# Statistical Time-Frequency Multiplexing of  HD Video Traffic in DVB-T2

Authors: Mehdi Rezaei; Imed Bouazizi; Moncef Gabbouj
Journal: International Journal of Digital Multimedia Broadcasting
 (2009)

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## Abstract

Digital video broadcast-terrestrial 2 (DVB-T2) is the successor of DVB-T standard that allows a two-dimensional multiplexing of broadcast services in time and frequency domains. It introduces an optional time-frequency slicing (TFS) transmission scheme to increase the flexibility of service multiplexing. Utilizing statistical multiplexing (StatMux) in conjunction with TFS is expected to provide a high performance for the broadcast system in terms of resource utilization and quality of service. In this paper, a model for high-definition video (HDV) traffic is proposed. Then, utilizing the proposed model, the performance of StatMux of HDV broadcast services over DVB-T2 is evaluated. Results of the study show that implementation of StatMux in conjunction with the newly available features in DVB-T2 provides a high performance for the broadcast system.


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## Body

## 1. Introduction

Digital video broadcast-terrestrial 2 (DVB-T2) is going      to be
a new European Telecommunications Standards Institute (ETSI) standard
specification for digital terrestrial television. DVB-T2 is an upgrade of the
DVB-T system designed to provide new high quality services. It utilizes
advanced techniques that provide more flexibility for the broadcast system. Figure1 shows an overview of the DVB-T2 system with its main
components. The generic stream encapsulation (GSE) module encapsulates protocol
data units in a protocol-independent manner into GSE packets, which are
arranged into the so-called baseband (BB) frames by
the input stream processor module. Forward error
correction (FEC) encoding is performed at the bit-interleaved coding module using a  low-density parity
code (LDPC) concatenated to a BCH code.
Subsequent interleaving and mapping to physical
layer (PL) frames as well as OFDM
symbol mapping is performed at the frame mapper module. The resulting PL frames are then passed to the modulator modules for modulation and transmission. The newly
defined modulation modes 64 and 256 QAM and OFDM carrier modes significantly
enhance the spectral efficiency; achieving bandwidths of up to 40 Mbps (not
accounting for signaling overhead) thus, enabling the broadcast of HDTV
services over terrestrial networks.Figure 1
Overview of DVB-T2 system.As yet, another new feature, DVB-T2,
utilizes an optional time-frequency slicing (TFS) scheme for data transmission
that provides a great flexibility for system design so that a different range
of services can be deployed in the system. In this approach, multiple radio
frequency (RF) channels are combined into a coherent high-capacity channel to
utilize advantages of statistical multiplexing (StatMux) across several high-definition
(HD) services. It allows implementing a
two-dimensional StatMux over the services to improve the performance of the broadcast
system.In digital communications, video
signals are compressed in order to use transmission bandwidth efficiently. In
video compression, a video sequence can be encoded at a constant bit rate (CBR)
or a variable bit rate (VBR) bit stream. With a similar average bit rate, VBR
bit streams consume more resources in terms of transmission bandwidth and delay
than CBR bit streams. When encoding a CBR bit stream, a rate controller
strictly controls the bit rate mainly by adjusting the quantization parameter (QP).
Generally, a CBR can be achieved by large variations in QP and also in video
quality. A VBR video bit stream can be produced by encoding a video sequence with
or without a rate controller. In uncontrolled VBR, a constant QP is used for
encoding to provide a quasiconstant
and better visual quality for compressed video. In controlled VBR, the QP is controlled
by a soft rate controller to smooth the variations in the bit rate and also in
the quality. Generally, in comparison with CBR, controlled VBR can provide a better
visual quality at the expense of more variations in the bit rate. On the other
hand, in comparison with uncontrolled VBR, controlled VBR can provide less
variation in bit rate at the expense of more variations in the quality.In video broadcasting,
the video sources are encoded to VBR bit streams to provide a better average
quality for broadcasted services. However, VBR services need more resources in
terms of transmission bandwidth and delay than CBR services. When several VBR
video services are broadcasted simultaneously, utilizing StatMux can improve
the bandwidth efficiency and end-to-end delay of the broadcast system.In StatMux, a
fixed bandwidth communication channel is shared for transmitting several bit
streams. The channel is virtually divided into several variable bandwidth
channels that are adapted to the variations in the bit rate of the bit streams.
The attempt is to distribute the channel capacity among the bit streams
dynamically according to the required bandwidth by the bit streams such that a
virtual variable bandwidth channel is allocated to each bit stream.The performance of StatMux depends on
the statistical properties of the multiplexed bit streams as well as the number
of bit streams. The statistical properties of video bit streams depend on the
encoding parameters such as bit rate, frame rate, and picture size as well as video
content and the rate control method. On the other hand, the number of services
depend on the service bit rates and the channel capacity. Consequently, the
performance of StatMux is application dependent and it should be evaluated
specifically for each application. The TFS, introduced in DVB-T2, that allows
implementation of StatMux in two dimensions, makes this application more
specific. The main goal of this research is to evaluate the performance of
StatMux specifically in DVB-T2 by computer simulations. To obtain accurate
evaluation results, multiplexing simulations should be repeated many times with
different video bit streams. A huge amount of traffic is needed that can be
provided synthetically by a video traffic model. The accuracy of the simulation
results depends on the accuracy of the model. Therefore, the first attempt is
to provide an accurate model for video traffic in this application. Studying
statistical properties of HDV traffic, a model for VBR video traffics is
proposed in this paper. Then, the proposed traffic model is used to generate
synthetic traffic for evaluating the performance of StatMux in DVB-T2.The rest of this paper is organized
as follows. Background information about the VBR video traffic modeling is
presented in Section2. The proposed model for VBR video traffic is presented
in Section 3. In Section 4, the performance of StatMux in DVB-T2 is
evaluated. Some simulation results are presented in Section 5. The paper is
closed with conclusions in Section 6.


