. The value of the average queue size

does not change significantly when the P̂ (C )PEP changes and ishigher in the driver case. This can be explained by the fact that

in the driver case, the wireless medium quality is lower and

therefore, the transmission-buffer service rate is lower. Similar

discussions can be carried out concerning Fig. 5, where the

performance in terms of loss probability in the transmission

buffer is shown and calculated as in [4].

q = φ(sQ,a ,j) = minq̄∈[1,31]

q̄ such that ∃ [q j+1, . . . , q GI ] for which :F (k)

(q k) = F (j)

(q̄ ) ∀k ∈ [ j + 1, . . . , GI ]sQ + Ra,j(q̄ ) +GI

k=j Ra,j(q k) − (GI − j + 1) · Ñ (n) ≤ K θ

(26)


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Fig. 3. Transmission-buffer size pdf for P̂ (C )PEP = 10

−

2 (a) in the pedestrian case and (b) in the driver case.

Fig. 4. Average transmission-buffer size and mean delay versus the target error probability P̂ (C )PEP.

Fig. 6 shows the performance related to the encoding quality.

In particular, it can be observed that, for high values of P̂ (C )PEP,due to the high amount of available bandwidth, the most likely

PSNR level is the highest. On the contrary, for low values of

P̂ (C )PEP, as a result of the large amount of redundancy introduced

by AFEC, the available bandwidth is low, and therefore, the

video source reduces the encoding quality. For this reason, the

lower the value of the target PEP in the wireless link P̂ (C )PEP,

the greater the probability of poorer PSNR levels. In order to

better quantify the influence of the choice of the target value

P̂ (C )PEP on the encoding performance, in Fig. 6, the average

PSNR level is shown. As expected, the worst case for the av-

erage PSNR level is given when the AFEC has a very stringent

target for the maximum PEP P̂ (C )PEP. When a less stringent targetvalue for the PEP is required, the encoding quality increases.

Obviously, the average PSNR value, and thus encoding quality,

is higher in the pedestrian case.

VI. CONCLUSION

In this paper, we have defined an analytical framework for

the evaluation of the performance of real-time MPEG video

transmission over a wireless link that applies AFEC to keep the

PEP below a given threshold.

The MPEG encoder uses a rate controller that adapts the

output rate by appropriately setting the QSP to follow the

bandwidth variations while maximizing encoding quality and

stability. The whole system has been modeled by an emission

process that feeds the transmission buffer; the server of thisbuffer behaves according to the channel conditions, i.e., the


11/12


Fig. 5. Packet loss probability in the transmission buffer versus the target error probability P̂ (C )PEP.

Fig. 6. Average PSNR level versus the target error probability P̂ (C )PEP.

service rate is higher when channel conditions are good and

lower when channel conditions are bad.

SBBPs have been used to model both the MPEG video source

[4], [15], [17] and the server process of the transmission buffer

that coincides with the time-varying available bandwidth in the

network. Accordingly, the whole system has been modeled as

an SBBP/SBBP/1/ K process.

The analytical framework proposed in the paper has been

used to evaluate the performance in terms of the distortion

introduced by the quantization mechanism in the encodingprocess, which are the loss and mean delay in the transmission

buffer. Numerical results show that our system is very robust

and reliable due to the implemented feedback law that main-

tains almost constant the mean delay and the loss probabil-

ity in the output buffer. Moreover, the corruption probability

in the wireless channel is also limited in spite of possible

variations in time in the wireless-channel BER. The proposed

model allows the designer to evaluate the introduced encoding

quality variation that represents the cost of using this ap-

proach. The results obtained in the paper can be used to obtain

the best tradeoff between encoding quality and informationcorrectness.


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[27] M. Zorzi and R. R. Rao, “On the statistics of block errors in burstychannels,” IEEE Trans. Commun., vol. 45, no. 6, pp. 660–667, Jun. 1997.[28] M. Zorzi, R. R. Rao, and L. B. Milstein, “Error statistics in data trans-

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Laura Galluccio received the Laurea degree in elec-trical engineering and the Ph.D. degree in electrical,

computer and telecommunications engineering, bothfrom the University of Catania, Catania, Italy, in2001 and 2005, respectively.

Since 2002, she has been with the Italian NationalConsortium of Telecommunications (CNIT), whereshe is working as a Research Fellow within the Vir-tual Immersive Communications (VICOM) Project.From May to July 2005, she was a Visiting Scholarat the COMET Group, Columbia University, New

York, NY. Her research interests include ad hoc and sensor networks, protocolsand algorithms for wireless networks, and network performance analysis.

Dr. Galluccio served and will serve in the Program Committee of the4th Academic Network for Wireless Internet Research in Europe (ANWIRE)International Workshop on Wireless Internet and Reconfigurability, the 20thInternational Symposium on Computer and Information Sciences (ISCIS 05),and Networking 2006.

Giacomo Morabito (M’02) received the Laureadegree in electrical engineering and the Ph.D.degree in electrical, computer, and telecommunica-tions engineering from the University of Catania,Catania, Italy, in 1996 and 2000, respectively.

From November 1999 to April 2001, he was withthe Broadband and Wireless Networking Laboratoryof the Georgia Institute of Technology as a ResearchEngineer. Since May 2001, he has been with theSchool of Engineering at Enna of the University of Catania, where he is currently an Assistant Professor.

He is serving as a Guest Editor on the editorial board of Computer Networksand Mobile Networks and Applications (MONET). He is also a Member of thetechnical program committee of several conferences. Moreover, he has beenthe Technical Program Co-Chair of Med-Hoc-Net 2004. His research interestsinclude mobile and satellite networks, self-organizing networks, quality of service (QoS), and traffic management.

Dr. Morabito is serving on the Editorial Board of IEEE Wireless Communi-cations Magazine.

Giovanni Schembra received the degree in elec-trical engineering from the University of Catania,Catania, Italy, in 1991. Working in the telecom-munications area, he received the Master’s degreefrom CEFRIEL, Milan, Italy, in 1992, with his thesisfocusing on the analytical performance evaluation inan ATM network. He received the Ph.D. degree inelectronics, computer science, and telecommunica-tions engineering with a dissertation on multimediatraffic modeling in a broadband network.

He is currently an Assistant Professor in Telecom-munications at the University of Catania.

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