Performance Analysis of a Serial UEP System

Based on Time-Division Multiplexing Codes

Satoshi Yamazaki* and David Asano†

* Numazu National College of Technology, Japan

s-yamazaki@numazu-ct.ac.jp

† Faculty of Engineering, Shinshu University, Japan

david@cs.shinshu-u.ac.jp

Abstract— Previously, we proposed a serial unequal error

protection (UEP) code system or use with information sources

that contain a mixture of both important and less important data.

Moreover we showed the effectiveness of the proposed system

with symmetrical signal constellations (2RING type). In this

paper, we show theoretical analysis of the asymmetrical signal

constellations, which are called TRAP (trapezoid) type in

AWGN channels and evaluate the validity using computer

simulations. In addition, we show the performance in fading

channels. Therefore, we showed the effectiveness of the TRAP

type in the propose UEP system.

I. INTRODUCTION

In certain communication systems an information

sequence may consist of several parts that have different

degrees of significance and hence require different levels of

protection against noise. Codes that are designed to provide

different levels of data protection are known as unequal error

protection (UEP) codes [1]. For example, in packet

communications, the header must be protected more than the

payload, because in the worst case, if the destination address

is lost the entire packet will be lost. Similarly, UEP is useful

for protecting the unique word in data frame transmission and

for protecting data in the layered coding schemes used in

digital terrestrial broadcasting systems. UEP codes were first

studied by B. Masnick and J. K. Wolf [2] and later have been

studied by several authors [3]-[10]. Previously, we proposed

an improvement of the time multiplexing approach mentioned

in [4], [5] and confirmed the effectiveness for additive white

Gaussian noise (AWGN) channels using theoretical analysis

and computer simulations [10]. Moreover, we proposed our

UEP system using MMSE-FDE (frequency-domain

equalization based on the minimum mean square error

criterion) by using the fact that importance levels are changed

every few symbols, i.e., every block, and confirmed the

improvement in BER (Bit error rate) performance for ring

type signal constellations with 2 levels of importance, which

are called 2RING [11].

The 2RING type mentioned in [10], [11] is symmetrical

signal constellations. In [12], we proposed asymmetrical

signal constellations, which are called TRAP (trapezoid) type,

and confirmed the effectiveness in AWGN channels using

computer simulations. In this paper, we show theoretical

analysis of the TRAP type in AWGN channels and evaluate

L L

H H

L

H

Different parts from the proposed AWGN model [10]

Importance Level Decision

(Switching)

L

HImportance Level Estimation

(Selector)

Modulator-L

Data

Source

(#5) select L or H

(#11) both L and H

Data

Destination

(#3) select

L or H

(#12)(#15)

(#1)

AWGN

(#7)

Serial /

Random

Transmitter

Receiver

Encoder-L

(#14)

(#2)

TCM Level-L(#4)

Modulator-HEncoder-H

TCM Level-H(#4)

Demodulator-LDecoder-LLevel-L(#13)

Demodulator-HDecoder-H

Level-H(#13)

(#8)

Fading

(#9)

Adaptive

Equalization

Interleaving

Interleaving

Deinterleaving

Deinterleaving

CP Insertion

(#6)

CP Removal

(#10)

Figure 1 The proposed UEP scheme in fading channels for two levels of

importance [11].

the validity using computer simulations. We compare the

performance of the TRAP type with the 2RING type. In

addition, we show the performance in fading channels.

The rest of our paper is organized as follows. In section 2,

the proposed UEP schemes are described. In section 3, we

present theoretical analyses of our system for TRAP type. In

section 4, we present simulation results to show the

performance of our system. Finally, we present our

conclusions in section 5.

II. PROPOSED UEP SCHEME

Previously in [10], we described the proposed scheme and

the difference between it and previous schemes in detail. In

this section, we describe the proposed UEP scheme. First, we

show the proposed system model and describe details of the

processing. Second, we show the proposed signal

constellations that allow us to distinguish among importance

levels. Finally, we describe the system assumptions.