## 2. VBR Video Traffic Modeling

Accurate modeling of VBR video
traffic is important in this research. A good model predicts or provides a
desired metric or a set of desired metrics for the modeled data similar to the original
data. For example, if the packet loss probability is the desired metric, then a
good model produces traffic that precisely provides this metric of interest in
simulations.Generally, the performance of a
communication network in terms of delay, data drop rate, and bandwidth usage
depends on the statistical properties of the traffic in the network. For
example, the autocorrelation function (ACF) of the service traffic has a major
impact on the performance of communication networks. VBR video traffic was
found to exhibit self-similar characteristics [1]. In
mathematics, a self-similar object is exactly or approximately similar to a
part of itself, for example,
the whole has the same shape as one or more of the parts. Self-similarity is a
typical property of fractals. A fractal is a rough or fragmented geometric
shape that can be subdivided in parts, each of which is (at least approx.) a reduced-size
copy of the whole.The main feature of self-similar
processes is that they exhibit long range dependence (LRD), that is, their
autocorrelation functionr(k) decays less than exponentially fast, and is
nonsummable, that is, r(k)~k−β, as k→∞, for 0<β≤1. The quantity H=1−β/2 is called Hurst parameter or Hurst exponent. The Hurst
exponent was originally developed in hydrology [2]. It shows
whether the data is a purely random walk or has underlying
trends. The Hurst exponent is related
to the fractal dimension and it is a measure of the smoothness of
fractal time series based on the asymptotic behavior of the rescaled
range of the process. The Hurst exponent is defined as
(1)H=E[log(R/S)]log(T),
where T is the duration of the data sample and R/S is the corresponding value of the rescaled
range, where S denotes the standard deviation of the sample
data and R stands for the difference between the max and
min of accumulated deviation from the mean value during the time period T.
If H=0.5,
the behavior of the time series is similar to a random walk process and samples
are uncorrelated. When H>0.5,
the time series covers more distance than a random walk. In this case, the
process is, namely, persistent and samples are positively correlated.
This means that if the time series is increasing, it is more probable that it
will continue to increase. When H<0.5, the time series covers less distance than a
random walk, in which case the process is, namely, antipersistent and
samples are negatively correlated. This means that if the time series is
increasing, it is more probable that it will then decrease, and vice versa.In communication networks, the Hurst  exponent of traffic
is relevant to the buffering requirements for traffic transmission. Considering
the definition ofR in (1), in
fact it is equal to the minimum buffering space for perfect transmission of the
data during the time period T by a channel with a bandwidth equal to the
average of the bit rate. Therefore, the performance of communication networks depends
on the statistical properties of traffic such as self-similarity and
smoothness. Many video traffic models attempt to capture these relevant
statistics.Several stochastic models for video
traffic have been proposed in the past [3]. Maglaris et al. [4] used two models for a video source: a
continuous-state autoregressive (AR) Markov model and a discrete-state
continuous-time Markov process. Heyman et al. [5] and Lucantoni et al. [6] also used a Markov chain process to develop
models for video traffic at the frame level. Grunenfelder et al. [7] used an autoregressive moving-average (ARMA)
process to model video conference traffic at ATM cell level. Ramamurthy and
Sengupta [8] proposed a hierarchical composite model which
uses three processes: two AR processes and one Markov chain. The first AR process attempts to match ACF at
short lags while the second attempts to match ACF at long lags. The Markov
process captures the effects of scene changes. A combination of the three
processes yields the final model. Another hierarchical model was proposed by
Heyman and Lakshman in [9] that consists of three different stochastic
processes for video scene length, size of the first frame in the scene, and the
size of other frames in the scene, respectively. The scene change process was
found to be uncorrelated and it was enough to match the distribution of scene
length. It was found that the scene length distribution fits Weibull, Gamma,
and Pareto distributions. It was also found that the number of ATM cells in a
frame of a scene change fits Weibull and Gamma distributions. A Markov chain
was used for the frame size within a video scene. Melamed et al. [10] developed a model for video traffic based on Transform-Expand-Sample (TES)
process for the number of bits in one group of pictures (GOPs). TES processes are
designed to fit simultaneously both the distribution and ACF of the empirical
data. Lazar et al. [11] and Reininger et al. [12] used a TES process for modeling of frame and
or slice sizes. A process was used for each type of I, P, and B frames (or
slices). The final model is composed according to a deterministic structure of the
GOP. Garrett and Willinger [13] used a fractional autoregressive integrated moving
average (F-ARIMA) process to provide a model for video traffic at the frame
level. They used a hybrid
distribution which consisted of a concatenation of a Gamma and a Pareto distributions
for the frame size distribution. A background sequence is generated by an F-ARIMA process based
on a desired value for Hurst exponent and the final sequence is generated by a transformation on the
background sequence based on the parameters of the desired distribution. In a
similar approach, Huang et al. [14] used an F-ARIMA process to generate background
sequences for different frame types based on the value of Hurst
exponent. The background sequences were
transformed by a weighted sum of exponentials to match the distribution. Kruns
and Tripathi [15] proposed a model in which the video scene
length is generated by a geometric distribution. The size of I frames is modeled
by the sum of two random components: a scene-related component and an AR-2
component that accounts for the fluctuation within the scene. The sizes of P
and B frames are modeled by two processes of i.i.d. random variables with Lognormal
distributions. The final model is obtained by combining the three submodels according to a
given GOP pattern. Liu et al. [16] proposed a video traffic model in which a
hybrid Gamma-Pareto distribution is used for all three types of frames and the
autocorrelation structure is modeled using two second-order nested AR
