IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005 369

An Analytical Framework for the Design of

Intelligent Algorithms for Adaptive-Rate

MPEG Video Encoding in Next-Generation

Time-Varying Wireless Networks

Laura Galluccio,Francesco Licandro,Giacomo Morabito,and Giovanni Schembra

Abstract—Adaptive rate video encoding is required to maximize

efﬁciency when wireless links are involved in the communication.

In fact,wireless channels are characterized by high,time-varying

bit error rates.To cope efﬁciently with this problem adaptive

forward error correction schemes have been proposed.These

schemes introduce an amount of redundancy dependent on the

channel conditions.Accordingly,the bandwidth available at the

application layer changes:it increases when channel conditions

improve,and decreases when channel conditions worsen.Ob-

viously,the encoding parameters must be tuned to adapt the

video source transmission rate to the available bandwidth.This

adaptation is achieved by means of appropriate feedback laws,

which are relationships between the encoding parameters to be

used and other variables representing the state of the system.In

this paper,an analytical framework is introduced which can be

used for the design of the feedback laws.To this purpose both the

channel and the video source are modeled by means of Markov

models.The resulting model of the whole system is denoted as

SBBP/SBBP/1/

.Analysis is derived which allows to evaluate the

most signiﬁcant performance measures and,therefore,to design

optimal feedback laws.

Index Terms—Forward error correction (FEC),MPEG,

quality-of-service (QoS),switched batch Bernoulli process

(SBBP),wireless channels.

I.I

NTRODUCTION

M

OBILE access to video applications is among the most

important services users expect to receive by next gen-

eration networks.This,however,still represents a challenging

task.In fact,on the one hand,video services require a large

amount of bandwidth and reliable delivery of the information

data to provide users with satisfactory perceived quality.On the

other hand,wireless links,which are utilized to obtain mobile

access,are characterized by a limited amount of available band-

width and high time-varying bit-error rates (BERs).To cope

with these issues.

• Video compression/encoding techniques,e.g.,MPEGand

H.263,are utilized at the source to decrease the bandwidth

Manuscript received December 1,2003;revised May 15,2004.The work

of L.Galluccio was supported in part by MIUR under Contract VICOM.The

work of G.Morabito was supported in part by the European Commission under

Contract ANWIRE-IST 2001-38835.

The authors are with the Dipartimento di Ingegneria Informatica e

delle Telecomunicazioni,University of Catania,6-95125 Catania,Italy

(e-mail:lgalluccio@diit.unict.it;ﬂicandro@diit.unict.it;gmorabi@diit.unict.it;

schembra@diit.unict.it).

Digital Object Identiﬁer 10.1109/JSAC.2004.839386

requirements.In this paper,we will focus on MPEG en-

coding although the proposed approach can be extended

to any video encoding technique.

• Forward error correction (FEC) schemes are utilized in the

wireless link to improve reliability and,thus,decrease the

bit-error rate (BER).

However,FEC schemes introduce redundancy which decreases

the amount of bandwidth available at the application layer.Thus,

in order to increase efﬁciency,adaptive FEC (AFEC) schemes

can be utilized,which adapt the amount of redundancy to the

current link conditions [3],[4],[9],[10].

More speciﬁcally,in this paper,we propose to use adaptive

FEC solutions which exploit the fact that:

• when link conditions are good,i.e.,BER is low,low

amount of redundancy is introduced;

• when link conditions are bad,i.e.,BER is high,high

amount of redundancy is introduced.

Accordingly,the amount of bandwidth available at the appli-

cation layer changes depending on the channel conditions.The

video source must adapt its transmission rate to the amount of

available bandwidth by tuning appropriately the encoding pa-

rameters.To this purpose,the

MPEG encoder uses a rate con-

troller which adapts the output rate by appropriately setting the

quantizer scale parameter (QSP) [18],[11],[31] to the cur-

rent available bandwidth.In order to achieve this target,the rate

controller monitors the available bandwidth,the activity of the

frame which is being encoded,the encoding mode,and the state

of the transmission buffer to take into account the amount of

data used to encode the previous frames;then it chooses the ap-

propriate QSP in such a way that the transmission buffer at the

source never saturates.The relationship between the QSP and

the above parameters is called feedback law.

The target of this paper is to deﬁne an analytical framework

which can be applied to the design of the feedback law and the

other rate controller parameters to optimize performance.To

this aim,we model the whole system as an emission process

which feeds the transmission buffer;the server of this buffer

behaves according to the channel conditions estimated by the

adaptive error controller.In particular,the service rate is higher

when channel conditions are good and lower when channel

conditions are bad.We denote the whole transmission system

model as SBBP/SBBP/1/

1

because it is a queueing system

1

represents the buffer queue length.

