# On the Efficient Broadcasting of Heterogeneous Services over Band-Limited Channels: Unequal Power Allocation for Wavelet Packet Division Multiplexing

Authors: Maurizio Murroni
Journal: International Journal of Digital Multimedia Broadcasting
 (2008)

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## Abstract

Multiple transmission of heterogeneous services is a central
aspect of broadcasting technology. Often, in this framework, the
design of efficient communication systems is complicated by
stringent bandwidth constraint. In wavelet packet division
multiplexing (WPDM), the message signals are waveform coded onto
wavelet packet basis functions. The overlapping nature of such
waveforms in both time and frequency allows improving the
performance over the commonly used FDM and TDM schemes, while
their orthogonality properties permit to extract the message
signals by a simple correlator receiver. Furthermore, the scalable
structure of WPDM makes it suitable for broadcasting heterogeneous
services. This work investigates unequal error protection (UEP) of
data which exhibit different sensitivities to channel errors to
improve the performance of WPDM for transmission over band-limited
channels. To cope with bandwidth constraint, an appropriate
distribution of power among waveforms is proposed which is driven
by the channel error sensitivities of the carried message signals
in case of Gaussian noise. We address this problem by means of the
genetic algorithms (GAs), which allow flexible suboptimal solution
with reduced complexity. The mean square error (MSE) between the
original and the decoded message,ψwhich has a strong
correlation with subjective perception, is used as an optimization
criterion.