processes. One AR process is used to generate the mean frame size of the scenes
to model the long-range
dependence and the other is used to generate the fluctuations within the
scene to model the short-range
dependence. Sarkar et al. [17] proposed another model for VBR video traffic
in which a video sequence is segmented using a classification based on size of
three types of video frames. In each class, the frame sizes are produced by a shifted
Gamma distribution.
Markov renewal processes model video segment transitions. Dai et al. [18] presented a hybrid wavelet framework for modeling
VBR video traffic. They modeled the size of I frames in the wave domain and the
size of P and B frames based on the intra-GOP correlation. The reviewed models
above are samples of different approaches. The review is not exhaustive and
some related approaches are not reviewed in this paper.The proposed models for VBR video
traffic in earlier works attempt to fit some statistical properties such as
frame size distribution, ACF, and Hurst exponent for sample video traffic data
that are encoded for a special application (e.g., video conference) by a
particular encoder (e.g., H.263, MPEG-4). Then, the proposed models have been
validated based on some practical measures such as data drop rate and delay in
buffering simulations.There are some concerns about the
previous proposed traffic models. The first concern is that most of the models
have been built based on a limited number of sample real bit streams; therefore,
the accuracy of these models is
limited to special applications in terms of video content, encoding method, and
encoding parameters. The second concern is that, although these models capture
some statistical properties of the traffic that may be correlated with practical
metrics of interest, the correlation may not be always accurate. For example,
it is possible to find bit streams with different Hurst exponents and similar practical
performance in terms of data drop rate and delay and also it is possible to
find bit streams with similar statistical properties that have different
performances in terms of data drop rate and delay. Some examples are shown in
Section5. The other concern is that all practically possible traffics may not
be covered by a model that captures only some statistical parameters. On the
other hand, some synthetic bit streams may be generated by the models which is
difficult to find a match for them among the real bit streams because some
practical constraints that exist on real bit streams are not considered in the
models. These concerns affect the accuracy of the simulation results, where
synthetic traffics are used.Considering the concerns above, in a
new approach, a model for VBR video traffic is proposed in this paper. In the
new approach, the first attempt is to capture the practical metrics of
interest, such as buffering parameters, while some statistics are used. The new
model is not limited to any special distribution, ACF, or range of
Hurst exponent. The new modeling
approach simulates the interaction between the video encoder and the video
source to generate a synthetic video traffic. The interaction of the encoder
with the video source is controlled by a rate controller. Unlike previous modeling
approaches in which first statistical properties such ACF are captured to
achieve practical properties such as buffering parameters, in the new approach,
practical properties are captured directly. The model is tuned similar to a
video encoder with a rate controller to generate traffics with desired
buffering properties. The practical and statistical properties of a video
traffic depend on the video content properties, encoding method, and rate
control algorithm. Accordingly, the proposed model can generate various
traffics according to the content, for example, sport, movie, news, and so on. Also, it can
produce video traffics according to the encoding parameters such as bit rate,
frame rate, picture size, and so on. Moreover, it can produce video traffics
according to rate control parameters such as buffering delay. These features
are beneficial in simulation
tasks in which the effects of content properties and encoding parameters on the
results of simulation are studied.From a modeling point of view, the
self-similarity properties of VBR video traffic depend on the degree of control
that is imposed on the bit rate. While uncontrolled VBR bit streams usually
have persistent behaviors with a large Hurst exponent, the controlled VBR bit streams, depending
on the degree of control, tend toward the antipersistent case.We proposed a model for antipersistent
video traffic in [19]. A multi-Gamma model
was proposed for video frame sizes in which a Gamma distribution is considered
for each picture type (e.g., I, P, and B) in each video scene. The proposed
model has many parameters to be determined. Considering the functionality of
the video rate controller and assuming uniform distributions over some
parameters of the model, the final model parameters are reduced to few
parameters. Later on, statistics collected from a large video database showed
that the assumed uniform distributions should be modified to Gamma
distributions. Accordingly, a modified version of the model is presented in [20]. The modified
parts of the model are used for the case in which synthetic bit streams are
generated without any prototype bit streams. However, the results presented in
[19, 20] do not show the effect of these modifications because the models
have been validated for the case in which they have been parameterized based on
extracted parameters from a prototype bit stream not based on the provided statistics
in the modified parts.The proposed traffic model in this
paper is a modified and a generalized form of our previous models. The previous
models can generate only antipersistent traffics in whichH<0.5, while the
new model proposed in this paper can be used for both persistent and
antipersistent traffics, that is, the Hurst exponent can assume any value in
the range of 0<H<1. The previous models were targeted for controlled VBR
with small variations in the bit rate while the new model can be used for a
wider range of VBR video including controlled and uncontrolled bit streams with
any level of variations in the bit rate. In the previous models, a constant
average bit rate is assigned to all video scenes while in the new model video
scenes may have different average bit rates that are defined according to a Gamma
distribution and also according to the buffering constraint imposed on the bit
stream. The self-similarity and LRD properties of video traffics are captured
indirectly when the buffering constraint is imposed on the bit stream.
Generating synthetic traffic by the proposed model is straightforward with a
low degree of complexity.