0733-8716/$20.00 © 2005 IEEE

370 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

Fig.1.Video transmission system architecture in mobile terminal.

model characterized by two switched batch Bernoulli processes

(SBBPs) [13],one modeling the trafﬁc at the input of the buffer,

and the other modeling the buffer queue server.

This model is used in the paper to evaluate performance in

terms of the distortion introduced by the quantization mech-

anism in the encoding process and transmission buffer queue

length statistics,at different target packet error probabilities

achieved using AFEC,comparing two different feedback laws.

Support of video applications in wireless networks has re-

ceived much attention in the recent past.Optimization schemes

have been developed which operate at the source [28],[34],

[20],on the wireless links [16],and at the destination [14].

At the video source,methodologies for the joint control of

MPEG and FEC encoding schemes have been proposed [20],

[28],[34].However,all these solutions are based on heuris-

tics and,therefore,they require an analytical support.The

analytical framework introduced in this paper can be used to

evaluate the performance of any joint MPEGand FECencoding

mechanism.

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

describes the wireless MPEG transmission system considered

in the paper.Section III proposes an analytical framework

of the whole video transmission system,accounting for both

the video source and the transmission channel.Sections IV

and IV-B provide derivation of the performance parameters.

Section V applies the analytical framework to a case study,

in order to demonstrate the model’s capability of providing

performance insights for system design.Finally,Section VI

concludes the paper.

II.S

YSTEM

A

RCHITECTURE

The architecture of the video transmission system in the

mobile terminal considered in this paper,as shown in Fig.1,

consists of three components:the adaptive-rate source,the

transmission buffer,and the adaptive error controller.In the

following sections,the three components will be described

in detail.

A.Adaptive-Rate Source and Transmission Buffer

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

source over a user datagram protocol/Internet 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 [1],[2].In the MPEG encoding

standard,the frame,which corresponds to a single picture in

a video sequence,is the basic displaying unit.Three encoding

modes are available for each frame:intraframes (I),predictive

frames (P),and interpolative frames (B).In encoding each

frame,it is possible to tune both the number of bits needed to

represent the frame and its quality,by appropriately choosing

the so-called quantizer scale parameter (QSP).Its value can

range in the set [1],[31]:1 being the value giving the best

encoding quality but the maximum number of bits required

to encode the frame,and 31 being the value giving the worst

encoding quality,but the minimumnumber of required bits.

The QSP can be dynamically changed according to the feed-

back lawimplemented 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 packetizer according

to the UDP/IP protocol suite:the packetizer fragments the infor-

mation ﬂow into data units of

bytes.

2

These units constitute

the payloads for the UDP,which adds a header of 8 bytes;then

each UDP packet is put in the payload ﬁeld of an IP packet,with

an IP header of 20 bytes.

2

If RTP/RTCP protocols are also used over the UDP/IP protocol suite the

related overhead should be considered.

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 371

The IP packets are then sent to a transmission buffer whose

service rate is time-varying and depends on the redundancy

introduced by the adaptive error controller according to the

channel conditions estimated,as will be explained below.The

main target of the

rate controller is to avoid buffer saturation,

which causes losses and long delays,and maximize the en-

coding quality and stability.To this end,the rate controller

chooses the QSP according to a feedback law monitoring the

activity of the frame being encoded,its encoding mode (I,

P,or B),the current number of packets in the transmission

buffer as well as the available link capacity at the output of

the transmission buffer.The model introduced in the paper is

so general that it can be applied whatever the feedback law

is,provided that the parameter to be varied is the QSP.More

speciﬁcally,two feedback laws are considered and compared

in Section V-A.The ﬁrst law,working on frame base,has the

target of maintaining the output buffer queue length constant

at the end of each frame encoding;instead the second law,

working on group of pictures (GoP) base,will be deﬁned in

such a way that a given number of packets are present in the

transmission buffer at the end of each GoP,while pursuing a

constant distortion level within the GoP.

B.Adaptive Error Controller

Packets leaving the adaptive-rate source enter the adaptive

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

problem of wireless link unreliability.Given that wireless

channel conditions change dynamically,AFEC encoding is

applied,as proposed in [3],[4],[9],and [10].The FEC block

creator divides packets into sets of

blocks.These blocks

are given as input to the AFEC Encoder and encoded in sets

of

blocks,with

.If any set of

blocks related to

the same packet is received correctly,then the original packet

can be reconstructed correctly.Obviously,the larger the value

of

,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

has to be chosen by the FEC controller in such a way that

the packet error probability,i.e.,the probability that a packet

cannot be reconstructed at the receiver station,is no higher than

a target value,

.The AFEC encoder requires knowledge

of 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

so that

the requirement on the packet error probability is satisﬁed.The

value of

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

the available capacity,

,also changes in time as

(1)

being

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

any time the service rate of the transmission buffer is set equal

to

.Accordingly,both the MPEG encoder output process

and the transmission buffer service process are stochastic pro-

cesses,the ﬁrst depending on the behavior of the source and the

Rate Controller,the second on the BER behavior of the wire-

less channel.These processes will be modeled with two dis-

crete-time SBBP processes,

and

,respectively,as

described in detail in Section III.