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## Body

## 1. Introduction

Unequal error
protection (UEP) is a channel coding
technique used to increase the robustness of data that exhibit different
sensitivities to transmission errors. This is often the case of digital
multimedia compressed streams such as JPEG2000 [1] or MPEG [2]. Due to the
extensive use of predictive and variable length codes, a compressed stream is
in general more vulnerable to data losses and
transmission errors, which can desynchronize the decoder causing
spatial and temporal error propagation [3]. In broadcasting, feedback channel
is not available, thus UEP relies on differentiated forward error correction
(FEC) coding [4]: depending on their sensitivities to channel errors, data are
protected with codes with higher or lower error correcting capabilities. Reed-Solomon (RS) or Turbo Codes
(TC) are frequently used [5, 6], but also more performing techniques, based on
Rate-Compatible (RC) codes [7], have been proposed by the research community. Unequal
power allocation (UPA) is an alternative UEP technique which is deployed when,
for several reasons, FEC coding is not efficient [8]. For broadcasting
multiplexed communications (e.g., DVB, DAB), for instance, the available
channel bandwidth per service is a key constraint and the use of FEC-based UEP
schemes is barely suitable. In fact, FEC is a discrete nature coding scheme. It is subjected to some
constraint which restricts the protection level (i.e., the code rate) only to a
set of fixed values. Therefore, the overhead
introduced by FEC codes can be a significant limitation for the efficient use
of the bandwidth. On the other hand, UPA aims at distributing the available
budget power over the parts of the stream, according to their sensitivities to
channel error, to achieve improved final quality on transmitted data without
any increase of the transmission bandwidth. Basically, UPA is performed by
assigning different power weights to the data according to their “importance” (i.e.,
channel error sensitivities) within the stream: higher
transmission power is assigned to more sensible data. As to this, UPA is a “continuous”
process in the sense that weights are chosen in a real set with an accuracy which
can be a priori selected and in theory infinite. Therefore, against FEC, UPA allows
more flexibility in the protection of sensible data.Wavelet packet modulation for orthogonally multiplexed
communication was introduced as a promising technique to improve performance of
conventional FDM and TDM schemes in both Gaussian and impulsive noises
[9–11]. The properties of wavelet
packets are exploited to embed data into waveforms which are mutually orthogonal
both in time and frequency. Several studies conducted on this technology have
shown that opportune design allows minimizing the energy of timing error
interferences, which impair conventional TDM systems [10]. The overlapping bandpass
nature of the transmission pulses (i.e., wavelets) allows better exploitation
of the bandwidth respect to classical FDM [10], and it also intrinsically
mitigates fading effects [12]. Moreover, due to the scalability of its
structure, wavelet packets permit to multiplex data with different format (e.g.,
JPEG2000 and MPEG-2), therefore being a desirable choice for
broadcasting heterogeneous services.In this work, a UPA scheme for wavelet packet division multiplexing
(WPDM) is proposed. UPA applied to WPDM consists on assigning different power
to wavelet packets according to the importance of the message signals carried
on. In other words, considering a generic bit pattern, individual bits are weighted
differently taking the channel conditions (i.e., the signal-to-noise ratio
(SNR)) into account and transmitted on separate wavelet packets. As to the optimization,
we use the mean square error in the parameter domain(1)MSEu=E{[u(τ)−u^(τ)]2}
with
u(τ) and u^(τ) being the transmitted and decoded parameter, respectively. The nontrivial
complexity of the problem does not allow closed-form analytical solution,
which, thus, has to be sought by numerical approach. In literature, solutions
based on the gradient algorithm have been proposed [8]. The complexity of such
optimization methods increases with the size (i.e., number of bits) of the
frame to be transmitted. In this work, we address UPA by exploiting the
potentialities of the Genetic Algorithm (GA) to reduce the computation complexity. The use of GA as to the
weights optimization is one of the novel aspects of this work. A genetic
algorithm [13] is a search technique used in computing to find true or
approximate solutions to optimization and search problem. GAs are
extensively used in literature in different application fields of communication
engineering such as network design, unicast, and multicast routing [14–16]. They allow finding
iterated numerical solution to complex problems with accuracy dependent on the
number of iterations selected. The major advantage of genetic algorithms is
their flexibility and robustness as a global search method. They can deal with
highly nonlinear problems and nondifferentiable functions as well as functions
with multiple local optima. They are also readily amenable to parallel
implementation, which renders them appropriate in real-time adaptive
communications, extensively used for reconfigurable broadcasting services.Results show that the proposed UPA-WPDM scheme allows increasing resilience
of data which exhibit different sensitivities to channel errors during their
transmission over AWGN channel. The performance improvement in terms of quality
achieved in the parameter domain (i.e.,MSEu) has been proved against an equally distributed
WPDM- and FEC-based UEP systems, in the presence of similar bandwidth
constraint. Moreover, the bandwidth gain for target quality (i.e., fixed MSEu) at a fixed bit error rate has been evaluated beside
UEP FEC-based techniques.In the following
section, an overview on the WPDM technology is given. Section3 formally
defines UPA for WPDM by describing in detail the weighting optimization
procedure and the GA-based proposed solution. The performance of the proposed
UPA-WPDM scheme on Gaussian channel is analyzed and compared to equally power
distributed equivalent schemes and to channel coding UEP systems in Section 4.
Conclusions follow in Section 5.


