A Near Optimal QoE-Driven Power Allocation Scheme for
SVC-Based Video Transmissions Over MIMO Systems
Xiang Chen1, Jenq-Neng Hwang1, Chiung-Ying Wang2, Chung-Nan Lee3
1
Department of Electrical Engineering, Box 352500, University of Washington,
Seattle, WA 98195, USA. Email: {xchen28, hwang}@uw.edu
2
Department of Information Management, TransWorld University,
Yunlin, Taiwan, ROC. Email: ann@mail.twu.edu.tw
3
Department of Computer Science and Engineering, National Sun Yat-Sen University,
Kaohsiung, Taiwan, ROC. Email: cnlee@cse.nsysu.edu.tw
Abstract²In this paper, we propose a near optimal power
allocation scheme, which maximizes the quality of experience
(QoE), for scalable video coding (SVC) based video transmissions
over multi-input multi-output (MIMO) systems. This scheme
tries to optimize the received video quality according to video
frame-error-rate (FER), which may be caused by either
transmission errors in physical (PHY) layer or video coding
structures in application (APP) layer. Due to the complexity of
the original optimization problem, we decompose it into several
sub-problems, which can then be solved by classic convex
optimization methods. Detailed algorithms with corresponding
theoretical derivations are provided. Simulations with real video
traces demonstrate the effectiveness of our proposed scheme.
Keywords²power allocation; QoE; SVC; MIMO; convex
optimization
I.
INTRODUCTION
Due to the exponentially increasing demands of wireless
multimedia applications; offering higher quality video
transmissions over wireless environments becomes an
everlasting endeavor for multimedia service providers [1].
However, the error prone and band-limited nature of wireless
channels creates obstacles for these bandwidth consuming
applications [2]. Multi-input multi-output (MIMO) technology,
which can provide more reliable and efficient wireless
communications, has been considered as one of the solutions
for better wireless video delivery [3]. Among plenty of existing
MIMO techniques, spatial multiplexing (SM) approach, which
simultaneously transmits independent data streams on each
antenna to achieve higher spectral efficiency [4], is suitable for
high data rate video transmissions. Scalable video coding (SVC)
is another attractive technique in wireless video transmissions.
Videos can be encoded with different temporal (frame rates),
spatial (picture resolutions) and quality (image fidelity)
scalabilities [5]. Parts of the encoded bit streams (higher
enhancement layers) can be removed and the resulting substreams (base layer and lower enhancement layers) can still
form another valid bit streams with lower resource
consumptions but lower video qualities [6]. Therefore, SVC
provides a way for adaptive switch between different video
qualities according to different available resources or channel
conditions at the user end.
Significant amount of researches have been conducted in
The research is based on work supported by the Ministry of Economic Affairs
(MOEA) of Taiwan, under Grant number MOEA 102-EC-17-A-03-S1-214.
transmitting SVC-based videos over MIMO-SM systems,
which require jointly optimizations of physical (PHY) layer
structures and video characteristics in application (APP) layer.
Antenna selection is one of the major techniques to improve
the video qualities. For instance, an adaptive channel selection
(ACS) scheme has been proposed in [7]. In this system, bit
streams with higher priorities will be transmitted through the
antennas with higher signal-to-noise ratios (SNRs). A crosslayer dynamic antenna selection (CLDAS) scheme [8] is
designed to jointly optimize the rate-distortion characteristics
of source-channel encoding and the multiplexing-diversity
tradeoff to mitigate the end-to-end video distortion.
Power allocation has also been adopted in video
transmissions with MIMO-SM techniques. A maximumthroughput delivery of SVC-based video over MIMO systems
has been proposed in [1], in which the traditional capacityachieving water-filling (WF) algorithm [9] is improved when
discrete modulation levels are considered in real applications.
However, this scheme is targeted on improving the throughput
of the system, which may not directly reflect quality of
experience (QoE) of users. In [10], the proposed power
allocation scheme can enhance the quality of SVC video
streaming over MIMO systems by a modified WF (M-WF)
algorithm such that unequal error protection (UEP) is applied
by setting different bit-error-rate (BER) requirements on base
layer and enhancement layers. Nevertheless, due to the
empirical nature, the fixed BER requirements may not be
optimal in different channel conditions.