III.A

NALYTICAL

M

ODEL OF THE

S

YSTEM

Here,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-A and B will describe the models

of the noncontrolled MPEG encoder output and the available

capacity of the channel as switched batch Bernoulli processes

(SBBPs) [13].Then,the whole system will be modeled as an

SBBP/SBBP/1/

queueing system in Section III-C,where

is the maximumnumber of packets the transmission buffer can

contain.For the sake of completeness,the Appendix provides a

brief outline of SBBP emission processes.

A.Model of the Noncontrolled MPEG Video Source

The noncontrolled MPEGvideo source is the part of the adap-

tive-rate source shown in Fig.1 comprising the video source,

the MPEG encoder and the packetizer.We denote it as noncon-

trolled because we are assuming it works with a constant QSP,

,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

,modeling the emission of the noncontrolled MPEG video

source at the packetizer output for each QSP

.

This model was calculated by the authors in [7] and [23].

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

works in order to deﬁne the notation.The model captures

two different components:the activity process

3

behavior and

the activity/emission relationships.As input it takes the ﬁrst-

and second-order statistics of the activity process,and the

three functions,one for each encoding mode (I,P,or B),

characterizing the activity/emission relationships.The state

of the underlying Markov process of

is a double variable,

,where

is the

state of the underlying Markov chain of the activity process,

,and

is the frame to be encoded in the GoP

at the slot

.The state set

represents the set of activity

levels to be captured,each of which is a state of the underlying

Markov chain of the activity SBBP.

According to [8],in our example,we have

.The set

,on the

other hand,represents the set of frames in the group of pictures

(GoP) and depends on the GoP structure;for example,if the

movie is encoded with the GoP structure IBBPBB,the set

is

deﬁned as

.

As demonstrated in [7],[23],the underlying Markov chain

of

is independent of

.Therefore,we will indicate its tran-

sition probability matrix as

instead of

,and the set

3

The activity of a frame only depends on the peculiarities of the picture itself.

More speciﬁcally,three elements are considered to encode a picture:luminance

,chrominance

and chrominance

.In particular,the activity of a frame

is calculated considering only its luminance,which is the most relevant compo-

nent.

372 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

for each

,deﬁnes the SBBP emission

process modeling the output ﬂow of the noncontrolled MPEG

encoder,when it uses a constant QSP value

.

B.Model of the Service Process

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

process

,representing the service process of the transmis-

sion buffer when AFEC is employed.As said so far,it closely

depends on the amount of redundancy the AFEC encoder intro-

duces to achieve the target maximum packet error probability

,due to the wireless channel.

As usual,(e.g.,[19],[30],and [33]),we assume that the

channel behavior can be described by means of an

-states

Markov process.Accordingly,channel statistical behavior can

be described by an

transition probability matrix

,

and by the bit-error rates

,for each state of the process

.

Thus,the service SBBPmodel is represented by the following

parameters:

• the maximum number of packets that can be transmitted

in a time slot

;

• the state space

;

• the matrix set

containing the transition

probability matrix and the channel transmission proba-

bility matrix.

Obviously,the transition probability matrix

of the un-

derlying Markov chain of the process

coincides with the

channel transition probability matrix

,as calculated in [12],

[33].The state space,

coincides with the channel state

space,i.e.,

.Instead,in order to calculate

,

we have to calculate the bandwidth reduction due to the AFEC

redundancy,for each state

of the channel SBBP.This depends

on the BER characterizing the state

.

The FEC redundancy to be introduced to achieve the target

value for the maximum packet error probability

should

be such that the resulting packet error probability for any state

of the channel,

is lower than or equal to the target one,

i.e.,

(2)

According to the notation introduced in Section II,let us in-

dicate the number of blocks which are encoded together by the

AFEC encoder as

,the number of blocks created by the AFEC

encoder each time it encodes

blocks as

,and the size of

each block,expressed in bits,as

.Assuming that losses intro-

duced by the wireless channel are independent and uniformly

distributed within a block,

4

the packet error probability when

the channel is in the generic state

can be calculated as follows:

(3)

4

This assumption is accurate if interleaving is utilized,which is usual in wire-

less communications [35].