## 2. Wavelet Packet Division Multiplexing

WPDM is a multiple signal transmission technique in which the message
signals are waveform-coded onto wavelet packet basis functions for
transmission. To define the wavelet packet basis functions, we refer to
wavelet multiresolution analysis (MRA), the details of which can be found in a number of
textbooks [17–23] and tutorial
articles [24–31].Letg0[n] be a unit-energy real causal FIR filter of
length N which
is orthogonal to its even translates; that is, ∑ng0[n]g0[n−2m]=δ[m],
where δ[m] is the Kronecker delta, and let g1[n] be the (conjugate) quadrature mirror filter
(QMF), g1[n]=(−1)ng0[N−1−n].
If g0[n] satisfies some mild technical conditions [17, 31], we can use an iterative algorithm to find the function ϕ01(t)=2∑ng0[n]ϕ01(2t−nT0) for an arbitrary interval T0.
Subsequently, we can define the family of functions ϕlm, l≥0, 1≤m≤2l in the following (binary) tree-structured
manner: (2)ϕl+1,2m−1(t)=∑ng0[n]ϕlm(t−nTl),ϕl+1,2m(t)=∑ng1[n]ϕlm(t−nTl),
where Tl=2lT0.
For any given tree structure, the function at the leafs of the tree forms a  wavelet packet. They have a finite
duration, (N−1)Tl,
and are self- and mutually-orthogonal at integer multiples of dyadic intervals,
and hence they are a natural choice for scalable multiplexing applications [9, 10]. In Figure 1, the wavelet packet functions (a) and the relevant power
spectrum (b) for three-level (i.e., eight size wavelet packet) standard 12-tap
Daubechies filters decomposition [23].(a) Time and (b)
frequency portrait for 12-tap Daubechies wavelet packets.
(a)(b)In WPDM, binary messagesxlm[n] have polar representation (i.e., xlm[n]=±1), waveform-coded by pulse amplitude
modulation (PAM) of ϕlm(t−nTl) and then added together to form the composite
signal s(t).
WPDM can be implemented using a transmultiplexer and a single modulator [10] as
Figure 2 illustrates for a two-level decomposition. In this case, (3)s(t)=∑kx01[k]ϕ01(t−kT0), where x01[k]=∑(l,m)∈Γ∑nflm[k−2ln],
with Γ being the set of terminal index pairs and flm[k] the equivalent sequence filter from the (l,m)th terminal to the root of the tree, which can be
found recursively from (2). The original message can be recovered from x01[k] using (4)xlm[n]=∑kflm[k−2ln]x01[k].Figure 2
Transmitter and receiver
for two-level WPDM system.An example of WPDM tree for a system that can be used for broadcasting
heterogeneous services is shown in Figure3(a). In this case, the transmission
system uses two wavelet packets composed by two and four waveforms (i.e.,
wavelets), respectively. In Figure 3(b), the relevant subband structure is displayed:
the total bandwidth is equally shared between the two packets, but a different
partitioning (two against four) is implemented within each packet. Differently
formatted streams can be transmitted by associating them to the appropriate wavelet
packets.(a) WPDM tree structure suitable for
broadcasting heterogeneous services. (b) Symbolic subband structure of the
system in (a).
(a)(b)


## 3. Unequal Power Allocation For WPDM

Without loss of generality to model, a generic bitstream exhibits
different error sensitivities to channel conditions, we consider a discrete periodic
(periodτ) memoryless source S: ∀τ→u(τ) and an analog to digital process AD: ∀u(τ)→x¯(τ) with x¯(τ)∈(x¯k∣k=1,2,…,2M), x¯k=(xk(1),xk(2),…,xk(M)), xk(M) being the LSB. Each xk(i) is then multiplied
with the specific weight wi∈ℝ+ of the diagonal matrix W¯=diag(w1,w2,…,wM). The weighted bit pattern y¯(τ)=W¯⋅x¯(τ) is then transmitted by a Mth order WPDM over a channel affected by additive
white Gaussian noise (AWGN) n(t) with zero mean and variance N0/2.
The signal at the receiver front end is r(t)=s(t)+n(t) with s(t) as in (1) and T0=2−lτ.After
demodulation, the distributed vector isz¯(τ)=y¯(τ)+n¯rel(τ),
where n¯rel=(nrel(1),nrel(2),…,nrel(M)), represents the demodulated noise along the M signal message components (i.e., relevant
noise). Following decision based on Maximum Likelihood (ML) criterion, the
estimate u^(τ) is produced by inverse digital to analog (DA)
process. A sketch of the system is depicted in Figure 4.Figure 4
System model for UPA-WPDM.


