Unequal error protection by partial superposition transmission using low-density parity-check codes

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Published in IET CommunicationsReceived on 23rd December 2013Revised on 25th March 2014Accepted on 1st May 2014doi: 10.1049/iet-com.2013.1168

348The Institution of Engineering and Technology 2014

ISSN 1751-8628

Unequal error protection by partial superpositiontransmission using low-density parity-check codesKechao Huang1, Chulong Liang1, Xiao Ma1, Baoming Bai2

1Department of Electronics and Communication Engineering, Sun Yat-sen University, Guangzhou 510275,

People’s Republic of China2State Key Laboratory of ISN, Xidian University, Xi’an 710071, People’s Republic of China

E-mail: [email protected]

Abstract: In this study, the authors consider designing low-density parity-check (LDPC) coded modulation systems to achieveunequal error protection (UEP). They propose a new UEP approach by partial superposition transmission (PST) called UEP-by-PST. In the UEP-by-PST system, the information sequence is distinguished as two parts, the more important data (MID) and theless important data (LID), both of which are coded with LDPC codes. The codeword that corresponds to the MID is superimposedon the codeword that corresponds to the LID. The system performance can be analysed by using discretised density evolution.Also proposed in this study is a criterion from a practical point of view to compare the efficiencies of different UEP approaches.Numerical results show that, over both additive white Gaussian noise channels and uncorrelated Rayleigh fading channels,(i) UEP-by-PST provides higher coding gain for the MID compared with the traditional equal error protection approach, butwith negligible performance loss for the LID; and (ii) UEP-by-PST is more efficient with the proposed practical criterion thanthe UEP approach in the digital video broadcasting system.

1 Introduction

In many practical communication systems such as wirelessnetworks, control applications and interactive systems, datacan be partitioned into several parts that have differentdegrees of significance. For example, in wirelesscommunication system, headers of the medium accesscontrol frame such as frame control, duration and addressare more important than the frame body, because an error inthe header may lead to the rejection of the frame whileerrors in the frame body are usually tolerable. Traditionalequal error protection (EEP) approach is usually not themost efficient way to guarantee the quality of the importantdata. Hence unequal error protection (UEP) is required tomake the best use of the resources (say bandwidth).A practical approach to achieving UEP is based on

modulation. In [1], the author introduced a UEP approachbased on a non-uniform arrangement of the signalconstellation, also known as multiresolution modulation [2]or hierarchical modulation [3]. In such a constellation, moreimportant bits in a constellation symbol have larger minimumEuclidian distance than less important bits. In [4], a UEPapproach using uniformly spaced constellation was proposed,where different bits in a constellation symbol have differentaverage number of nearest neighbours. However, these UEPapproaches can achieve only a limited number of UEP levelsfor a given constellation. More recently, the authors of [5]proposed a method of achieving arbitrarily large number ofUEP levels by using multiplexed hierarchical quadratureamplitude modulation (QAM) constellations.

An alternative approach to achieving UEP is based onchannel coding. In this approach, more powerfulerror-correction coding is applied to the more importantdata (MID) than the less important data (LID). UEP codeswere firstly introduced by Masnick and Wolf [6]. In [7], theauthors found all the cyclic UEP codes of odd length up to65 by computer searching. In [8], a UEP approach usingrate-compatible punctured convolutional (RCPC) codes wasproposed whereby the more important bits were puncturedless frequently than the less important bits. In [9],turbo codes were employed for UEP in the same way asRCPC codes. Research on UEP low-density parity-check(LDPC) codes can be found in [10–13]. In [10–12], UEPLDPC codes were constructed by designing the variablenode degree distribution of the code in an irregular way. In[13], the authors proposed a new class of UEP LDPC codesbased on Plotkin-type constructions. In order to providemore efficient UEP, error-correction coding and modulationcan be jointly used [14, 15]. These methods based onchannel coding and/or modulation have been widely usedfor image and layered video transmission [16–21].To the best of our knowledge, all the existing UEP

approaches improve the performance of the MID bysacrificing the performance of the LID. Another issue isthat no simple criteria were mentioned in the literatures tocompare the efficiencies of different UEP approaches. Inthis paper, motivated by recent work on constructing longcodes from short codes by block Markov superpositiontransmission [22], we propose a new approach for UEP bypartial superposition transmission (referred to as UEP-by-PST