TABLE I

P

ARAMETERS IN THE

P

EDESTRIAN

C

ASE

(

Hz)

TABLE II

P

ARAMETERS IN THE

D

RIVER

C

ASE

(

Hz)

where

represents the probability that a block is cor-

rupted when the channel is in the state

,and can be evaluated

as follows:

(4)

Now,substituting (3) in (2),we can numerically ﬁnd the min-

imum value of

verifying the inequality in (2) for each value

of the channel state.Let us indicate this value as

.Accord-

ingly,the bandwidth

,(in [packets/s]),which is actually avail-

able to the application to obtain a packet error probability lower

than

in the wireless channel when its state is

,can be

calculated as follows:

(5)

where

is the channel bandwidth when no FEC encoding is

applied,(in [packets/s]).

Finally,denoting

the packet payload size at the applica-

tion level,and

the header overhead introduced by the under-

lying layers,the available bandwidth at the application layer,in

(packets/slot),when the channel state is

,is given by

(6)

In general,from (6),we obtain a noninteger value for

.

However,we can assume that,when the channel state is

,in

each slot the channel is able to transmit either

packets with a probability of

,or

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 373

TABLE III

R

EDUNDANCY

B

LOCKS AND

N

ET

L

INK

C

APACITY

O

FFERED TO THE

A

PPLICATION FOR

D

IFFERENT

C

HANNEL

S

TATES

AND

T

ARGET

E

RROR

P

ROBABILITIES

IN THE

D

RIVER

C

ASE

,W

HEN THE

G

ROSS

L

INK

C

APACITY

I

S

Mb/s

packets with a probability of

,where we have

indicated the largest integer not greater than

as

.

Summarizing,the transmission probability matrix of the

SBBP modeling the channel can be calculated as follows:

if

if

otherwise

(7)

where the maximumnumber of packets that can be transmitted

in one slot is

(8)

The transition probability matrix and the state space,together

with the channel transmission probability matrix and the max-

imumnumber of packets that can be transmitted in one slot de-

ﬁned in (7) and (8),completely characterize the channel SBBP

model.

C.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

of the QSP to be used by the MPEGencoder for each

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

sion systemas a whole,indicated here as

.To this aim,we use

a discrete-time queueing system model.

Let

represent the maximumnumber 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 which can leave the queue at each time slot,is a sto-

chastic process which coincides with the channel SBBP process

.

The input of the queue system coincides with the emission

process of the adaptive-rate source,indicated here as

.

Therefore,at the slot

the transmission buffer queue size is

incremented by

,and decremented by

.Both the

input and the output processes can be characterized as two

SBBP processes,as discussed above,and the slot duration is

the frame duration,

.

To model the queueing system,we assume a late arrival

system with immediate access time diagram [17],[5]:packets

arrive in batches,and a batch of packets can enter the service

facility if it is free,with the possibility of them being ejected

almost instantaneously.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.

Acomplete description of

at the

th slot requires a three-di-

mensional Markov process,whose state is deﬁned as

,where:

•

is the transmission buffer queue state in

the

th slot,i.e.,the number of packets in the queue and

in the service facility at the observation instant;

•

is the state of the underlying Markov chain of the

channel SBBP

;

•

is the state of the underlying Markov chain of

,which coincides with that of

,for any

.

According to the late arrival systemwith immediate access time

diagram,the transmission buffer state in the slot

,can be

obtained through the Lindley equation

(9)

where

is the transmission buffer state in the generic slot

,

while

and

are the server capacity and the number of arrivals

at the slot

.

The channel SBBP

,modeled in Section III-B,can be

equivalently characterized through the set of transition proba-

bility matrices,

,which are transition probability ma-

trices including the probability that the server capacity is

(in

374 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

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

[packets/slot]).These matrices can be obtained fromthe param-

eter set

as follows:

(10)

The adaptive-rate source emission process is modeled by an

SBBP whose emission probability matrix depends on the trans-

mission buffer state.In order to model this process,we use the

SBBP models of the noncontrolled MPEG video source de-

scribed in Section III-A,

,for each

.So,we

have a parameter set

,which

represents an SBBP whose transition matrix is

,and whose

emission process is characterized by a set of emission matrices,

.So,at each time slot,the emission of the

MPEG video source is,therefore,characterized by an emission

probability matrix chosen according to the QSP value deﬁned

by the feedback law

,where

is the transmis-

sion buffer state,

is the activity and

is the set of frames.