## 3. Proposed Model for VBR Video Traffics

A video sequence includes several
scenes and each scene includes a number of video frames from different types
such as I, P, and B frames According to the proposed model, a Gamma
distribution is used for each frame type in each video scene. Note that at the
sequence level, each frame type can have a PDF which may be very different from
the scene level because the PDFs
of video scenes are combined together at the sequence level. In the proposed
model, the PDF of each frame type can have any distribution at the sequence
level. Although other distributions such as Lognormal may be used at the scene
level, the Gamma distribution has been used because it fits well enough the
practical results and it simplifies the modeling approach. According to the
model, a Gamma PDF for the size of frame (x) of type i in scene s is considered as
(2)Gamma(x,kis,θis)=xkis−1e−x/θisθiskisΓ(kis),x>0,
where kis>0 is the shape parameter and θis>0 is the scale parameter of Gamma distribution. i stands for I, P, or B frame type. s=1,…,S denotes the scene index.To generate a synthetic video traffic
by the proposed model, several parameters should be determined. The main
parameters include the total number of frames in the video sequence (N), structure of GOP, that is, the number of P pictures (NP) and B picture (NB) in GOP, the length of video scenes as well as their parameters (kis,θis), average bit rate (B), frame rate (F), and smoothing buffer size (SB). To produce synthetic traffics, the main parameters such as N,NP,NB,B,F, and SB are set directly by the user whereas the remaining parameters are
determined as explained in the sequel.Statistics collected from a large video
database show that a Gamma PDF can be considered over the length of video
scenes as(3)PLs=Gamma(Ls,kLs,θLs), where Ls denotes the length of a video scene s.
This distribution is used to generate the length of video scenes. The shape and
scale parameters (kLs,θLs) are
content dependent. Moreover, the statistics show that a Gamma PDF can be
assumed also for the shape parameters kIs,kPs, and kBs used in (2)
over the scenes as
(4)PkI=Gamma(kI,kkI,θkI),PkP=Gamma(kP,kkP,θkP),PkB=Gamma(kB,kkB,θkB).
These distributions
are used to generate the shape parameters of the distributions used in (2). A sample histogram of kP and its related Gamma PDF are depicted in Figure 2. More details about the collected statistics are
presented in Section 5.Figure 2
Histogram of shape parameter for Gamma distributions of P frames (kP) over video scenes that is fitted to a Gamma PDF.As a new measure,relative coding complexity is defined. This measure reflects the video content properties as well as the encoding
parameters. The relative coding complexity is defined between two picture
types. The relative complexity of I to P and I to B pictures in a scene s is defined as XPs=I¯s/P¯s and XBs=I¯s/B¯s,
respectively, where I¯s,P¯s, and B¯s denote the average size of I, P, and B
pictures, respectively, in the scene s.
The relative coding complexity is a known concept that is used in some control
algorithms, for example, in [21, 22]. Experimental
results show that the values of relative complexities are not only dependent on
the properties of video content such as motion activities but they are also dependent
on the encoding parameters, such as bit rate, frame rate, GOP structure, and
picture dimensions. Moreover, they are affected by the rate control algorithm
and the smoothing buffer size. Statistics from different video sequences which
are encoded with similar encoding parameters show that the values of XPs−1 and XBs−1 have distributions close to Gamma PDF over the
scenes as
(5)PXP−1=Gamma(XP−1,kXP,θXP),PXB−1=Gamma(XB−1,kXB,θXB).
These distributions are used to generate values for the relative complexities. A sample
histogram of XP collected from real traffics and related Gamma
PDF are shown in Figure 3.Figure 3
Histogram of the relative complexityXP over video scenes that is fitted to a Gamma PDF.To find the remaining
parameters, a long-term average bit rate is defined for the video sequence,
while it may exhibit a large variation over the scenes. In our previous models presented
in  [19, 20]  for antipersistent traffic, it was assumed
that all video scenes in the sequence have a similar average bit rate. To
generalize the model, it is assumed that video scenes can have different
average bit rates Bs.
However, some constraints over the average bit rates of a video scene are
imposed to provide a buffering constraint over the final bit stream. Generally,
a Gamma PDF can be assumed for the average bit rate of video scenes as follows: (6)PBs=Gamma(Bs,kBs,θBs), where the
distribution parameters depend on the control strength and smoothing buffer
size. Using this distribution, preliminary values for the average bit rates are
generated. The preliminary values are modified if the final bit stream should
be constrained to a buffering constraint. Consider that the desired bit stream
has an average bit rate B over all scenes and it preserves a buffering constraint with buffer size SB.
To achieve the buffering constraint, similar to a rate controller, the
following constraints are imposed on the preliminary values of the scene bit
rates: (7)0<(∑s=1nBs⋅Ls/F−B/F⋅∑s=1nLs)<SB,n=1,…,S, where F denotes the video frame rate. The first term in the parenthesis
corresponds to the expected value of the overall input to the buffer and the
second term corresponds to the overall output from the buffer. Therefore, this
condition can guarantee a kind of buffering constraint based on the expected
values of scene bit rate. This condition is examined for all n from 1 to S.
If it is not met for some values of n,
then the value of Bn is corrected by a minimum change such that the condition is met. The
resulting bit stream is constrained to an expected buffer size. However, the
buffer constraint is not strict because it is imposed based on expected values
of scene bit rates. To ensure a
strict buffering constraint
for the bit stream, margins are considered for the critical buffer conditions and formula
(7) is rewritten as (8)MLSBF<(∑s=1nBsLs−B∑s=1nLs)<MHSBF,n=1,…,S, where ML and MH are two margins (e.g., 0.2 and 0.8) for low
and high buffer fullness states, respectively.For a GOP in a video scene, the
average frame size can be estimated as(9)x¯=μIs+NPμPs+NBμBs1+NP+NB=BsF. From the definition of
relative complexity, it is concluded that (10)μIs=μPsXPs=μBsXBs, where μis denotes the mean frame size of type i in a video scene s.
Combining (9) and (10), the values of μIs,μPs, and μBs are obtained for each video scene. For a Gamma
distribution, Mean=kθ; and therefore, the scale parameters are
obtained as (11)θIs=μIskIs,θPs=μPskPs,θBs=μBskBs. The shape parameters
have been already generated by (4).
Now, all the required parameters for generating
the video scenes and the desired bit stream are available.There are only few parameters that
are defined by the user for the model and still they can be reduced.
Experimental results show that the model is not very sensitive to the shape
parameters used in Gamma distributions (3), (4), and (5) for a relative
wide range of bit streams. Therefore, it is enough to consider constant values
for kSL,kkI,kkP,kkB,kXP, and kXB in the model. The user only defines the mean values for Ls,kI,kP,kB,XP, and XB then the scale parameters are calculated
according to the shape parameters and the mean values by Mean=kθ.
Typical values for kSL,kkI,kkP,kkB,kXP, and kXB are 1.5,5,3,3,2.5, and 2.5, respectively. The algorithm of
generating synthetic video traffics is summarized as follows.
(1)
Define the desired encoding parameters
including the number of frames (L), the average bit rate (B), the frame rate (F), and the GOP structure (NP,NB).(2)
Define the mean values forLs,kI,kP,kB,XP, and XB according to the content and encoding parameters.(3)
Using the mean values ofLs,kI,kP,kB,XP, and XB,
calculate the scale parameters θLs,θkI,θkP,θkB,θXP, and θXB according to Mean=kθ.(4)
Using (3), generate S scene length Ls, such that
(12)∑s=1SLs≥L.(5)
Using (6) and (8), generate the scene bit rates.(6)
Using (5), generate the
relative complexities XPs and XBs.(7)
Combine (9) and (10), calculate μIs,μPs, and μBs for each video scene.(8)
Using (4), generate kIs,kPs,kBs.(9)
Using (11), calculate θIs,θPs, and θBs for the scenes.(10)
Using (2), generate the frame sizes for each video
scene.