IET Commun., 2014, Vol. 8, Iss. 13, pp. 2348–2355doi: 10.1049/iet-com.2013.1168

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for convenience) using LDPC codes. In the UEP-by-PSTsystem, the information sequence is distinguished as twoparts, the MID and the LID, both of which are coded withbinary LDPC codes. The codeword that corresponds to theMID is superimposed on the codeword that corresponds tothe LID. The transmitted sequence consists of two parts.One is the codeword that corresponds to the MID, and theother is the superposition of the respective codewords thatcorrespond to the MID and the LID. We then propose adecoding algorithm of the UEP-by-PST system, which canbe described as an iterative message processing/passingalgorithm over a high level normal graph. Discretiseddensity evolution is conducted to predict the convergencethresholds for the MID and the LID of the UEP-by-PST.Simulation results verify our analysis and show that, overboth additive white Gaussian noise (AWGN) channels anduncorrelated Rayleigh fading channels, UEP-by-PSTprovides higher coding gain for the MID compared with thetraditional EEP approach, but with negligible performanceloss for the LID. To compare the UEP-by-PST with otherapproaches, we propose to use as a criterion the minimumsignal-to-noise ratio (SNR) that is required to guarantee thequalities of both the MID and the LID. Simulation resultsshow that, under this practical criterion, UEP-by-PSTprovides more efficient UEP compared with the UEPapproach in the digital video broadcasting (DVB) system[16], which is referred to as UEP-by-mapping in this paper.The rest of this paper is organised as follows. We present
the encoding and decoding algorithms of the UEP-by-PSTsystem in Section 2. In Section 3, we present theasymptotic performance analysis of the UEP-by-PST.Numerical results are provided in Section 4. Section 5concludes this paper.

2 UEP by partial superposition transmission

2.1 Encoding algorithm

Consider a binary LDPC code C[n, k] with dimension k andlength n, which is referred to as the basic code in this paperfor convenience. Assume that the information sequence ucan be equally grouped into L + 1 blocks

u = ( u(0), u(1), . . . , u(L) ) (1)

where u(0) and ( u(1), . . . , u(L) ) are the MID of length k andthe LID of length kL, respectively. The encoding algorithm ofthe UEP-by-PST is described as follows, see Fig. 1 forreference.

Algorithm 1: Encoding of the UEP-by-PST system

Fig. 1 Encoding structure of the UEP-by-PST system


† Encoding: For 0 ≤ ℓ ≤ L, encode u(ℓ) into v(ℓ) [ Fn2 bythe (systematic) encoding algorithm of the basic code C.† Interleaving: For 1 ≤ ℓ ≤ L, interleave v(0) by the ℓthinterleaver Pℓ of size n into w(ℓ).† Superposition: For 1 ≤ ℓ ≤ L, compute c(ℓ) = w(ℓ) ⊕ v(ℓ),where ‘⊕’ represents component-wise modulo-2 addition.† Combining: Output sequence c = ( c(0) , c(1) , . . . , c(L) )of length N, where c(0) = v(0) and N = n(L + 1).

Remarks:

† In principle, the basic code C can be chosen as any othertypes of codes, such as convolutional codes and turbo-likecodes.† The basic code C can also be chosen as a UEP code. In thiscase, the proposed UEP-by-PST system provides multilevelUEP.† It is necessary to emphasise that the superposition isimplemented in the binary field instead of the real field.Hence the proposed UEP-by-PST system is different fromthe UEP based on superposition coded modulation (SCM)in [23, 24].† For the EEP approach considered in this paper, theencoded sequences v(ℓ) for 0 ≤ ℓ ≤ L are sent directly tothe modulator.