More concisely,as we did in (10) for the channel SBBP,we

characterize the emission process of the adaptive-rate source

through the set of matrices

,each

matrix representing the transition probability matrix including

the probability of

packets being emitted when the buffer

state is

.Accordingly,the generic element of the matrix

can be obtained from the above parameter set,

as follows:

(11)

where:

•

is the QSP chosen when the frame to

be encoded is the

th in the GoP,the activity is

,and

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 375

Fig.3.Average values and normalized standard deviation of the PSNR in the Pedestrian [(a) and (c)] and the Driver [(b) and (d)] case,when FFL is used.

the transmission buffer state before encoding this frame is

.

•

is the probability that the generic frame

in the GoP has an activity

when its activity level is

.This function,as demonstrated in [21],[22],and [26],

is a Gamma probability density function,whose mean

value and variance characterize the video trace.

•

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

and

,the generic element of the

transition matrix of the video transmission system as a whole,

,can be calculated thanks to (10) and (11),as follows:

(12)

where

is a boolean condition for the queue

state behavior and is deﬁned as follows:

if

otherwise

(13)

IV.P

ERFORMANCE

A

NALYSIS

A.System Solution

Once the matrix

is known,we can calculate the steady-

state probability array of the system

as the solution of the

following linear system:

(14)

376 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

where

is a column array whose elements are equal to 1,and

is the steady-state probability array,whose generic element

is

(15)

Direct solution of the system in (14) may be difﬁcult since

the number of states grows explosively as the maximum trans-

mission buffer size

increases.Nevertheless,many algorithms,

e.g.,[15],[24],and [29],enable us to calculate the array

,

while maintaining a linear dependency on

.

We explicitly observe that all computations reported in this

section do not need to be executed in real time.Indeed,they are

done off-line when designing the feedback laws.

B.Transmission Buffer Analysis

Let us nowcalculate the mean value and the normalized stan-

dard deviation of the transmission buffer queue length.They can

be derived from the marginal steady-state probability array of

the queue length as follows:

(16)

The marginal steady-state probability array of the queue

length used in (16) can be easily derived fromthe whole system

steady-state probability as follows:

(17)

C.Quantization Distortion Analysis

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

statistics of the quantization distortion,represented by the

process

.

More speciﬁcally,we will ﬁrst calculate the mean value and

the normalized standard deviation of the PSNR process.

In addition,we will quantize the PSNR process with a set

of

different levels of distortion,

,each rep-

resenting an interval of distortion values where the quality per-

ceived by the users can be considered constant.For each of these

PSNR levels,we will calculate the steady-state probability,and

the average duration of the time intervals in which the PSNR

remains within this level.As an example,for the movie Evita,

froma subjective analysis obtained with 300 tests,the following

levels of distortion were envisaged:

dB,

dB,

dB,

dB,and

dB.

Let us calculate the mean value of the standard deviation of

the PSNR process.Observe that the PSNR only depends on

Fig.4.Probability density function of the quality level in the Pedestrian (a)

and Driver (b) case.

the QSP value and the type of frame;thus,in our model it can

assume a ﬁnite set of values

.Accordingly,the mean

value and the normalized standard deviation of the PSNRcan be

derived fromthe pdf of the PSNRprocess,

as follows

[23]:

(18)

(19)

The pdf

can be easily calculated from the

transition probability matrix and the steady-state probability

array of the whole system,which have been derived in (12) and

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 377

(14),respectively,as shown in (20),at the bottom of this page.

In (20),the following parameters are used:

•

which is a Boolean condition deﬁned as

follows:

if

otherwise

(21)

•

used in (21) which is the so-called distortion

curve [8],[23],[27] for the generic frame

,representing

the curve linking the average PSNR to the QSP value

used to encode the frame.

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

process,let us deﬁne the array

whose generic element,

,

for each

,is the QSP range providing a distortion be-

longing to the

th level for a frame encoded with encoding mode

.Of course,by so doing,we are assuming that a

variation of

within the interval

does not cause any appre-

ciable distortion.Fromthe distortion curves for the movie Evita,

we have calculated the following QSP ranges corresponding to

the above distortion levels

,for each

• for I-frames:

• for P-frames:

• for B-frames:

Let

be the feedback law,linking the trans-

mission buffer state at the beginning of a generic slot

,

,the activity of the frame in the same slot,

,and

the position in the GoP of the frame to be encoded,

,to

the QSP to be used to encode the current frame.Moreover,for

each

and

,let

be the range of values of the transmission buffer state for

which the rate controller chooses QSP values belonging to the

level

,according to the adopted feedback law.By deﬁnition,

it follows that a variation of the transmission buffer state within

does not cause any appreciable distortion variation.