A. System Model

The proposed scheme is outlined in fig.1. This scheme uses

two importance levels. This is an improvement of the time

multiplexing approach mentioned in previous schemes [4], [5].

2013 International Workshop on Smart Info-Media Systems in Asia (SISA 2013), Sept. 30 – Oct. 2, 2013

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In these schemes, it is assumed that the data stream is

separated into two parallel data streams, consisting of data-H

and data-L and periodic switching is needed. However, as the

serial data stream that we consider has a random mixture of

important and less important data. So, the proposed scheme

encodes the data by randomly switching between two codes

which use different signal constellations to realize UEP,

which are shown in fig.2. No extra information about which

code was used is added to denote importance. This method

has the advantage of not reducing the information rate. As

more important information should be more strongly

protected from errors, it’s allocated to a large ring. The

opposite can be said about less important information. In the

same way, we can construct a UEP system having in general

M importance levels. In fig.3, we show this concept for two

importance levels in the TRAP type.

In previous schemes [4], [5], the information source

decided the importance level. However, in the proposed

system, the information source does not decide the

importance level. Instead, the importance level is evaluated by

the importance level decision block every Nc bits. That is, Nc

is defined as the switching rate of the importance level and 1

frame consists of Nc bits. Also, information is processed in

serial by using switches.

B. Processing Details [11]

In fig.1, we describe the main processing steps used in the

proposed scheme shown in fading channels for two levels of

importance. The numbers in the explanation, for example #1,

correspond to the numbers in fig.1.

2.B.1 Transmitter

Step1. The input data comes from an information source

which outputs random data {0, 1}. Also, the input data

is transmitted to the importance level decision block

(#1). Step2. The importance level of the data is evaluated by the

importance level decision block every Nc symbols (#2).

This decision controls the switch ahead. In this paper,

in order to focus on the UEP implementation itself, we

decide the importance level randomly. In Fig.1, if the

output of the importance level decision block is “L”,

then the switches will be in the “up” position. If the

output is “H”, then the switches will be in the “down”

position (#3).

Step3. We prepare codes which have different signal

constellations according to the importance level.

Moreover, we combine coding and modulation using

Trellis coded modulation (TCM) with four states [1] at

the same time (#4). Here, interleaving in units of

symbols is done after coding. Information bits are

allocated to signal points based on Gray coding. The

distance between the signal points is larger for data-H,

resulting in stronger error protection. Moreover, we

encode the data differently according to the

importance level to create UEP characteristics.

(a) (b)

dC

dL

dH

4

5

7

6 2 3

01

：code-L (0,1,2,3)

dL：distance between signal points in the code-L

dH：distance between signal points in the code-H

dC：minimum distance between signals in the code-L

and signals in the code-H

β： ring ratio of ring-L and ring-H (β=dL/dH)

I

Q

I

Q

dL

dC

0

1

2

3

4

5

6

7

dH

θθ

Figure 2 Proposed Signal Constellation [12].

(a) 2RING type, (b) TRAP type.

I

Q

I

Q

The case of level-L. The case of level-H.

I

Q

This code (code-L) is used. This code (code-H) is used.

0

1

2

3

4

5

6

7

4

5

6

7

0

1

2

3

Figure 3 The proposed concept to realize UEP for two levels of importance.

Step4. The data is selected by changing the switches

according to the importance level decision performed

in step 2 every Nc symbols (#5).

Step5. A block consists of Nc symbols, and a cyclic-prefix

(CP) consisting of a part of the end of the block (size:

Ng symbols) is inserted at the beginning of the block

(#6).

2.B.2 Channel

Step6. AWGN affects the transmitted signal in the channel

(#7).

Step7. Multi-path fading affects the transmitted signal in the

channel (#8).

2.B.3 Receiver

Step8. The CP is removed (#9).

Step9. The MMSE-FDE is done to combat fading (#10).

Step10. The channel output is sent to all the decoders

regardless of the importance (#11).