2.2 Decoding algorithm

The proposed UEP-by-PST system can be represented by ahigh-level normal graph [25, 26]. In a general normalgraph, edges represent variables, while vertices representconstraints. As shown in Fig. 2, the normal graph of theUEP-by-PST system has four types of nodes: L + 1 nodes

of type a node of type , L nodes of type and L

nodes of type . Then the normal graphical realisation of

the UEP-by-PST system can be divided into L + 1 layers,

an MID layer and L LID layers, where the MID layer

consists of a node of type and a node of type ,

whereas each LID layer consists of a node of type , a

node of type and a node of type , see Fig. 2 forreference.A message associated with a discrete variable is defined as

its probability mass function (pmf) here. We focus on randomvariables defined over F2. For example, a message associatedwith a random variable X over F2 can be represented by a real

Fig. 2 Normal realisation of the UEP-by-PST system

2349& The Institution of Engineering and Technology 2014

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vector PX (x), x [ F2, such that PX(0) + PX(1) = 1. Let X be arandom variable corresponding to the edge connecting twovertices A and B. We use the notation P(A�B)
X (x), x [ F2[27] to indicate the direction of the message flow.To describe the algorithm more clearly, we introduce a

basic rule for message processing at an arbitrary node. LetA be a node connecting to Bj with random variables Zjdefined over F2(0 ≤ j ≤ d − 1), as shown in Fig. 3.Assume that all incoming messages are available, which are

denoted by P(Bj�A)Zj

(z), z [ F2. The node A, as a message

processor, delivers the outgoing message with respect toany given Zj by computing the likelihood function

P(A�Bj)Zj

(z)/ Pr{A is satisfied

|Zj = z}, z [ F2

(2)

Because the computation of the likelihood function is

irrelevant to the incoming message P(Bj�A)Zj

(z), we claim

that P(A�Bj)Zj

(z) is exactly the so-called extrinsic message.For simplicity, we assume that the codeword c of length N

is modulated and transmitted over a memoryless channel,resulting in a received vector y. In more general settings,we assume that the a posteriori probabilities Pr{Ci =0, 1|y}, 0≤ i <N are computable [The computation in thisstep is irrelevant to the code constraints but depends onlyon the modulation and the channel.], where Ci is the ithcomponent of C. Then, these a posteriori probabilities areused to initialise the decoding algorithm of the UEP-by-PST

P |�=( )C(0)j

(cj) = Pr{C(0)j = cj|y}, cj [ F2 (3)

for 0≤ j≤ n− 1, and

P |�+( )C(ℓ)j

(cnℓ+j) = Pr{C(ℓ)j = cnℓ+j|y}, cnℓ+j [ F2 (4)

for 0≤ j≤ n− 1 and 1 ≤ ℓ ≤ L, where ‘|→ = ’ and ‘|→ + ’are used to indicate that the messages are from the channel.The iterative decoding algorithm of the UEP-by-PST can

be described as an iterative message processing/passingalgorithm over a high-level normal graph scheduled asfollows, see Fig. 2 for reference.

Algorithm 2: Iterative decoding of the UEP-by-PST system

† Initialisation: All messages over the intermediate edgesare initialised as uniformly distributed variables. Initialisethe messages P |�=( )

C(0) c(0)( )

and P |�+( )C(ℓ) c(ℓ)

( )for 1 ≤ ℓ ≤ L

according to (3) and (4), respectively. Select a maximumlocal iteration number Imax > 0 and a maximum globaliteration number Jmax > 0. Set J = 0.

Fig. 3 A generic node A as a message processor


† Iteration: While J < Jmax

(1) The MID layer performs a message processing/passingalgorithm scheduled as

In the above procedure, the message processor at each nodetakes as input all available messages from connecting edgesand delivers as output extrinsic messages to connecting

edges. The node performs the sum–product algorithm[28] with maximum local iteration number Imax to computethe extrinsic messages.