Transmission errors such as damaged or lost packets will
degrade video qualities [11]. If SVC-based videos are
transmitted, decoding errors in base layer frames will cause
propagation errors in the corresponding enhancement layer
frames. Moreover, directly minimizing BER in PHY layer will
not necessarily minimize video frame error rate (FER) in APP
layer due to different packet sizes and video coding structures.
These characteristics motivate us to develop an effective power
allocation scheme to optimize the received video QoE. In this
paper, we propose a near optimal QoE-driven power allocation
scheme for SVC-based video transmissions over MIMO-SM
systems. Our proposed scheme tries to maximize the overall
video quality based on video FER where video packet sizes,
SVC layer structures and PHY layer BERs for different
modulations are jointly considered. Due to the complexity of
this optimization problem, we decompose it into several sub-
problems which can then be solved by classic convex
optimization methods. Detailed algorithms for searching the
optimal solutions and its corresponding theoretical analyses are
provided. Moreover, simulations with real SVC-based video
traces are conducted to demonstrate the effectiveness of our
proposed scheme.
This paper is organized as follows. In the next section,
system overview including SVC-based video coding and
MIMO-SM system are described. Problem formulations are
provided in Section III. In Section IV, we will describe our
proposed optimization search algorithms together with
theoretical analyses. Simulation results and conclusion remarks
are given in Section V and VI respectively.
Notations: Upper (lower) boldface letters are used for
matrices (column vectors). diag(h) is a diagonal matrix with
the elements of h sitting on the diagonal. 1 denotes a column
vector all of whose components are one. (.)H means the
Hermitian. (.)T is the transpose. IN denotes the N×N identity
matrix. dom f means the domain of function f.
II.
SYSTEM OVERVIEW
A. SVC-Based Video
An SVC encoded video consists of base and enhancement
layers in a hierarchical dependency structure, where the video
layers with higher qualities can be processed when the
corresponding low-quality video layers are successfully
decoded. Therefore, the base layer is mandatory to decode all
the other enhancement layers [12][13]. SVC can support all of
the temporal, spatial and quality scalabilities. In this paper, we
only consider videos encoded with quality scalability.
However, the similar idea can be applied to videos with
temporal or spatial scalabilities.
The QoEs at user ends are normally measured in utility
values [14]. In order to maximize the overall utilities of the
recovered videos, we choose a perceptual quality model [15]
for SVC-based videos with quality scalability:
ul
c 1 q q
­
e 1 min °
® c1ql qmin c1ql 1 qmin e
°̄e
,l 1
,l t 2
,
(1)
where c is a video dependent model parameter; ql is the
quantization stepsize of the lth video layer; and qmin is the
minimum quantization stepsize which correspond to the video
layer with highest quality.
B. Proposed System Structure
The proposed MIMO-SM system for SVC-based video
transmissions is shown in Fig. 1. A video sequence is encoded
into one base layer and L-1 enhancement layers, which are fed
into a MIMO system with Nt (Nt•/) transmitter antennas and
Nr receiver antennas. At the transmitter side, an adaptive
channel selection (ACS) module [1][7] is implemented so that
video layers with higher importance, such as base layer, are
transmitted through the channels (antennas) with higher SNR.
The power allocation module allocates appropriate power to
modulated symbols on each channel based on the cross-layer
video information and channel state information (CSI) fed back
from receiver side so that the overall utility is maximized. After
precoding, the data symbols are transmitted through wireless
channels. At the receiver side, a channel estimation module
sends CSIs back to the transmitter side. In this paper, we
assume the CSIs containing full channel knowledge are fed
back without any estimation error and delay. Similar as in [1],
we assume the channel selection sequences and modulation
schemes are known at the receiver side through control
channel. After decoding, detection, demodulation and channel
selection, the received bit-streams are fed into SVC decoder for
video reconstruction. We assume no error concealment
techniques are applied in the system. Therefore, video frames
with any single bit error are dropped. Moreover, if the lth layer
is not successfully decoded, all higher layers (i.e., from l+1 to
L) of this frame are also dropped.