## 3.1. Weight Optimization

Considering
bipolar binary representationxk(i)=±1,
if bits in x¯(τ) are inverteddue to AWGN, a wrong decision x^(τ) is made at the receiver, thus
producing a
distortion d(τ)=[u(τ)−u^(τ)].
Aim of the optimization process is to calculate optimal weights in the sense of a minimized expected value E{[d2(τ)]}.
Assuming ergodicity, it is possible to calculate E{d2} as follow: (5)E{d2}=∑k=12M∑h=12Mdk,h2P(x¯k)⋅P(x¯^h∣x¯k), where dς,η=uς−u^η are the different possible parameter values, P(x¯k) the occurrence of the reproduction levels uk,
and P(x¯^h∣x¯k) the transition probabilities between
transmitted and received bit patterns. Due to the orthogonal properties of WPDM
waveforms and to the independence of the noise samples, the transition
probabilities are [4, 32]: (6)P(x¯^h∣x¯k)=(∏i=1xk(i)≠x^h(i)MPb(i))⋅(∏i=1xk(i)=x^h(i)M(1−Pb(i))).
By imposing  Eb=(1/M)∑i=1MEb(i)=1,
we can write [8] Eb(i)=wi2Eb and impose the following constraint on the
weights wi(7)∑i=1Mwi2=M.
WPDM is based on binary amplitude modulation, thus, the bit error probabilities in (6) are [33] (8)Pb(i)=12erfc(wiN0).Mathematically, the optimization problem
is to minimize (5) under the constraint (7). In other words, UPA raises (wi>1) the immunity to noise channel for more
significant bits, paying as a counterpart lower robustness (wi<1) on less significant one, to achieve
average improved performance on the transmission of parameter u(τ) in the sense of minimum expected distortion d(τ)=[u(τ)−u^(τ)].The complexity of the above optimization
problem, which increases with the size of framesM,
does not allow closed form solutions. Therefore, to identify the
solution, we use a numerical approach based on Genetics Algorithms (GAs).


## 3.2. Genetics Alghoritms (GAs)

GAs are implemented as a computer simulation in which a population of
abstract representations (chromosomes)
of candidate solutions (genes) to an
optimization problem evolves toward better solutions. The evolution usually
starts from a population of randomly generated chromosomes and happens in
generations. In each generation, the fitness of every chromosome in the
population is evaluated, multiple chromosomes are stochastically selected from
the current population (based on their fitness), and modified (mutated or
recombined) to form a new population. The new population is then used in the
next iteration of the algorithm.In
the proposed system, the chromosomesare defined as arrays ofM genes wi∈ℝ+.
The range of possible values of wi is constrained by (7). An initial population {INIT} of  L chromosomes is randomly selected. The
fitness function is as defined as in (5). Two operations are allowed to
determine the evolution of the initial population: crossover (with probability Pcross) used
to interchange the elements of two chromosomes and mutation (with probability Pmut) which modify the value of one or more genes within a chromosome with
the aim of leading the search out of local optima. In particular, the most
fitting part of the population {BEST} is selected and directly inserted
in the new generation, while the rest of the population {WORST} is
discarded and replaced by a subpopulation created by means of the crossover and
mutation operators. In the case of two identical chromosomes resulted after the
crossover and mutation operations, two individuals are randomly generated. The
termination condition is satisfied once either the algorithmreaches a selected number of iterations (IT) or the fitness function maintains the same value for ITMAX iterations. At the end of the process, the
chromosome with low score in the fitness function (i.e., lower distortion on
the reconstructed frame) will be selected for the transmission.Figure5 gives an example of the crossover and mutation operations.Figure 5
Example for
crossover and mutation operators in case of chromosomes composed by four
genes.In this particular case, chromosomes are composed by four genes; at iterationk+1,
the crossover operator swaps the first two genes
of the chromosomes p and q as they were at iteration k, whereas the mutation varies the
chromosome r by multiplying the second and fourth genes for the quantity Δi∈ℝ+ with i={2,4},
respectively. The
flowchart of the proposed GA is shown in Figure 6.Figure 6
Flowchart of the proposed GA.The accuracy of such approach is
strictly dependent on the values of IT and ITMAX, whereas the complexity of the algorithm depends also on the
definition of chromosomes, on the size L of the initial population and on
the Pcross and Pmut probabilities. Chromosomes are arrays of genes
which are real values. The higher the precision on the representation of the
genes (i.e., the number of decimal digits used to approximate real values), the higher the accuracy achieved by
the UPA, but also, the higher the complexity of the algorithm. Similarly, big-size
populations guarantee higher performance, but also lead to time consuming
processing. A critical matter is the selection of Pcross and Pmut probabilities: high values can determine
instability of the GA which could diverge, whereas, on the other side, low
values likely lead to slow convergence.