Step11. Also, the data is transmitted into the importance level

estimator (#12). In parallel with the decoding (#13),

the encoder used in the transmitter, i.e., the importance

level, is estimated every Nc symbols using an

importance level estimation algorithm [10] based on

2013 International Workshop on Smart Info-Media Systems in Asia (SISA 2013), Sept. 30 – Oct. 2, 2013

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maximum likelihood detection (MLD) (#14).

Processing #13 and #14 are done in parallel to prevent

throughput degradation. The output data is decided

based on the estimated result (#11). In this way, the

receiver can determine the importance of the

information.

C. Signal Constellations

2.C.1 2RING type

As shown in fig.2 (a), the 2RING type constellations have two

double QPSK from whose amplitude is different, they can

support two importance levels: high and low. Data-H is

assigned to the outer RING and data-L to the inner RING.

2.C.2 TRAP type

As shown in fig.2 (b), we arrange four signal points whose

phases are different, they are symmetrical to a y-axis. The

four points for the right side are important-H and the outside

are important-L. As shown in Fig.2 (b), if the rotation angle θ

(0<θ< π) is taken, arrangement as shown in fig.4 will be taken

with the value of θ.

D. System Assumptions

(a) In this paper, to evaluate the UEP implementation itself,

we do not consider the importance definition and methods

to determine the importance level. We merely assume that

the importance level has been decided and changes every

N bits (1 frame) in the importance level decision block.

(b) Since we want to evaluate the UEP properties of the

proposed system, it is assumed that the frame

synchronization of the receiver to the transmitter is ideal.

III. THEORETICAL ANALYSIS

We analyzed 2RING type constellations theoretically and

show the validity [10]. In this paper, we analyze the TRAP

type constellations shown in fig.2 (b).

A. Geometrical Constraint

The distance between signal points in the code-L is dL, while

the distance between those in the code-H is dH. The minimum

distance between signals in the code-L and signals in the

code-H is given by dc. Then, the expressions (1) and (2) are

formed as well as RING type.

1<β<0,HL dd β= ................................................. (1)

cH dd γ= . ................................................................. (2)

B. Average Energy

Since each transmitted signal has a different energy, the

average energy is used to calculate the SNR. In terms of the

signal constellations, the energy of each signal is just the

squared Euclidean distance of the signal point from the origin.

We use equally probable signals, so each signal's energy is

given the same weight in the calculation of the average energy.

The average energy is defined as

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

In Phase

Low

High

32

1 0

4 5

67

(a) θ=0, β=1/ 2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

In Phase

Low

High

1

2

0

3

4

7

5

6

(b) θ=π/4, β=1/ 2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

In Phase

Low

High

0

2

3

1

4

5

6

7

(c) θ=π/2, β=1/ 2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

In Phase

Low

High

7

40

3

2

1

5

6

(d) θ=3π/4, β=1/ 2

Figure 4 Operation Examples of Trap Constellation.

2013 International Workshop on Smart Info-Media Systems in Asia (SISA 2013), Sept. 30 – Oct. 2, 2013

141

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∑==

K

iiE

KE

1

1. ............................................................ (3)

where Ei is the energy of the ith signal and K is the number of

signals in the constellation. In terms of the signal constellation,

Ei is just the squared Euclidean distance of the ith signal point

from the origin. The average energy for the TRAP type is

given by

[ ] 222 )sin23)(1(cos)1(228

1cdE θβγθβγ +++++= ................... (4)

C. Importance Level Estimation Error Rate

As we mentioned in section 2.B.3-Step11, in the receiver, it is

necessary to estimate the encoder, that is, the importance level

used in the transmitter correctly. For example, for level-H, if

encoder-H is used in the transmitter, we must estimate code-H

in the receiver. The same can be said for level-L. The

importance level estimation error rate Ple is the probability

that code-H is estimated incorrectly to be code-L or vice-versa.

We show a theoretical upper bound for the TRAP type. Here,

we omit the derivation.