C. MIMO Channel Model
The system equation can be described as:
y
Hx n ,
(2)
where y is an Nr×1 complex received signal vector, x is an
Nt×1 complex transmitted symbol vector with E[xxH]=diag(p)
=diag(p1, p2« pNt), subject to normalized power 1Tp=1 and
each element in p is not less than 0. n is an Nr×1 independent
and identically distributed (i.i.d.) complex additive white
Gaussian noise (AWGN) vector. H is Nr×Nt channel matrix in
Fig. 1. Proposed MIMO System for SVC-Based Video Transmissions
which all elements are i.i.d. circularly symmetric complex
Gaussian (ZMCSCG) random variables with zero mean and
variance 1, i.e.,
^0,1` . Therefore, the average SNR of
sk ·
§ l
max ¦ ul ¨ – 1 Pbk pk ¸
p
l
©k1
¹
subject to pk t 0; ¦ k 1 pk
L
the system is ʌ=1Tp /N0=1/N0.
MIMO channel matrix H can be decomposed by the
singular value decomposition (SVD):
H U/V H ,
(3)
where U and V are unitary matrices. ȁ is a diagonal matrix
specified as:
/
diag
O1 , O2 ,..., OR ,0,...,0 ,
(4)
where R=min(Nr, Nt) is the rank of channel matrix H, and
Ȝ1• Ȝ2•«• ȜR are eigenvalues of H H H . If correct and full
channel knowledge is available at both transmitter and
receiver sides, the symbols are precoded with V before
transmission and decoded with UH at receiver. Therefore, the
received signal before detection can be expressed as:
y
UH HVx UH n
/x n .
(5)
H
Since U is a unitary matrix, each element of n=U n still
follows the complex Gaussian distribution, i.e.,
0, N 0I N . It is clear that by using precoder and
^
r
`
decoder, a MIMO channel can be decomposed into R
independent single-input single-output (SISO) channels [1].
III.
PROBLEM FORMULATION
In error prone wireless channels, the receiver bit error
rate (BER) of M-QAM can be approximated as [16]:
1 ·
§
2 ¨1 ¸ §
M ¹ ¨
©
Pb |
Q¨
log 2 M
¨
©
§ 3log 2 M
¨
¨
M 1
©
¸· 2E
·
¸ ,
¸ N 0 ¸¸
¹
¹
b
where pl is the lth element of power vector p. Suppose there
are sl bits in total for transmitting the lth layer of a single
video frame. The FER of layer l can be calculated as:
l
fl p 1 – 1 Pbk pk .
sk
(8)
k 1
Our optimization problem is to maximize the system utility
based on video frame error rate (FER) subject to certain
power constraints:
1.
Here, we consider a linear mapping between utilities and
FER for simplicity. In fact, the actual utility model, as a
decreasing function of FER, can vary when different error
concealment techniques are applied. Thus, minimizing FER
will be more general in real applications. Furthermore,
directly solving optimization problem in Eq. (9) is not an
easy task. Therefore, we decompose Eq. (9) into L subproblems: if up to the lth layer is allowed to be transmitted,
the corresponding frame correction rate of layer l, denoted
as f l p 1 f l p , can be optimized:
min log fl p p
¦ s
l
k
log 1 Pbk pk (10)
k 1
subject to pk t 0;
¦
l
k 1
pk
1.
Note that in this case, pl+1=pl+2 « pL=0 are implied since
the layers higher than l are not allowed to be transmitted. If
th
p*l denotes the solution of the l sub-problem in Eq. (10), in
our proposed scheme, the solution of Eq. (9) is found by:
(11)
p* arg max uk f k p*l .
¦
p*l
k
Please note that as the original problem is solved by finding
the best among solutions of the sub-problems, the solution
of Eq. (11) is a near-optimal solution of the original
problem. In Section V, we will demonstrate the
effectiveness and the near-optimality of the proposed
scheme comparing with the global optimal points obtained
by exhaustive searches.