(2) For 1 ≤ ℓ ≤ L, the ℓth LID layer performs a messageprocessing/passing algorithm scheduled as

(3) For 0 ≤ ℓ ≤ L, compute the full messages PV (ℓ) v(ℓ)( )

as

PV (ℓ) v(ℓ)( )/ P C�=( )

V (0) v(0)( )

P =�C( )V (0) v(0)

( ), ℓ = 0

P C�+( )V (ℓ) v(ℓ)

( )P +�C( )V (ℓ) v(ℓ)

( ), 1 ≤ ℓ ≤ L

⎧⎨⎩

(5)

then make hard decisions on v(ℓ) resulting in v(ℓ); if all v(ℓ) arevalid codewords, declare the decoding successful, output u(ℓ)

for 0 ≤ ℓ ≤ L, and exit the iteration.

(4) Increment J by one.

† Failure report: If J = Jmax, output u(ℓ) for 0 ≤ ℓ ≤ L and

report a decoding failure.

3 Asymptotic performance analysis

Density evolution, which was developed by Richardson andUrbanke [29], is an effective analysis tool for computingthe noise tolerance thresholds and optimising degreesequences [30] of LDPC codes. In this section, discretiseddensity evolution [31] is conducted to predict theconvergence thresholds for the MID and the LID of theUEP-by-PST.Assume that all-zeros codeword c is transmitted over

the AWGN channel with binary phase-shift keying (BPSK)modulation and noise variance σ2. To describe the densityevolution, it is convenient to represent the message as inits equivalent form, the so-called log-likelihood ratio(LLR). For example, the message computed in (2) can bedenoted as

L(A�Bj)Zj

D logP(A�Bj)Zj

(0)

P(A�Bj)Zj

(1)

⎛⎝

⎞⎠ (6)


Table 1 Thresholds of the UEP-by-PST based on densityevolution

Threshold (Eb/N0) UEP-by-PST EEP

L = 1 L = 2 L = 3

MID, dB 0.80 0.61 0.47 1.11LID, dB 1.17 1.17 1.17

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The LLR messages from the channel can be computed as [32]
L(C)D logPr{C = 0|y}Pr{C = 1|y}

( )

= 2

s2y

(7)

Consider the quantised function

Q(x)D

−(2b−1 − 1) · D, x

D≤ −(2b−1 − 1)

x

D

[ ]· D, −(2b−1 − 1) ,

x

D, 2b−1 − 1

(2b−1 − 1) · D, x

D≥ 2b−1 − 1

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

(8)

where b is the quantisation bit, Δ is the quantisation intervaland [w] denotes the nearest integer to the real w.Assume that the interleaversPℓ are very large and random.

With this assumption, we can investigate the ensemble of theUEP-by-PST system.

† At node , the message updating rule is the same as

shown in [31]. After a fixed number of local iterations Imax,

we can obtain the extrinsic messages L C�=( )V (0) , L C�+( )

V (ℓ) for

1 ≤ ℓ ≤ L and their corresponding pmfs PL C�=( )V (0)

, PL C�+( )V (ℓ)

for

1 ≤ ℓ ≤ L, respectively. We can also compute the fullmessages LV (ℓ) and their corresponding pmfs PLV (ℓ)

for0 ≤ ℓ ≤ L.† At node , the message updating rule is the same as thatof the variable node in a binary LDPC code.† At node , the message updating rule is similar to that ofthe check node in a binary LDPC code. The only difference isthat the messages associated with the half edge are availablefrom the channel observations.

In summary, for a given parameter L and a local iterationnumber Imax, we can iteratively update the pmfs PLV (ℓ)

for0 ≤ ℓ ≤ L according to the decoding procedure scheduled as

Therefore, we may determine (by commonly-usedone-dimensional search) the minimum Eb/N0 such that thebit-error rate (BER) for the MID (or the LID) tends to zeroas the number of global iterations tends to infinity.

4 Numerical results

In this section, we first give the thresholds of the UEP-by-PSTby using the discretised density evolution techniques. Thenwe compare the BER performance of the UEP-by-PST withthose of the traditional EEP approach over AWGN channelsand uncorrelated Rayleigh fading channels. For theuncorrelated Rayleigh fading channels, we assume that thechannel state information is available at the receiver.Finally, we compare the UEP-by-PST and theUEP-by-mapping in the DVB system from a practical pointof view.