## 4. Performance of Statmux in DVB-T2

In this section, the
performance of StatMux in DVB-T2 is evaluated by simulations. In the TFS
transmission scheme as defined by DVB-T2, the service data is transmitted as
time-frequency slices, that is, time-slice frames that are transmitted by
parallel radio channels. The time slices have durations of about a few hundred
milliseconds (typically 180 milliseconds) and a number of maximum 6 RF channels
can be used for transmission of time-sliced data. Figure4 shows an example of a TFS frame for 4 RF channels and
15 services. There is a time shift between the services in different RF
channels to enable frequency hopping at the receiver. At the beginning of each
frame, two synchronizing symbols are inserted (shown as P1 and P2 in the figure).
The synchronization symbols allow a receiver to rapidly detect the presence of
DVB-T2 signal, as well as to synchronize to the frame. Data related to a number
of different services can be statistically multiplexed over the two dimensions
of time and frequency. Performance of StatMux in DVB-T2 depends on the
bandwidth of the coherent transmission channel, the number of multiplexed services,
and the statistical properties of service traffics. A set of comprehensive
simulations were performed to evaluate the performance of StatMux of HDV
services over DVB-T2.Figure 4
Example of a TFS frame for 4 RF channels and 15 services.


### 4.1. Simulations

To evaluate the performance of StatMux in DVB-T2, StatMux is compared with
deterministic multiplexing (DetMux) in which a fixed bandwidth is allocated to
each service. To provide accurate results, the multiplexing simulations were
performed as close as possible to a real system. Service traffics were
generated with parameters similar to typical real traffics and typical values
were selected for simulation parameters. According to the simulation, for each
service, video frames are packetized into protocol data unit (PDU) and then GSE
packets [23]. BB frames are
formed from the GSE packets and FEC parity check data with a code rate of 1/4
were added [24]. BB frames are
buffered in the service buffers. In a real system, convolutional interleaving
is performed on BB frames, that is not essential for the multiplexing
performance and, hence, it is not implemented in the simulations. Multiplexing
simulations are performed over the BB frames stored in the service buffers.
Detailed simulation parameters are presented in Section 5. Multiplexing
algorithms are explained in the sequel.