IV.
(6)
where M is the number of constellation points; Q(.) is the
complementary error function, and Eb /N0 is the average bit
energy to average noise power ratio. Since SNR can be
calculated from Eb /N0, i.e. SNR=log2(M)×Eb/N0, in our
proposed MIMO-SM system, BER for the lth channel can be
derived as:
§
1 ·
2 ¨1 ¸
¨
·
M l ¸¹ § § 3 ·
©
,
(7)
Pbl pl |
Q¨ ¨
¸ UOl pl ¸
¨ © M l 1 ¹
¸
log 2 M l
©
¹
(9)
ALGORITHM DESIGN
A. Log-Concavity of Objective Functions in Sub-problems
To simplify the notations, we express Eq. (7) as:
Pbl pl | AQ
l
Bl UOl pl
Al Al )
Bl UOl pl , (12)
where Al and Bl are corresponding constants in Eq. (7) and
their values are determined by Ml; ) (.) is the cumulative
distribution function of the standard normal distribution. The
objective function in Eq. (10) can be expressed as:
log fl p ¦ s
l
k
k 1
log 1 Ak Ak )
Bk UOk pk
. (13)
As stated in [17], a function g(x) is log-concave if and only if
for all x  dom g x ,
g x g '' x d g ' x ,
2
(14)
where g¶x) and g¶¶x) are, respectively, the first and second
derivatives of function g. If we define function gk as:
gk pk 1 Pbk pk 1 Ak Ak )
Bk UOk pk , (15)
which is non-negative. Its first derivatives gk¶is:
g k ' pk Ak Bk UOk
2 pk
I
Bk UOk pk
Ak Bk UOk
2 2S pk
e
B UO p
k k k
2
wL p, ȟ,X pk
,(16)
Ÿ
where I (.) is the probability density function (pdf) of the
standard normal distribution. And its second derivative is:
g k '' pk Ak Bk UOk
4 2S
e
Bk UOk pk
2
p 1.5
k
Bk UOk pk 0.5
,(17)
0
pk* ,[k* ,X *
sk ˜ Ak ˜ I
Bk ˜ UOk pk* ˜
2 1 Ak Ak )
[
Bk ˜ UOk
Bk ˜ UOk p
*
k
*
k
(19)
*
k
X*
0.
p
For convex optimization problems, if any point satisfies the
KKT conditions, it is primal and dual optimal, with a zero
duality gap [17].
which is non-positive for pk•. Due to gk¶¶pk)gk(pk””
(gk¶pk))2, gk(pk) is log-concave. Also, Eq. (13) is nonnegative sum of convex functions, which is also convex [17].
Therefore, the optimization problem in Eq. (10) can be
solved by classic convex optimization methods. Examples of
log(gk(pk)) are plotted in Fig. 2.
The above KKT conditions imply:
sk ˜ Ak ˜ I
X t
*
Bk ˜ UOk pk* ˜
2 1 Ak Ak )
Bk ˜ UOk
Bk ˜ UOk p
*
k
(20)
*
k
p
and
·¸ p
0. (21)
f
(22)
§
*
¨ * sk ˜ Ak ˜ I Bk ˜ UOk pk ˜ Bk ˜ UOk
¨X 2 1 Ak Ak ) Bk ˜ UOk pk*
pk*
¨
©
*
k
¸
¸
¹
There are two cases when Eq. (21) holds:
1)
pk*
0 , which implies:
X* t
2)
Ll p, ȟ,X l
¦ sk log 1 Ak Ak )
k 1
Bk ˜ U pk Ok
(18)
§ l
·
¦ [ k pk X ¨ ¦ pk 1¸ ,
k 1
©k 1
¹
l
where ȟ and X are Lagrange multipliers associated with the
inequality constraints and equality constraint respectively.
The Karush-Kuhn-Tucker (KKT) conditions can be written
for each value of k «l as:
1.
Primal feasible: pk* t 0;
2.
Dual feasible:
¦p
*
k
1.
[ p
*
k
3.
Complementary slackness:
4.