4.1 Thresholds of UEP-by-PST

Example 1: Consider a random (3, 6) regular LDPC code [33]with rate 1/2 for the basic code C. The local iteration numberImax for LDPC decoding process is 50. The quantisationinterval Δ = 25/512 with 10-bit quantisation. Table 1 givesthe convergence thresholds for the MID and the LID of theUEP-by-PST with BPSK signalling over AWGN channels.Also included in the table is the threshold of the traditionalEEP approach. It can be seen that the thresholds for theLID with different L (1, 2 and 3) are the same [Actually,variations can be found if five decimal places are used.].The gap of the thresholds for the MID between L = 1 andL = 2 is 0.19 dB, while that of the MID between L = 2 andL = 3 is 0.14 dB. From these thresholds, we can see that,UEP-by-PST theoretically provides higher coding gain forthe MID compared with the traditional EEP approach, butwith negligible performance loss for the LID.

4.2 Performance of UEP-by-PST

In the following examples, L random interleavers, each of sizen, are used for encoding. The iterative decoding algorithm ofthe UEP-by-PST is implemented with maximum globaliteration number Jmax = 20 and maximum local iterationnumber Imax = 50, while the iterative decoding algorithm ofthe traditional EEP approach is implemented withmaximum iteration number 100.

Example 2: Consider a random (3, 6) regular LDPC code [33]with length 1024 for the basic code C. The BER performancesof the UEP-by-PST with BPSK signalling over AWGNchannels and uncorrelated Rayleigh fading channels areshown in Figs. 4 and 5, respectively. From Figs. 4 and 5,we can see that, over both AWGN channels anduncorrelated Rayleigh fading channels, UEP-by-PSTprovides higher coding gain for the MID compared with thetraditional EEP approach, but with negligible performanceloss for the LID. For example, at BER = 10−5,

† over AWGN channels, UEP-by-PST achieves about 0.7,1.0 and 1.1 dB extra coding gain for the MID comparedwith the traditional EEP approach when L = 1, 2 and 3,respectively;† over uncorrelated Rayleigh fading channels, UEP-by-PSTachieves about 1.0, 1.3 and 1.4 dB extra coding gain for theMID compared with the traditional EEP approach whenL = 1, 2 and 3, respectively.

Example 3: Consider a random (3, 6) regular LDPC code withlength 10 000 for the basic code C. The BER performances ofthe UEP-by-PST with BPSK signalling over AWGN channelsand uncorrelated Rayleigh fading channels are shown inFigs. 6 and 7, respectively. From Figs. 6 and 7, we can seethat, over both AWGN channels and uncorrelated Rayleigh


Fig. 5 Performances of the UEP-by-PST with BPSK signallingover uncorrelated Rayleigh fading channels in Example 2. Thebasic code is a random (3, 6) regular LDPC code with length 1024

Fig. 7 Performances of the UEP-by-PST with BPSK signallingover uncorrelated Rayleigh fading channels in Example 3. Thebasic code is a random (3, 6) regular LDPC code with length 10 000

Fig. 6 Performances of the UEP-by-PST with BPSK signallingover AWGN channels in Example 3. The basic code is a random(3, 6) regular LDPC code with length 10 000

Fig. 4 Performances of the UEP-by-PST with BPSK signallingover AWGN channels in Example 2. The basic code is a random(3, 6) regular LDPC code with length 1024

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fading channels, UEP-by-PST provides higher coding gainfor the MID compared with the traditional EEP approach,but with negligible performance loss for the LID. Forexample, at BER = 10−4,

† over AWGN channels, UEP-by-PST achieves about 0.4,0.6 and 0.7 dB extra coding gain for the MID comparedwith the traditional EEP approach when L = 1, 2 and 3,respectively;† over uncorrelated Rayleigh fading channels, UEP-by-PSTachieves about 0.4, 0.7 and 0.9 dB extra coding gain for theMID compared with the traditional EEP approach whenL = 1, 2 and 3, respectively.