### 4.2. Multiplexing Algorithms

In an ideal case of StatMux, the available bandwidth is distributed between the
services proportional to their temporal required bandwidth. A multiplexing algorithm
was used in the simulation that performs close to the ideal case. According to
the method used, the TFS frames are formed such that the number of allocated BB
frames to each service is proportional to the amount of stored BB frames in the
service buffer. As a simple case, consider the case ofN services being multiplexed that have similar
average bit rates and each TFS frame carries BTFS number of BB frames. When forming a TFS frame,
if the service buffers contain B1,B2,…, and BN number of BB frames, b1,b2,…, and bN number of BB frames from services 1,2,…, and N, respectively, are used for forming
the TFS frame such that (13)bi=BTFSBi∑j=1NBj,i=1,2,…,N.In a general case in which the
multiplexed services have different average bit rates, the buffer occupancies
are normalized to the average service bit rates as(14)bi=BTFSBi/Ri∑j=1NBj/Rj,i=1,2,…,N, where Ri denotes the average bit rate of the ith service.In the simulation of DetMux, TFS frames
are formed such that a fixed number of BB frames is allocated to each service
in all TFS frames. Details of simulation parameters are presented in Section5.


## 4.1. Simulations

To evaluate the performance of StatMux in DVB-T2, StatMux is compared with
deterministic multiplexing (DetMux) in which a fixed bandwidth is allocated to
each service. To provide accurate results, the multiplexing simulations were
performed as close as possible to a real system. Service traffics were
generated with parameters similar to typical real traffics and typical values
were selected for simulation parameters. According to the simulation, for each
service, video frames are packetized into protocol data unit (PDU) and then GSE
packets [23]. BB frames are
formed from the GSE packets and FEC parity check data with a code rate of 1/4
were added [24]. BB frames are
buffered in the service buffers. In a real system, convolutional interleaving
is performed on BB frames, that is not essential for the multiplexing
performance and, hence, it is not implemented in the simulations. Multiplexing
simulations are performed over the BB frames stored in the service buffers.
Detailed simulation parameters are presented in Section 5. Multiplexing
algorithms are explained in the sequel.


## 4.2. Multiplexing Algorithms

In an ideal case of StatMux, the available bandwidth is distributed between the
services proportional to their temporal required bandwidth. A multiplexing algorithm
was used in the simulation that performs close to the ideal case. According to
the method used, the TFS frames are formed such that the number of allocated BB
frames to each service is proportional to the amount of stored BB frames in the
service buffer. As a simple case, consider the case ofN services being multiplexed that have similar
average bit rates and each TFS frame carries BTFS number of BB frames. When forming a TFS frame,
if the service buffers contain B1,B2,…, and BN number of BB frames, b1,b2,…, and bN number of BB frames from services 1,2,…, and N, respectively, are used for forming
the TFS frame such that (13)bi=BTFSBi∑j=1NBj,i=1,2,…,N.In a general case in which the
multiplexed services have different average bit rates, the buffer occupancies
are normalized to the average service bit rates as(14)bi=BTFSBi/Ri∑j=1NBj/Rj,i=1,2,…,N, where Ri denotes the average bit rate of the ith service.In the simulation of DetMux, TFS frames
are formed such that a fixed number of BB frames is allocated to each service
in all TFS frames. Details of simulation parameters are presented in Section5.