=

0

2

42

1

N

NderfcP c

le

........................................ (5)

D. Relationship between the Signal Constellation and the

Error Rate

The error rate performance largely depends on the distances

between signal points. Namely, the average bit error rate for

each code (code-H or code-L) is related to the distance dH or

dL and the importance level estimation error rate is related to

the distance dc. To evaluate the relationship between the

signal constellation and the error rate, we introduce the

following minimum squared Euclidean distances normalized

by the average energy: dc2/ E , dH

2/ E , dL

2/ E . They are given by

(6), (7), (8) from fig.2 (b).

)sin23)(1(cos)1(22

822

22

θβγθβγγ

+++++=

E

d H ..................... (6)

E

d

E

d HL

22

2

β= ........................................................................... (7)

E

d

E

d HC

2

2

21

γ=

........................................................................... (8)

In fig.5, dH2/ E (level-H) versus dc

2/ E is shown as a function

of β for 0 < β <1 in 2RING type. In fig.6, dL2/ E (level-L)

versus dc2/ E is shown as a function of θ for β =1 in the TRAP

type. From fig.5 and fig.6, in both level-H and level-L,

2RING type can have more distances dH or dL than the TRAP

type for same β. Otherwise, the TRAP type can have more

distances dc than 2RING type. From the above, 2RING type

has more improvement of BER performance in individual

codes while the TRAP type has more improvement of

importance level estimation error rate.

E. Asymptotic Coding Gain

We examine the asymptotic coding gain, G, to examine the

improvement of coding relative to an uncoded system. The

asymptotic coding gain, G, of a code is given by ( )( )

uncoded

coded

Ed

EdG

/

/

2min

2min= . ................................................. (9)

As a sample implementation of the proposed UEP system, we

use the rate 1/2, four-state trellis code for the code-H. In this

case, the minimum squared Euclidean distance is given by ( ) ( ) ( )6,45,46,4 2222

min dddd ++= . .................... (10)

where d2(i,j) is the squared Euclidean distance between signal

i and signal j. Since the rate of the code-H is 1/2 and there are

4 points in the code-H signal sub-constellation, the

information rate for the bits-H is 1.0 bit/T. To achieve less

error protection for the bits-L, we do not use any coding. This

also increases the information rate for the bits-L to 2.0 bits/T.

We use uncoded BPSK as a reference. For uncoded BPSK,

the denominator of (9) is 4. The asymptotic coding gain of the

data-H, GHigh, is given by (11) after substituting (10) into (9).

Otherwise, the asymptotic coding gain of the data-L, GLow, is

given by (12) because no coding is used.

][4

sin45log10

2

dBE

dG H

High

+=

θ ................................. (11)

][4

log1022

dBE

dG H

Low

=

β .............................................. (12)

For example, in Fig.7, the asymptotic coding gains, GHigh

and GLow, versus dc2/ E for β=1/ 2 for the TRAP type is

shown. GHigh and GLow are decreasing mostly to alignment

according to increase of dc. In particular, the fact is

remarkable in area whose dc2/ E is larger than 2. This is due to

the fact that dH and dL are less to keep the same average

energy while dc is larger for the same β.

IV. PERFORMANCE EVALUATION

First, we confirm the validity of theoretical analysis

mentioned in section 3 and the effectiveness of the TRAP

type in AWGN channels. Next, we show the performance in

fading channels. We show the simulation parameters in

table.1.

A. AWGN channels

In fig.8, the importance level estimation error rate versus

Eb/N0 is shown for β=1/ 2 and dc2/ E =0.3. In addition, we

showed the theoretical upper bound of the importance level

estimation error rate mention in section 3.C. If the value of β

is constant, the performance also improves quickly as NC is

decreased. This is due to the fact that if NC is large, that is, the

switching rate of the importance level is slow, importance

level estimation errors are less likely to occur. In the case of θ

= π/2, the performance is worst degreed. This is due to the

fact that the signal distance between signals in the code-L and

signals in the code-H is the smallest in fig.4 (c). On the other

hand, the opposite can be said for the case of θ = 0. Also, in

the cases of θ = π/4 and 3π/4, they have mostly equal

performance from their signal constellations. Moreover, since

the simulation results correspond to the theoretical upper

bound in the case of NC is 30 and θ is π/2, which is the worst

performance in the importance level estimation error rate, we

confirm the validity of the expression (6).