Gradient of Lagrangian vanishes:
Bk ˜ UOk
2 1 Ak Ak ) 0 0
X
*
sk ˜ Ak ˜ I
Bk ˜ UOk pk* ˜
2 1 Ak Ak )
.
(23)
pk*
Case 1 is trivial since when pk* 0 , the video layers higher
than k are not allowed to be transmitted, and it is equivalent
to solving the (k-1)th sub-problem. Therefore, we only
consider Case 2 specified in Eq. (23). And for different X * ,
any solution p*l satisfying Eq. (23) and power constraint
¦
l
k 1
pk
th
1 is an optimal point of the l sub-problem in Eq.
(10).
C. Proposed Algorithm
Based on Eq. (23), we define the function hk as:
0.
Bk ˜ UOk
Bk ˜ UOk pk*
hk pk* log 2 2S 1 Ak Ak )
[k* t 0 .
*
k
pk* ! 0 , which implies:
Fig. 2. Examples of log(gk(pk)) when ʄk=1 and ʌ=1.
B. Conditions of Optimal Solutions in Sub-problems
The Lagrangian of the lth sub-problem, in Eq. (10), can be
derived as:
sk ˜ Ak ˜ I 0 ˜
log sk ˜ Ak ˜ Bk ˜ UOk Bk ˜ UOk pk*
p (24)
*
k
Bk ˜ UOk pk*
.
2
The proposed bisection search algorithm is shown in Fig. 3,
which is to find the optimal point p*l of the lth sub-problem.
1.
upper= min( hk (1) ), for k «l
2.
lower= max(hk (ǻIRUk «l
3.
while(
¦p
*
k
1 ! ' )
4.
ȝ=(upper+lower)/2;
5.
pk*
6.
if ( ¦
hk1 P ;
l
k 1
pk* 1 )
lower= ȝ;
7.
8.
else
upper= ȝ;
9.
10.
end if
11. end while
Fig. 3. Proposed Bisection Search Algorithm for the lth Sub-problem.
+HUHǻLVDVPDOOSRVLWLYHQXPEHUDQGLVVHWDVLQRXU
implementation. The overall optimization problem in Eq. (9)
is solved by the proposed algorithm shown in Fig. 4.
1.
Umax=0;
2.
for l=1:L
3.
Obtain p*l by solving the lth sub-problem
4.
Ul
5.
if (Ul•Umax)
¦
l
k 1
Umax=Ul;
7.
p*
9.
Figure 5 illustrates a snapshot of the system utilities
calculated by the objective function in Eq. (9). The optimal
curve, obtained by exhaustive searches, is included for
comparison. QPSK modulation is adopted for all the video
layers. The average SNR is set as 13dB. There are 30
simulation results included with different channel matrices. It
is clear that our proposed algorithm is very close to the
optimal solutions. Even though WF algorithm is optimal in
terms of PHY layer capacities, it is no longer optimal in APP
layer utilities. M-WF is better than WF since UEP scheme on
base layer and enhancement layers is applied. But it is still
far from optimal.
f k p*l uk ;
6.
8.
layers of City are u=[0.5459, 0.2749, 0.0826, 0.0966] with
an empirically chosen c=0.13 [15]. The encoded network
abstraction layer unit (NALU) is fragmented by link layer
with packet size as 48 bytes [8] and then transmitted through
PHY layer. A 4×4 MIMO-SM system is applied with 100
KHz bandwidth. The CSI is fed back every channel coherent
time, which is assumed to be 1ms. At the receiver side, we
assume the packets containing control messages such as
video coding parameters are correctly received. Also, perfect
error detection scheme is assumed so that bit errors at the
receiver side can be detected. The undecodable NALUs,
including erroneous bits caused by channel degradation or
unsatisfied dependencies, are discarded before passing
through the SVC decoder. We compare our proposed scheme
with traditional WF algorithm, M-WF algorithm in [10] and
the simple equal power allocation scheme in the simulations.
p*l ;
end if
end for
Fig. 4. Proposed Algorithm for the Optimization Problem in Eq. (9).
V.