Let us now calculate the probability that the value of the

process

is in the generic interval

,and the

pdf

of the stochastic variable

,representing the dura-

tion of the time the process

remains in the generic

interval

without interruption.They are deﬁned as shown in

(22) and (23) at the bottom of this page.The term

in

(22) can be calculated from the pdf

obtained in (20)

as follows:

(24)

In order to calculate the pdf

in (23),let us indicate the

matrix containing the one-slot probabilities of transition toward

system states in which the distortion level is

as

.It

can be obtained from the transition probability matrix of the

system

[6],as shown in (25) at the bottom of this page.

Therefore,the pdf

can be calculated as the probability

that the system

,starting from a distortion level

,remains

in the same level for

consecutive slots,and leaves this

level at the

th slot,that is

(20)

(22)

(23)

if

otherwise

(25)

378 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

Fig.5.Average values and normalized standard deviation of the queue.(a) and (c) Pedestrian case.(b) and (d) Driver case.

where

(26)

The array

in (26) is the steady-state probability array in

the ﬁrst slot of a period in which the distortion level is

.The

array

,on the other hand,is the steady-state probability

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

and is deﬁned as

(27)

The mean value of

can be obtained as follows:

(28)

where

is the identity matrix.

V.C

ASE

S

TUDY

The target of this section is to consider a case study to show

howthe proposed framework can be applied to design the main

parameters of both the adaptive-rate source and the adaptive

error controller of the systemdescribed in Section III.The char-

acteristics of the systemwe will consider in this case study will

be described in Section V-A.Two feedback laws have been

considered in the paper.They will be formally deﬁned in Sec-

tion V-B.Finally,Section V-C will provide numerical results.

A.System Characterization

We analyzed the statistical characteristics of one hour of

MPEG video sequences of the movie Evita.To encode this

movie we used a frame rate of

frames/s,and a frame

size of

macroblocks.The GoP structure IBBPBB

was used,selecting a ratio of total frames to intraframes of

,and the distance between two successive P-frames or

between the last P-frame in the GoP and the I-frame in the next

GoP as

.The size of the transmission buffer has been

set to

packets.The gross link capacity assigned to

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 379

Fig.6.Average values and normalized standard deviation of the PSNR.(a) and (c) Pedestrian case.(b) and (d) Driver case.

the video application is 2 Mb/s.The IP packets at the wireless

terminal are divided into 40 bytes blocks,as usual in the UMTS

environment [32].The AFEC module encodes sets of

blocks into sets of

.

In this case study,we use the eight-state FSMC model intro-

duced in [33] for the wireless channel.More speciﬁcally,we

consider two different cases.

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

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

Assuming that wireless transmission is performed in the 2 GHz

band,which is the value used in UMTS [32],the maximum

Doppler frequency which is given by

[25] is

10 Hz in the ﬁrst case and

100 Hz in the second.

These values can be used as in [12],[33] to calculate

as given in Tables I and II for the pedestrian and driver cases,

respectively.The above matrices were calculated assuming

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

duration is

ms.

The target error probability values considered are

10

10

10

,and

10

.

Table III lists,for each state

of the server SBBP model,the

values of

and the resulting available link capacities,

,for

these

values in the driver case,taken as example.

B.Feedback Laws

In this case study,we will consider two different feedback

laws,both based on the statistics of the movie which is being

encoded,expressed in terms of rate and distortion curves [8],

[23],[29].The rate curves,

,give the expected number

of packets which will be emitted when the

th frame in the GoP

has to be encoded,if its activity value is

,and is encoded with a

QSP value

.The distortion curves,

,give the expected

encoding PSNR,and have been deﬁned in Section IV-C.The

rate and the distortion curves for the movie Evita we are consid-

ering in this paper are shown in Fig.2.

The ﬁrst feedback lawwe will consider in the following indi-

catedas FFL,is a frame-basedfeedback law,andit aims to main-

tain the number of packets in the Transmission Buffer queue

lower than a given threshold,

,at the end of each frame en-

coding interval.Indicating the frame to be encoded as

,its

activity as

,and the number of packets in the transmission

380 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

Fig.7.Probability density function of the quality level in the Pedestrian (a)

and Driver (b) case.

buffer queue before the encoding as

,the expected number

of packets to encode can be calculated from the rate curve,

.So,the FFL feedback lawworks by choosing the QSP

as follows:

such that

(29)

The second feedback law,indicated in the following as GFL,

is a GoP-based feedback law,because it aims to maintain the

number of packets in the Transmission Buffer queue lower

than a given threshold,

,at the end of each GoP interval,

while maintaining stable the PSNR during the whole GoP.

In this case,both the rate curves

,and the distortion

curves

are used.More speciﬁcally,if we indicate the

transmission buffer queue length and the channel available

bandwidth when the

th frame in the GoP has to be encoded as

and

,respectively,and being

the activity of this frame,

the QSP is chosen assuming that:

• the activity will remain constant during the rest of the GoP,

that is,

,for each frame

;

• the channel behavior and,therefore,the available network

bandwidth

remains constant during the rest of the

GoP,that is for each frame

.