## 4. Results

A WPDM system which deploys two packets of sizeM={4,8} is used to multiplex two streams having same
rate, but different format (see Figure 7). Standard Daubechies minimum-phase
scaling filters of length N=12 [31], which guarantee short delay and
substantial capacity advantage over conventional FDM systems [10], are
deployed. Without loss of generality, to model the parameters u1(τ) and u2(τ) delivered at time τ, we use zero-mean (η=0) Gaussian sources S1 and S2 with unitary variance (σ2=1). AD/DA processes deploy natural binary mapping
based on uniform quantizers.Figure 7
UPA-WPDM system for broadcasting two heterogeneous
services.At first, we
have run some preliminary tests to analyze the importance of the GA parameters.
The crossover operator was allowed to interchangeint[0.4⋅M] genes whereas
the mutation occurred on int[0.1⋅M] genes,
int[⋅] being the operator which produces the
integer part of the argument. In other words, at each iteration, a maximum of
40% of the chromosome parents could appear on the  next generation of
chromosomes and only 10% of a chromosome could vary. According to this, L was varied in the range {8,16,32,64,128}, Pcross and Pmut in the range 0.3÷0.7 and 0.01÷0.3, respectively. Finally for mutation Δi varied within the range {0.1,0.2,0.3}⋅wi. The maximum difference in terms of
fitness function value among all the solutions was observed to be less than 5%.
Therefore, the following considerations can be made: huge-size populations bring
to better solutions at the expense of a higher-processing time; the Pmut probability is suggested to be set equal to or higher than 0.1, whereas Δi above 0.2⋅wi to avoid an excessive number of iterations; the Pcross probability does not sort significant effects in the range used. As to
the outcome from the preliminary tests on GA behaviour applied to the UPA
problem, in the following experiments the {INIT} population was composed by L=32 chromosomes, eight decimal digits were used to
represent genes (i.e., wi), the probability Pmut=0.3, 0.25⋅wi and Pcross=0.5, whereas ITMAX=100 and IT=1000.
For the sake of clearness, Table 1 summarizes the parameter setting for the
experiments.Table 1
Parameters setting for experiments.
SymbolDefinitionSettingS1,S2SourceGaussian (η=0, σ2=1)AD/DAAnalog to
digital/digital to analog processesUniform quantizer,
natural binary mappingMBit frame size
(chromosome size)8LSize of initial
population32wiWeight (gene)∈R+, 8 decimal digits precisionPmutMutation probability0.3Δimutation quantity0.25⋅wiPcrossCrossover probability0.5ITNumber of iteration1000ITMAXMaximum number of iteration
with unchanged fitness100Achieved
quality in the parameters domain is expressed in terms of the signal-to-noise
ratio (SNRu) measured in decibel SNRu[dB]=10⋅log10[E{u2(τ)}/MSEu] with MSEu as in (1). SNRu[dB] is evaluated at varying average bit error
probabilities Pb=(1/M)∑i=1MPb(i) with Pb(i) as in (8).We have compared the proposed UPA with
a benchmark equal power allocation (EPA) WPDM system and an UEP scheme based on
FEC coding. In the latter system, we have deployed Reed-Solomon (RS) codes [33]. RS codes are nonbinary
cyclic codes with symbols made up of m-bit sequences, where m is
any positive integer having a value greater than 2. RS(n,k) codes on m-bit symbols exist for all n and k for which 0<k<n<2m+2, where k is the number of data symbols
being encoded, and n is the total number of code symbols in the encoded
block. The error-correcting capability of the generic RS(n,k) code is t=(n−k)/2.
UEP is implemented by protecting
data with codes with higher- or lower-code rate Rci=ki/ni. At varying the channel error rate, for every
WPDM channel, an appropriate RS(ni,ki) code is
selected for data protection according to the sensitivity to channel errors of
the data carried on. More significant data (e.g., MSB) are protected by codes
with higher error-correcting capabilities (i.e., higher-code rates). In
particular, for any average error rate Pb, the
optimization procedure aims at selecting the M codes so
that the SNRu is minimized under the bound of constant average code rate Rc=(1/M)∑i=1MRci.For our experiments, we have
selectedm=8 and Rc=32/38=0.84 which corresponds to an increase of the
total bandwidth of about 16%. To reduce
the complexity of the coding process, we have fixed the number of code symbols
in the encoded block ni=38. The average error correcting capability of the
system is therefore t=(38−32)/2=3 symbols per codeword. In other words,
on the average, such a scheme is able to correct up to 3 symbols that contain errors
in a codeword. Tables 2 and 3 report
the details (i.e., actual code rate Rci and
error correcting capability ti)
of the codes used at Pb=10−3 for the transmission of u1(τ) and u2(τ),
respectively.Table 2
Actual parameters for Reed-Solomon UEP coding atPb=10−3
for u1(τ)
transmission.
RS(ni,ki)RcitiRS (38,24)0.637RS (38,30)0.794RS (38,34)0.892RS (38,36)0.951Table 3