SIMULATION RESULTS
In this section, the effectiveness and the near-optimality
of our proposed algorithm are evaluated through plenty of
simulations. Video clips Foreman and City with resolution of
352×288 are encoded by the JSVM (Joint Scalable Video
Model) version 9.19 [18]. Frame rates are both set as 30fps.
GOP sizes are 8 with frame the pattern: IBBBBBBB. There
are 161 frames encoded in total so that 20 GOP groups with
one additional I frame are included. Three additional quality
enhancement layers are encoded with medium-grain
scalability (MGS). The basis quantization parameters of the
four layers (i.e., one base layer and three enhancement
layers) are set as QP=[45, 38, 35, 30] and the corresponding
uniform quantization stepsizes can be calculated by q=2(QP4)/6
[15]. Based on Eq. (1), the utilities of the four layers of
Foreman are u=[0.5719, 0.2614, 0.0772, 0.0895] with an
empirically chosen c=0.12 [15]. The utilities of the four
Fig. 5. Snapshot of System Utilities (QPSK, SNR: 13dB)
The successfully received NALUs by the four schemes,
with the same seeds for random number generations of
wireless channel environments, are fed into SVC decoder to
reconstruct the videos. Figure 6 shows the PSNRs of
reconstructed Foreman clip when the average SNR is 18dB
and QPSK modulation is used for all the video layers. It is
clear that our proposed method outperforms the other three,
even though our optimization objective function is not
PSNR. This is due to the fact that by applying our proposed
scheme with reasonable utility functions, more video frames
with higher quality layers are received. Since NALU sizes
are included in our objective function, unequal error
protection (UEP) capability on lower layers of large NALUs,
such as I-frames, is naturally inherent in our scheme.
Moreover, the better receiving of I-frames also leads to
higher PSNR of successive B-frames in the same GOP. Note
that M-WF algorithm is not necessarily a good choice when
transmitting NALUs with small sizes (i.e., B frames). This is
due to the fact that over-protection of base layer may lead to
waste of power.
terms of utility. Moreover, by applying our proposed scheme
with real-world SVC video traces, users can receive more
error-free video frames with higher quality layers, which
lead to better PSNR or QoE for the reconstructed videos.
Similar results of City are plotted in Fig. 7. Here, the
system average SNR is set as 20dB. The modulation
schemes are QPSK, 16-QAM, 16-QAM, 64-QAM for video
layer 1, 2, 3, and 4 respectively. Clearly, our proposed
scheme has higher PSNR than that of the other three
schemes. Since the BER of different modulation schemes are
part of our objective function, our proposed scheme has
much more obvious advantage comparing with the other
methods.
[1]
REFERENCES
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
Fig. 6. PSNR of Reconstructed Video (Foreman, QPSK, SNR: 18dB)
[10]
[11]
[12]
[13]
[14]
[15]
Fig. 7. PSNR of Reconstructed Video (City, l1: QPSK, l2: 16-QAM, l3: 16QAM, l4: 64-QAM, SNR: 20dB)
[16]
VI.
CONCLUSION
In this paper, we have proposed a near-optimal QoEdriven power allocation scheme for SVC-based video
transmissions over a MIMO-SM system. Detailed algorithms
are described with theoretical reasoning. Simulation results
demonstrate that our proposed scheme is near optimal in
[17]
[18]
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FDSDFLW\´ -RXUQDO RI 9LVXDO &RPPXQLFDWLRQ DQG ,PDJH
Representation, vol. 19, no. 8, pp. 520±528, Dec. 2008.
J.-N. Hwang, Multimedia networking: from theory to practice.
Cambridge University Press, 2009.
W. Ajib and D. HaccouQ³$QRYHUYLHZRIVFKHGXOLQJDOJRULWKPVLQ
MIMO-based fourth-JHQHUDWLRQ ZLUHOHVV V\VWHPV´ IEEE Network,
vol. 19, no. 5, pp. 43±48, 2005.
X. Chen, J.-N. Hwang, P.-H. Wu, H.-J. Su, and C.-N. /HH³$GDSWLYH
Mode and Modulation Coding Switching Scheme in MIMO
0XOWLFDVWLQJ6\VWHP´LQProc. of IEEE International Symposium on
Circuits and Systems (ISCAS), 2013, pp. 441±444.