Example 4: Consider an IEEE 802.11n LDPC code [34] withlength 1944 and rate 1/2 for the basic code C The BERperformances of the UEP-by-PST with BPSK signallingover AWGN channels and uncorrelated Rayleigh fadingchannels are shown in Figs. 8 and 9, respectively.


From Figs. 8 and 9, we can see that, over both AWGN channelsand uncorrelated Rayleigh fading channels, UEP-by-PSTprovides higher coding gain for the MID compared with thetraditional EEP approach, but with negligible performanceloss for the LID. For example, at BER = 10−5, over bothAWGN channels and uncorrelated Rayleigh fading channels,UEP-by-PST achieves about 0.3 dB extra coding gain for theMID compared with the traditional EEP approach, but withnegligible performance loss for the LID.

Remarks:

† From Figs. 4 and 6, we can see that the extra coding gainsat BER = 10−5 for the MID are similar to those at BER→ 0 aspredicted in Table 1 by the discretised density evolution. Wecan also see that the performance loss for the LID isnegligible, again as predicted by the discretised densityevolution.


Fig. 9 Performances of the UEP-by-PST with BPSK signallingover uncorrelated Rayleigh fading channels in Example 4. Thebasic code is an IEEE 802.11n LDPC code with length 1944 and

Fig. 8 Performances of the UEP-by-PST with BPSK signallingover AWGN channels in Example 4. The basic code is an IEEE802.11n LDPC code with length 1944 and rate 1/2

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rate 1/2

4.3 Comparison between UEP-by-PST andUEP-by-mapping

In the following example, we consider a 16-QAM mappingscheme used in the DVB system [16]. The mapping and its

Fig. 10 16-QAM mapping and the corresponding bit patterns


corresponding bit patterns are shown in Fig. 10. In thismapping, if the transmitted signal has a label whose mth bitis ‘0’, then an error occurs in the mth bit if the receivedsignal falls in the shaded region. As pointed out byAydınlık and Salehi [15], in such a 16-QAM mappingscheme, the average number of nearest neighbours for bit 0,1, 2 and 3 are 0.5, 0.5, 1.0 and 1.0, respectively. The firsttwo bits are more protected than the last two bits.Apparently, this 16-QAM mapping can provide two levelsof UEP. In the UEP-by-mapping, u(ℓ) for 0 ≤ ℓ ≤ L areencoded into c(ℓ) by the encoding algorithm of the basiccode C and then sent to the modulator.Assume that L = 3. In the UEP-by-PST, only the partial

superposition transmission contributes to UEP. Bits of thecodeword c(0) and those of the codewords ( c(1) , . . . , c(L) )are transmitted in separate signalling intervals. That is, inthe UEP-by-PST system, one 16-QAM signal point carrieseither four bits from the codeword c(0) or four bits fromthe codewords ( c(1) , . . . , c(L)). In contrast, in theUEP-by-mapping used in the DVB system [16], only themapping contributes to UEP. That is, a bit of the codewordc(0) and three bits of the codewords ( c(1) , . . . , c(L)) aremapped into one 16-QAM signal point, using the first bitposition and the last three bit positions, respectively.

Example 5: Consider the same random (3, 6) regular LDPCcode with length 1024 used in Example 2 for the basic codeC. The BER performances of the UEP approaches(UEP-by-PST and UEP-by-mapping) with 16-QAM overAWGN channels and uncorrelated Rayleigh fading channelsare shown in Figs. 11 and 12, respectively. The curvelabelled ‘EEP’ shows the performance of the traditional EEPapproach. From Figs. 11 and 12, we can see that, over bothAWGN channels and uncorrelated Rayleigh fading channels,

† UEP-by-PST provides higher coding gain for the MIDcompared with the traditional EEP approach while causesnegligible performance loss for the LID;† UEP-by-mapping provides higher coding gain for the MIDcompared with the traditional EEP approach but degrades theperformance of the LID.

For example, at BER = 10−5, over both AWGN channels anduncorrelated Rayleigh fading channels,

† UEP-by-PST achieves about 1.5 dB extra coding gain forthe MID compared with the traditional EEP approach, butwith negligible performance loss for the LID;† UEP-by-mapping achieves about 2.4 dB extra coding gainfor the MID compared with the traditional EEP approach bysacrificing about 1.0 dB coding gain for the LID.