Under these assumptions,the QSP is chosen as the minimum

QSP

,such that it is possible to ﬁnd a set of QSP values for the

next frames of the GoP

,so that:

• the PSNR of those frames is constant,and equal to the

value which should be achieved for the frame

;

• 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 which

will leave the queue until the end of the GoP,results lower

than the given threshold

.

In other words,the GFLworks by choosing the QSP,as shown

in (30) at the bottom of this page.

C.Numerical Results

In Fig.3,we show the average value,

,and

the normalized standard deviation

of the PSNR in both

the pedestrian and driver cases when the FFL feedback law is

utilized.In each ﬁgure,several curves are provided related to

different values of the target packet error probability

.The

values of

and

have been obtained using

(18) and (19),respectively.

In Fig.3(a) and (b),where we show the average value of the

PSNR in both the pedestrian and driver cases versus the target

queue length

,we observe that

increases as

the target queue length,

increases.This is obvious since

higher values of

result in lower constrains given by the

feedback law.Therefore,the video trafﬁc source can generate

a larger amount of trafﬁc and,therefore,higher PSNR can be

achieved.Also,we observe that in the pedestrian case slightly

higher PSNR values can be achieved when compared with the

driver case.This is because in the driver case link quality is

lower and,therefore,higher amount of FEC redundancy is re-

quired to achieve the desired

.Finally,we observe that the

average PSNR increases as the value of

increases.This

is an expected result because when the value of the target error

probability increases,lower amount of FEC redundancy is re-

quired and,therefore,a lower amount of bandwidth must be

wasted for transmitting overhead.

(30)

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 381

Fig.8.Average values and normalized standard deviation of the queue.(a) and (c) Pedestrian case.(b) and (d) Driver case.

In Fig.3(c) and (d),where we show the normalized standard

deviation in both the pedestrianand driver cases versus the target

queue length

,we observe that

is lowwhen the target

queue length,

,is either low,i.e.,

or close to its

maximum value,i.e.,

.This is caused by the queue

border effects.

Besides,using the probability density function of the PSNR,

given in (20),we can calculate the probability density function

of the PSNR level,

,according to (24).In Fig.4(a) and

(b),we show

versus the quality level,

,in both the

pedestrian and driver cases.These ﬁgures were obtained using

the FFL feedback lawand assuming that

and

10

.

In order to assess the ability of the FFL feedback law to

achieve its objective,in Fig.5,we show the average value and

the normalized standarddeviation of the queue length in both the

pedestrian and the driver cases,when FFL is utilized.In Fig.5,

we show several curves related to different values of the target

packet error probability,

.In Fig.5(a) and (b),we observe

that the average queue size is almost equal to the target queue

length,

,for any value of the target packet error probability,

.This is the evidence that the FFL feedback lawis able to

achieve its objective.In Fig.5(c) and (d),we observe that the

normalized standard deviation of the queue length decreases as

increases.

Now,we assume that GFLfeedback lawis utilized.Figs.6,7,

and 8 are the analogous of Figs.3,4,and 5 obtained assuming

that GFL feedback law is utilized.Similar observations can be

drawn.

By comparing the results obtained using FFL and GFL,we

observe that GFL achieves higher performance in terms of av-

erage PSNRand probability of encoding with the highest quality

level.

For the sake of comparison,in Fig.9,we show the average

PSNR in case no feedback law is used and,consequently,a

constant value for the quantizer scale parameter is applied.In

particular,three signiﬁcant values of the QSP parameter were

considered:

and

.As expected,the behavior

is independent of the case (pedestrian or driver),as well as of

the queue length target.In particular,it can be observed that the

382 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

Fig.9.Average PSNR when no feedback law is used.

Fig.10.Average queue length when no feed-back law is used.

higher the QSP,the lower the average PSNR.As expected,the

best case is

which,on the other hand,results in the

worst performance in terms of average queue length,as shown

in Fig.10.

The higher performance achieved by GFLwith respect to FFL

is also clear in Fig.11,where we show the average duration

(in slots) of a time interval spent by the video source encoding

frames with the highest quality level,

versus the target

queue length,

.This is because,consideringGFL,longer time

intervals can be exploited to comply with the target buffer queue

length and,therefore,the QSP parameter can be chosen more

conveniently.