Actual parameters for Reed-Solomon UEP coding atPb=10−3
for u2(τ) transmission.
RS(ni,ki)RcitiRS (38,24)0.637RS (38,28)0.745RS (38,30)0.794RS (38,32)0.843RS (38,34)0.892RS (38,34)0.892RS (38,36)0.951RS (38,36)0.951In Figures8 and 9, we refer to UEP RS-based coding as RS (38,32).
The analysis of the graphics reveals that UPA outperforms EPA along all the
variation ranges of the average bit error probability within the transmitted
frame with a peak gain of 6.84 dB at Pb=10−3 in case of u2(τ). Same behaviour is noticeable
with respect to RS coding for Pb>10−4,
with 3.57 dB the peak gain
for Pb=3.5×10−3 and for
u2(τ). For Pb<10−5, all the systems perform similarly with slight
prevalence of the RS coding which is more evident for u1(τ). Superior performance in case
of u2(τ) transmission can be justified by the higher
precision obtained by a finer power distribution performed with eight weights
with respect to a coarser allocation based on only four weights as for u1(τ).
More generally, the UPA prevalence is due to the capability of the optimization
procedure to obtain high accuracy by selecting weights in a range of real
values.Figure 8
Achieved quality for the parameteru1(τ).Figure 9
Achieved quality for the parameteru2(τ).In Figures10
and 11 show how for severe channel conditions the weights relevant to higher
significant bits (i.e., w11, w21, and w22) are emphasized with respect to all the
others. For Pb approaching 10−3, a decrease of the above weights corresponds to an increase of w12 and w23 which become also higher than 1. For Pb<10−5, all the weights converge to equal unitary
value, but still remaining slightly different for Pb>10−6.Figure 10
Weights
values at varying channel conditions for the parameteru1(τ).Figure 11
Weights values at varying channel conditions for the
parameteru2(τ).Figure12 shows the percentage
bandwidth gain achieved by UPA with respect to UEP based on RS coding for
target quality (i.e., fixed SNRu[dB]) on the transmitted parameters u1(τ) and u2(τ), at fixed Pb=10−3,
for the WPDM system used for experiments as represented in Figure 5. A minimum bandwidth gain above 20% is
noticeable whereas similar high variations are observed in both cases. This is
due to the discrete nature of RS codes, which are constrained to only a
definite set of possible code rates. On the other hand, UPA is a continuous
process which guarantees more flexibility in the protection of sensitive data.Percentage bandwidth gain for fixed quality on the transmitted parameteru1(τ)
(a) and
u2(τ) (b) achieved by UPA
against UEP by RS codes for the WPDM scheme in Figure 7.
(a)(b)In order to assess the suitability of the proposed scheme for real
applications, such as audio and video broadcasting, as a further test, we have
considered the specific multiplexed transmission of a standard image and a
stereo-audio sequence. Referring to the system proposed in Figure7, we have
used the well-known image “Lena” of size 512×512 in RGB format coded at 8 bpp
per color component (see Figure 13), as a transmission source S1. We have measured the quality
on the reconstructed image by standard PSNR metric expressed in decibel. On the
other hand, we have ripped a 5 seconds from a stereo-audio CD signal sampled at
44.1 KHz coded at 16 bps and used as a source S2. For the evaluation of the
quality on the received audio signal, we have used the perceptual evaluation of
audio quality (PEAQ) strategy [34]. PEAQ is technique recommended by the ITU,
which evaluates the quality of an audio signal by a single number, called
objective difference grade (ODG), which varies within a range [−4÷0],
with 0 the highest quality score. PEAQ has proven to be more performing than
conventional metrics based on mean square error on the evaluation of the
performance of the conventional audio codecs [34].Figure 13
Lena512×512
coded in RGB format at 16 bpp per color component.Table4 shows the results achieved in case of Pb=10−3.
The quality on the reconstructed image is slightly below 30 dB, whereas the PEAQ
measured on the received audio sequence is just up −2.9. This result is in line
with the typical performance of low-bit-rate audio and video codecs. For the
transmission of audio∖video at a rate of 64 Kbit/s, MP3/MPEG-4 codecs achieve
PSNR approaching 30 dB for the reconstructed frames [2] and PEAQ of around −3.36
for the audio sequence [35]. Since conventional DAB and DVB broadcasting
systems work at Pb≪10−3, the proposed system could be an alternative
solution for the broadcasting of multimedia heterogeneous contents in case of
extremely hard transmission condition, when
only little quality requirements are set.Table 4
Quality achieved by the proposed system atPb=10−3
for the
multiple transmission of the image  Lena and a stereo-audio CD
sequence.
SourcePSNR (dB)PEAQ (ODG)Lena (512×512, RGB, 8 bpp)29.8—Stereo-audio CD
(5 seconds, sampling rate
44.1 KHz, 16 bps)—−2.88