Fig. 12 Simulation results of the UEP-by-PST andUEP-by-Mapping with 16-QAM over uncorrelated Rayleigh fadingchannels in Example 5. The basic code is a random (3, 6) regularLDPC code with length 1024. The parameter L = 3

Table 2 Minimum SNR’s required by the UEP approaches

Minimum SNR EEP UEP-by-mapping UEP-by-PST

AWGN, dB 5.4 4.9 3.9Rayleigh, dB 7.9 7.0 6.4

Fig. 11 Simulation results of the UEP-by-PST andUEP-by-mapping with 16-QAM over AWGN channels in Example5. The basic code is a random (3, 6) regular LDPC code withlength 1024. The parameter L = 3

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From Figs. 11 and 12, we can see that, UEP-by-PST isbetter than UEP-by-mapping in terms of the LID, but worsethan UEP-by-mapping in terms of the MID. An interestingissue (but rarely mentioned in the literatures [In [23, 24], acriterion based on superposition gain was proposed tocompare UEP based on time-division-coded modulation andUEP based on SCM. However, this criterion cannot beapplied here directly since UEP-by-PST implements thesuperposition in the coded symbol field instead of thecoded signal field.]) is how to compare different UEPapproaches in terms of efficiency. To address this issue, wepropose the following criterion from a practical perspective.Assume that (ε0, ε1) are the error performance

requirements by the MID and the LID, respectively. Wedenote the minimum SNR required for the MID and theLID by SNR(ε0) and SNR(ε1), respectively. Thus, the


minimum SNR required for the UEP approach can becalculated as

SNRUEP = max SNR(10), SNR(11){ }

(9)

which specifies the minimum SNR required to guarantee thequalities of both the MID and the LID. Hence, it can be takenas a criterion to compare different UEP approaches.Assume that ε0≃ 10−5. From Figs. 11 and 12, we can see

that, over both AWGN channels and uncorrelated Rayleighfading channels, SNRUEP-by-PST > SNRUEP-by-mapping whenε1 > 1.0 × 10−1, whereas SNRUEP-by-PST < SNRUEP-by-mapping

when ε1 < 1.0 × 10−1. Suppose that we have an applicationthat requires ε0≃ 1.0 × 10−5 and ε1≃ 5.0 × 10−2. Table 2gives the minimum SNRs required by the UEP approachessuch that the error performance requirements (ε0, ε1) aresimultaneously satisfied. Also included in the table is theminimum SNR required by the traditional EEP approach.From Table 2, we can see that, for these parameters,

† UEP-by-PST performs 1.5 dB better than the traditionalEEP approach over both AWGN channels and uncorrelatedRayleigh fading channels;† UEP-by-PST performs 1.0 and 0.6 dB better thanUEP-by-mapping over AWGN channels and uncorrelatedRayleigh fading channels, respectively.

In summary, from a practical point of view, UEP-by-PST isan efficient approach to achieving UEP.

5 Conclusion

We have proposed a new UEP approach by partialsuperposition transmission using LDPC codes. Thepotential coding gain for the MID can be predicted bythe discretised density evolution, which also shows that theperformance loss is negligible for the LID. Simulationresults verified our analysis and showed that, over bothAWGN channels and uncorrelated Rayleigh fadingchannels, UEP-by-PST can provide higher coding gain forthe MID compared with the traditional EEP approach, butwith negligible performance loss for the LID. This isdifferent from the traditional UEP approaches that usuallydegrade the performance of the LID while improving theperformance of the MID. Simulation results also showedthat UEP-by-PST is more efficient than UEP-by-mapping inthe DVB system from a practical perspective by taking as acriterion the minimum SNR required to satisfysimultaneously the error performance requirements for boththe MID and the LID.

6 Acknowledgments

The authors would like to thank Mr. Shancheng Zhao fromSun Yat-sen University for useful discussions.


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Unequal error protection by partial superposition transmission using low-density parity-check codes