2013 International Workshop on Smart Info-Media Systems in Asia (SISA 2013), Sept. 30 – Oct. 2, 2013

142

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0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

β=0

β=0.25

β=0.5β=0.7071

β=1

Trap : π/4, 3π/4

2Ring

Trap : π/2

Trap : 0

Figure 5 dC

2/ E versus dH2/ E (β=1/ 2 for Trap) .

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

β=0β=0.25β=0.5β=0.7071β=1

2Ring

Trap : π/2

Trap : π/4, 3π/4

Trap : 0

Figure 6 dC2/ E versus dL

2/ E (β=1/ 2 for Trap) .

0 0.5 1 1.5 2 2.5 3 3.5 4-25

-20

-15

-10

-5

0

5

Asy

mp

toti

c C

od

ing

Gain

[dB

]

θ=π/2θ=π/4, 3π/4θ=0

Level-High

Level-Low

Figure 7 Asymptotic coding gain as a function dC

2/ E (β=1/ 2 ).

Table 1 Simulation parameters.

Transmitted Data 0, 1 (random)

Noise AWGN

Pulse shaping None

Synchronization Ideal

Importance level M 2 (High, Low)

Occurrence Probability of importance High: 1/2, Low: 1/2

Importance switching rate Nc

1, 10, 30 [symbols]

Channel coding rate High: 1/2, Low: 1

Demodulation Coherent

Decoding Viterbi decoding

Detection Hard-decision

Fading Time and Frequency selective Rayleigh

10-path exponential power delay model

Decay factor : 3[dB]

Delay interval : 1 sysmbol interval

Channel Estimation Perfect

Interleaving Size (L×R ) (L, R ) = (8,128)

Normalized Doppler Frequency fdT

s0.01

FFT size Nc

Ng/N

c (Here, Cyclic prefix N

g) 1/4

Channel model

-10 -5 0 5 10 15

10-4

10-3

10-2

10-1

100

Eb/No(dB)

Import

ance

lev

el e

stim

atio

n e

rror

rate

θ=π/2

θ=3π/4

θ=π/4

θ=0

- : Theoretical upper bound

Nc = 10

Nc = 1

Nc = 30

Simulation(Nc = 30)

Figure 8 Importance level estimation error rate versus Eb/N0.

(β=1/ 2 , dC2/ E =0.3)

0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

Eb/No(dB)

Import

ance

level es

tim

ation

erro

r ra

te

θ=π/2θ=3π/4π/4

θ=0

Figure 9 Importance level estimation error rate versus Eb/N0

(The dependency on the rotation angle θ for fdTs =0.01 and NC = 10).

B. Fading channels

In Fig.9, for example, the importance level estimation error

rate versus Eb/N0 is shown for the rotation angle θ for fdTs =

0.01 and NC is 10. Regardless of θ, the performance in fading

channels is similar to the performance in AWGN channels,

shown in fig.8. Therefore, we show the effectiveness of the

TRAP type in the propose UEP system.

V. CONCLUSIONS

Previously, we proposed a serial unequal error protection

(UEP) code system or use with information sources that

contain a mixture of both important and less important data.

Moreover we showed the effectiveness of the proposed

system with symmetrical signal constellations (2RING type).

In this paper, we showed theoretical analysis of the

asymmetrical signal constellations, which are called TRAP

(trapezoid) type and evaluate the validity using computer

simulations in AWGN channels. In addition, we showed the

performance in fading channels. Therefore, we showed the

effectiveness of the TRAP type in the propose UEP system.

EdC /2

EdH /2

EdC /2

EdL /2

EdC /2

2013 International Workshop on Smart Info-Media Systems in Asia (SISA 2013), Sept. 30 – Oct. 2, 2013

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