## 5. Conclusion

In this work, we have presented an orthogonal multiple
transmission system based on wavelet packet modulation suitable for the
resilient broadcasting of data which demonstrate different sensitivities to
transmission errors. A novel unequal error protection technique based on differentiated
allocation of the transmission power over the modulated waveforms allows improving
the final quality of the received parameters in case of AWGN channel, without
any increase of the transmission bandwidth. The optimization of the weights has
relied on Genetic Algorithms which allowed to achieve reduced complexity. Due
to its scalability properties, the proposed scheme is able to provide for multiple
transmissions of
heterogeneous services which can be independently protected according to their
specific format. Therefore, unequal power allocation applied to wavelet packet
division multiplexing offers improved flexibility to broadcaster. Nevertheless,
it is worthy to point out that particular attention has to be given to the
design of the wavelet filters which are real-valued and under the approach of
UPA could impair the performance of the transmission in case of wireless systems.
In fact, the
proposed UPA scheme may increase the dynamic range of the input signals to the
WPDM modulator in Figure4. Since g0[n] is real-causal FIR filter, the bigger input
amplitude range may increase the complexity of these filters. This may be a
disadvantage of UPA for implementation.Future work on this subject will investigate the capability of
the proposed scheme to deal with real-time varying transmission conditions
including the presence of fading effects and the broadcasting of reconfigurable
heterogeneous services.



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*Source: 523649-2008-02-25.xml*