7 :LHJDQG / 1REOHW DQG ) 5RYDWL ³6FDODEOH YLGHR FRGLQJ IRU
,379 VHUYLFHV´ IEEE Transactions on Broadcasting, vol. 55, no. 2,
pp. 527±538, 2009.
+ 6FKZDU] ' 0DUSH DQG 7 :LHJDQG ³2YHUYLHZ RI WKH 6FDODEOH
9LGHR &RGLQJ ([WHQVLRQ RI WKH +$9& 6WDQGDUG´ IEEE
Transactions on Circuits and Systems for Video Technology, vol. 17,
no. 9, pp. 1103±1120, Sep. 2007.
D. Song and C. W. Chen, ³6FDODEOH+$9&YLGHRWUDQVPLVVLRQ
over MIMO wireless systems with adaptive channel selection based
RQ SDUWLDO FKDQQHO LQIRUPDWLRQ´ IEEE Transactions on Circuits and
Systems for Video Technology, vol. 17, no. 9, pp. 1218±1226, 2007.
C.-H. Chen, W.-H. Chung, and Y.-&:DQJ³&URVV-Layer Design for
9LGHR 6WUHDPLQJ ZLWK '\QDPLF $QWHQQD 6HOHFWLRQ´ LQ IEEE
International Conference on Image Processing, pp. 3245±3248, 2011.
C. Oestges and B. Clerckx, MIMO Wireless Communications From
Real-World Propagation to Space-Time Code Design, 1st ed.
Academic Press, 2007.
4 /LX 6 /LX DQG & : &KHQ ³$ QRYHO SULRULWL]HG VSDWLDO
multiplexing for MIMO wireless system with application to H.264
69& YLGHR´ LQ Proc. of IEEE International Conference on
Multimedia and Expo (ICME), pp. 968-973, 2010.
S. Chikkerur, V. Sundaram, M. Reisslein, and L. J. Karam,
³2EMHFWLYH 9LGHR 4XDOLW\ $VVHVVPHQW 0HWKRGVௗ 3HUIRUPDQFH
&RPSDULVRQ´IEEE Transactions on Broadcasting, vol. 57, no. 2, pp.
165±182, 2011.
P.-H. Wu anG < + +X ³2SWLPDO /D\HUHG 9LGHR ,379 0XOWLFDVW
6WUHDPLQJ 2YHU 0RELOH :L0$; 6\VWHPV´ IEEE Transactions on
Multimedia, vol. 13, no. 6, pp. 1395±1403, 2011.
=<DQJDQG<=KDR³6FDODEOH9LGHR0XOWLFDVW2YHU0XOWL-Antenna
2)'06\VWHPV´Wireless Personal Communications, Jul. 2012.
C.-W. Huang, S.-M. Huang, P.-H. Wu, S.-J. Lin, and J.-N. Hwang,
³2/0 2SSRUWXQLVWLF /D\HUHG 0XOWLFDVWLQJ IRU 6FDODEOH ,379 RYHU
0RELOH:L0$;´IEEE Transactions on Mobile Computing, vol. 11,
no. 3, pp. 453±463, Mar. 2012.
Z. Ma, M. Xu, Y.-) 2X DQG < :DQJ ³0RGHOLQJ RI UDWH DQG
perceptual quality of compressed video as functions of frame rate and
TXDQWL]DWLRQ VWHSVL]H DQG LWV DSSOLFDWLRQV´ IEEE Transactions on
Circuit and Systems for Video Technology, vol. 22, no. 5, pp. 671±
682, 2012.
B. Sklar, Digital Communications - Fundamentals and Applications,
2nd ed. Prentice Hall, 2001.
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge
University Press, 2004.
Joint
Scalable
Video
Model
±
reference
software:
http://www.hhi.fraunhofer.de/de/kompetenzfelder/imageprocessing/research-groups/image-video-coding/svc-extension-ofh264avc/jsvm-reference-software.html