IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS,VOL.23,NO.2,FEBRUARY 2005 369
An Analytical Framework for the Design of
Intelligent Algorithms for AdaptiveRate
MPEG Video Encoding in NextGeneration
TimeVarying 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,timevarying
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,
qualityofservice (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 timevarying biterror 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 ANWIREIST 200138835.
The authors are with the Dipartimento di Ingegneria Informatica e
delle Telecomunicazioni,University of Catania,695125 Catania,Italy
(email: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
biterror 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.
07338716/$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 IVB 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 adaptiverate source,the
transmission buffer,and the adaptive error controller.In the
following sections,the three components will be described
in detail.
A.AdaptiveRate Source and Transmission Buffer
The adaptiverate source is an adaptiverate 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 socalled 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 timevarying 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 VA.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 adaptiverate 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
cretetime SBBP processes,
and
,respectively,as
described in detail in Section III.
III.A
NALYTICAL
M
ODEL OF THE
S
YSTEM
Here,we derive a discretetime 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 IIIA 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 IIIC,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
tiverate 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 secondorder 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 biterror 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 adaptiverate 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 discretetime 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 adaptiverate 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 threedi
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 IIIB,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.Ratedistortion 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 adaptiverate 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 IIIA,
,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 adaptiverate 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 steadystate 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 offline 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 steadystate probability array of
the queue length as follows:
(16)
The marginal steadystate probability array of the queue
length used in (16) can be easily derived fromthe whole system
steadystate probability as follows:
(17)
C.Quantization Distortion Analysis
In this section,we evaluate both the static and timevarying
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 steadystate 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 steadystate 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 socalled 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 Iframes:
• for Pframes:
• for Bframes:
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 oneslot 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 steadystate probability array in
the ﬁrst slot of a period in which the distortion level is
.The
array
,on the other hand,is the steadystate 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 adaptiverate 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 VA.Two feedback laws have been
considered in the paper.They will be formally deﬁned in Sec
tion VB.Finally,Section VC 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 Pframes or
between the last Pframe in the GoP and the Iframe 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 eightstate 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 IVC.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 framebasedfeedback 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 GoPbased 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 feedback 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 realtime 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 GoPbased
feedback 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 timevarying 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 GoPbased
feedback laws are utilized.
Numerical results show that both feedback laws achieve
good performance in terms of PSNR.However,results show
that GoPbased 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 discretetime 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,selforganizing
networks,qualityofservice 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 ProgramCoChair of
MedHocNet 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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