## 5. Simulation Results

Some simulation results are presented in
this section that can be divided into two parts. The first part is related to
the proposed video traffic modeling approach and the validation of the model.
The second part of the results presents the performance of StatMux in DVB-T2.To collect some statistics form real
video bit streams, a comprehensive study on a large set (40 sequences) of long
(about 2500 to 5000 frames per sequence) HDV sequences was performed. After a
preliminary study, a number of 25 HDV sequences with a resolution of1280×720 (720 p) were selected from [25–27]. The selected
video sequences, which were encoded with a bit rate higher than 6 MB/s, were
decoded and used as source signals when they are again encoded at a bit rate of
6 MB/s in our simulations. The video sequences were encoded several times by
the FFMPEG H.264/AVC encoder with different buffering constraints [28]. A VBR rate
controller is implemented in FFMPEG encoder that was used in the simulations. Smoothing buffers with sizes corresponding to
0.5,1,2,3,4, and 10 seconds buffering delay were used for the rate control.
Moreover, the sequences were encoded with constant QPs and without any
buffering constraint. Various statistics related to the proposed traffics model
were collected. These include video scene length, scene bit rate, relative
complexity of picture types, shape and scale parameters of the Gamma PDFs,
Hurst exponent, minimum buffering delay, variance, and mean of different
picture types. The collected statistics formed a rich database that was used
for building and parameterizing the proposed traffic model. Few hundred video
scenes were used in the simulations. Due to space limitation, the results presented
in this section constitute only a small part of collected results.As sample
results, Figure5 to Figure 10 compare the results of encoding “The Living Sea”
video sequence in two cases: uncontrolled VBR and controlled VBR cases. The other
encoding parameters such as average bit rate, frame rate, and GOP structure are
similar for both cases. The fullness of the decoder buffer (with zero buffering
period) and the size of the video frames for the two cases are shown in Figures 5
and 8. Histograms of I and P frames are depicted in
Figures 6 and 9 for the two cases.
Figures 7 and 10 show the ACF of video frames size for the two cases. The
figures show that the size of the video frames, the distribution of the video
frame size, and the ACF are very different in the two cases. These sample
results prove that the statistical properties of VBR video traffics depend on
the encoding process. Therefore, the encoding process is considered in the
proposed modeling approach.Buffer occupancy and frame size of “The
Living Sea” video sequence encoded with a constant QP.
(a)(b)Histograms of P and I frame size in “The Living Sea” video sequence encoded with
a constant QP.
(a)(b)Figure 7
ACF of picture size in “The Living Sea” video
sequence encoded with a constant QP.Buffer occupancy and frame size of “The
Living Sea” video sequence encoded with FFMPEG VBR video rate controller.
(a)(b)Histograms of P and I frame size in “The
Living Sea” video sequence encoded by FFMPEG VBR video rate controller.
(a)(b)Figure 10
ACF of picture size in “The Living Sea” video
sequence encoded with FFMPEG VBR video rate controller.To show the
relation between the statistical properties and the practical parameters of
real bit streams, the Hurst exponent and the minimum buffering delay for a number of encoded bit streams
were measured and are depicted in Figure11.
This figure shows that some bit streams with similar
Hurst exponents have very different buffering
requirements and also some bit streams with similar buffering requirements have
very different Hurst exponents. Note that there is a tradeoff between buffering requirement and
bandwidth in a communication network. Consequently, another important result is
that statistical properties may not always reflect the practical parameters and
thus previous models that rely only on capturing such statistical properties
may not be accurate for estimating practical metrics of interest. The proposed
model solves this problem by taking the practical parameters such as encoding
parameters and buffering constraints into consideration in the modeling
approach.Figure 11
Hurst exponent versus buffering delay in real traffics.The proposed traffic model is a modified
version of our previous models that were validated successfully in [19, 20]. To validate the
multi-Gamma video traffic model proposed in [20], we selected a
set of known video sequences including Foreman, Carphone,
Silent, New York, and Football sequences. We repeated and concatenated each of these
sequences to provide longer sequences (900 frames) and then the resulting sequences
were concatenated again to make a longer video sequence. The fact that the
resulting video sequence has several different scenes was suitable for
evaluating the model. The video sequence was encoded with a bit rate of 300 kb/s, a frame rate of 30 f/s, and a buffering delay of 0.4 second to produce a
prototype video bit stream. The model parameters were extracted based on the
prototype bit stream and a synthetic sequence was generated by the proposed
model. The prototype and the synthetic traffics were compared by several
measures including histogram, ACF, Hurst exponent, and buffering requirements.
The simulation results presented in [20] show that the multi-Gamma model can generate
synthetic bit streams close to the prototype real bit streams when they are
parameterized according to the prototypes. The modifications of the model are
related to the case in which the synthetic traffics are generated without the
use of any prototype. Therefore, the validation results presented in [20] are not repeated in this paper and only the
modified part of the model is validated. Generating the multi-Gamma model
parameters is part of these modifications. The collected
statistics from the real bit streams show that the Gamma distributions can be
fitted to the shape and the scale parameters of the multi-Gamma model over the
video scenes. Figure 2 shows the histogram of
the shape parameter of the Gamma
distributions of the P frames over the scenes (kP) as a sample. As shown, a Gamma PDF is fitted to the histogram. Moreover, the statistics show that other Gamma distributions can be
fitted to the relative complexities XP and XB over the video scenes. Figure
3 depicts the histogram of the relative complexity XP over the scenes and also a Gamma PDF that is fitted to the histogram. The
number of parameters that need to be determined for the multi-Gamma model is
proportional to the number of scenes in a video sequence. The above results are
used to generate the parameters of the multi-Gamma model by only few other Gamma
distributions each defined by only two parameters. In fact, we model the
parameters of the multi-Gamma model to decrease the number of parameters that
is required for generating synthetic traffic. Another part of the modification
of the model is related to the range of operation that is validated below.The model has been modified to generate
bit streams with a wide range of statistics and practical metrics of interest. To
validate the proposed model in a wide range of operation, the model was
parameterized to generate synthetic video bit streams with different buffering
constraints. Buffer sizes corresponding to target maximum buffering delays of 1
to 15 seconds were used in the model. For each buffer size or target delay, a
number of 20 bit streams, each including 3000 frames, with a bit rate of 6 MB/s
were generated. Values of100,180,46,46,3, and 4.3 were used for mean of Ls,kI,kP,kB,XP, and XB, respectively, as user-defined parameters. Buffering simulations were performed