VI.C

ONCLUSION

In this paper,we have deﬁned an analytical framework for

the evaluation of the performance of a real-time MPEG video

transmission systemover a wireless link which applies AFECto

keep the packet error probability below a given threshold.The

proposed framework can be used as a support to the design of

Fig.11.Mean time spent in the ﬁfth level for the frame- and GoP-based

feed-back laws.

appropriate control laws for the adaptation of the MPEG video

encoding to the current conditions of the network.

More speciﬁcally,the MPEG Encoder uses a rate controller

which adapts the output rate by appropriately setting the QSP

to follow the bandwidth variations while maximizing encoding

quality and stability.

The whole systemhas been modeled by an emission process

which feeds the transmission buffer;the server capacity of this

buffer depends on the channel conditions,i.e.,the service rate

is higher when channel conditions are good and lower when

channel conditions are bad.

SBBPs have been used to model both the MPEGvideo source

[7],[21],[23] and the server process of the transmission buffer

which,coincides with the time-varying available bandwidth in

the network.Accordingly,the whole system has been modeled

as an SBBP/SBBP/1/

process.

The analytical framework proposed in this paper has been

used to evaluate performance in case frame- and GoP-based

feedback laws are utilized.

Numerical results show that both feedback laws achieve

good performance in terms of PSNR.However,results show

that GoP-based solutions achieve higher average PSNR and

higher stability.The latter is demonstrated by the longer average

duration of the periods spent by the video source encoding with

the highest quality.

A

PPENDIX

S

WITCHED

B

ATCH

B

ERNOULLI

P

ROCESSES

(SBBP)

An SBBP,

,is a discrete-time emission process mod-

ulated by an underlying Markov chain [13].Each state of the

Markov chain is characterized by an emission probability den-

sity function (pdf):the SBBP emits data units according to the

pdf of the current state of the underlying Markov chain.There-

fore,an SBBP

is fully described by the state space

of the underlying Markov chain,the maximum number of data

units the SBBP can emit in one slot,

,and the matrix set

,where

is the transition probability matrix

GALLUCCIO et al.:AN ANALYTICAL FRAMEWORK FOR THE DESIGN OF INTELLIGENT ALGORITHMS 383

of the underlying Markov chain,while

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

as

,the generic elements of the matrices

and

are deﬁned as follows:

(31)

(32)

In the paper,we introduced 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 wire-

less channel capacity process.In the latter cases,we indicated

themas an

activity SBBP and a transmission channel SBBP,re-

spectively,and their matrices

as the activity probability

matrix and the channel transmission probability matrix.

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Laura Galluccio received the Laurea degree

in electrical engineering from the University of

Catania,Catania,Italy,in 2001.She is currently

working towards the Ph.D.degree at the University

of Catania.

She is also with the Italian National Consortiumof

Telecommunications (CNIT) since 2002,where she

is working as a Research Fellow within the Virtual

Immersive Communications (VICOM) Project.

Her research interests include ad hoc and sensor

networks,protocols and algorithms for satellite and

wireless networks,as well as network performance analysis.

384 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005

Francesco Licandro received the Laurea degree in

electrical engineering fromthe University of Catania,

Catania,Italy,in 2002.He is currently working to-

wards the Ph.D.degree at the University of Catania.

Since 2004,he has been working within the

NEWCOM Project.His research interests include

AQM techniques and models,methodologies for

QoS support and transmission of video on the

Internet,and network performance analysis.

Giacomo Morabito received the Laurea degree

in electrical engineering and the Ph.D.degree

in electrical,computer,and telecommunications

engineering fromthe University of Catania,Catania,

Italy,in 1996 and 2000,respectively.

From November 1999 to April 2001,he was with

the Broadband and Wireless Networking Laboratory,

Georgia Institute of Technology,Atlanta,as a Re-

search Engineer.Since May 2001,he has been with

the School of Engineering at Enna,University of

Catania,where he is currently an Assistant Professor.

His research interests include mobile and satellite networks,self-organizing

networks,quality-of-service and trafﬁc management.

Dr.Morabito is serving on the Editorial Boards of

Computer Networks and

the IEEE Wireless Communications Magazine,as a Guest Editor for Computer

Networks and MONET,and is a member of the technical programcommittee of

several conferences.Moreover,he has been the Technical ProgramCo-Chair of

Med-Hoc-Net 2004.

Giovanni Schembra received the degree in Elec-

trical Engineering from the University of Catania,

Catania,Italy,in 1991,the M.S.degree in telecom-

munications from CEFRIEL,Milan,Italy,in 1992,

and the Ph.D.degree in electronics,computer

science,and telecommunications engineering with

a dissertation on multimedia trafﬁc modeling in a

broadband network.His M.S.thesis was on the an-

alytical performance evaluation in an ATMnetwork.

He is currently an Associate Professor in Telecom-

munications at the University of Catania.

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