on the bit streams and the minimum (over the frames) buffering delay for zero
data drop rate was measured for each bit stream. The measured values have been
compared with the target maximum buffering delay in Figure 12.
As shown, the maximum (over 20 samples) delay obtained
is close to the target maximum delay in different operating points or target
delays. Moreover, delays obtained for 20 samples in each target delay have been
distributed below and are close to the maximum values. This is very similar to real conditions in which
the encoded bit streams by a rate controller may not use the whole available
range of the buffer space. When generating the bit streams above, only the sizes of buffer SB and kBs were changed for different operating points and all other parameters were
kept fixed. Simulation results show how well synthetic bit streams are in conformance
with the desired practical constraints. Previous traffics models are usually validated by
comparing the performance of real and modeled traffics in term of data drop
rate in a buffering delay. In the simulation above, we consider the performance
of modeled traffics in term of minimum delay for the zero data drop rate case
which is a fixed practical reference point. This is beneficial from two points
of view. First, when the model is used for simulation of StatMux in DVB-T2, we
are interested in the zero drop rate case. Second, when in practice a video
sequence is encoded, it is encoded with a buffering constraint for a zero data
drop rate not for a target nonzero drop rate. However, the proposed model can
be easily tuned by kBs for a target nonzero data drop rate and a
given delay. Therefore, the proposed model can be tuned similar to a video
encoder and a video rate controller. This is a great advantage of the proposed model.Figure 12
Resulted delay for modeled traffics versus target max delay.The above results show that the proposed
model can provide practical metrics of interest for the synthetic traffics with
a wide range of statistics. To assess the range of statistics of the metrics,
for the generated bit streams explained above, the Hurst exponents were computed and are
depicted in Figure13. An approximate exponential function between the
buffering delay and Hurst exponent can be considered over the results. This is in conformance with
collected statistics from real bit streams depicted in Figure 11.
Using the approximate exponential function, the model can be tuned to
generate bit streams with a target Hurst exponent in the whole range. Note that
our previous models are valid only for H<0.5 while the new model is valid for 0<H<1.Figure 13
Hurst  exponent versus buffering delay in modeled traffics.To evaluate the performance of StatMux
over video broadcast services in DVB-T2, the proposed traffic model was
parameterized to generate synthetic traffics corresponding to HDV contents with
3000 frames, 6 MB/s, and with a GOP structure as “I B P B P B P B P B P B”. The
model was tuned to generate traffics with different buffering constraints
including4,5, and 7 seconds target buffering delays. Multiplexing simulations
were performed over the synthetic video bit streams as explained in Section 4.
6 RF channels were considered in the simulations. The performance of StatMux was
compared with the performance of DetMux at several operating points in a two-dimensional
space of bandwidth utilization and delay. For each operating point, two
simulations corresponding to StatMux and DetMux were performed on a
number of 14 to 20 bit streams. To provide different operating points, the
number of multiplexed services has been changed from 14 to 20 while the
transmission bandwidth was kept constant. To get statistically acceptable
results, for each operating point, the simulations were repeated 5 times. The
whole procedure above was repeated 3 times to get 3 performance curves corresponding
to the bit streams with 3 different buffering constraints. The performance
curves are depicted in Figures 14 and 15.
The bandwidth utilization is depicted as a function
of buffering delay in StatMux and DetMux for three different groups of video
bit streams. The groups have different buffering constraints corresponding to
3,5,7 seconds. D3, D5, and D7 in the figures correspond to DetMux while S3,
S5, and S7 correspond to StatMux. Figure 15 is a zoomed version of
Figure 14 in a low-delay practical operating area. The high
delay end points on the curves of DetMux in Figure
14 are very close to the target delays (3,5,7 seconds)
used for generating traffics in the model. This closeness shows that the model
performs accurately in different operating points. Moreover, it proves the
accuracy of the multiplexing simulations. Sample results from the curves shown
in Figure 15 are presented in Tables 1–3. Moreover, the
gain of StatMux is presented for 5 operating points in the tables. The gain of
StatMux was computed in term of percentage of bandwidth increase with respect
to DetMux. According to Table 1, when the bit streams are constrained to a buffering
delay of 3 seconds, for a buffering delay between 26 to 200 milliseconds, a
gain of 42–58% increase in
bandwidth is expected. Table 2 shows that when the bit streams are constrained
to a buffering delay of 5 seconds, for a buffering delay between 33 to 232 milliseconds,
a gain of 54–70% increase in
bandwidth is expected. According to Table 3, when the bit streams are
constrained to a buffering delay of 7 seconds, for a buffering delay between 44
to 501 milliseconds, a gain of 64–86% increase in
bandwidth is expected. Simulation results show that using StatMux in DVB-T2 can
considerably improve the bandwidth efficiency and end-to-end delay of a broadcast
system.Table 1
Gain of StatMux in different buffering delays when the bit streams are
constrained to a buffering delay of 3 Seconds.
Delay “ms”Bandwidth utilizationGain in BW %DetMuxStatMux2650.680.058.104254.185.057.116157.290.057.3410562.695.052.7320067.295.642.26Table 2
Gain of StatMux in different buffering delays when the bit
streams are constrained to a buffering delay of 5 Seconds.
Delay “ms”Bandwidth utilizationGain in BW %DetMuxStatMux3347.180.069.855751.285.066.028654.790.064.5310558.692.257.3423261.895.053.72Table 3
Gain of StatMux in different buffering delays when the bit
streams are constrained to a buffering delay of 7 Seconds.
Delay “ms”Bandwidth utilizationGain in BW %DetMuxStatMux4443.180.085.618646.785.082.0117050.690.077.8725052.991.272.4050158.095.063.79Figure 14
Bandwidth utilization versus buffering delay
for StatMux and DetMux.Figure 15
Bandwidth utilization versus buffering delay
for StatMux and DetMux in low-delay operating area.From a video quality point of view, a
typical buffering constraint about 5 seconds is large enough to allow a
quasiconstant quality for an encoded video. According to the results presented
in Table2 for such high-quality bit streams, a bandwidth efficiency of 95% can
be achieved with only a buffering delay of 0.23 second by StatMux.


## 6. Conclusions

A model for variable bit rate video
traffics was proposed that can generate a wide range of synthetic video bit
streams with practical and statistical metrics of interest. The proposed model
was validated successfully and was used to study the performance of statistical
multiplexing of HDV services in a DVB-T2 broadcast system by computer
simulations. Simulation results showed that the TFS introduced in DVB-T2 in
conjunction with StatMux can provide a high performance in terms of bandwidth
efficiency, end-to-end delay, and video quality for the broadcast system.



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*Source: 186960-2009-01-28.xml*