Contribution of Multidimensional Trellis Coding in VDSL Systems

SETIT 2005
3 rd International Conference: Sciences of Electronic,
Technologies of Information and Telecommunications
March 27-31, 2005 – TUNISIA
Contribution of Multidimensional Trellis Coding in
VDSL Systems
Mohamed Tlich, Meryem Ouzzif, and Ahmed Zeddam
France Télécom Division R&D RESA
2, Avenue Pierre Marzin-22307 Lannion Cedex
mohamed.tlich@rd.francetelecom.com
meryem.ouzzif@francetelecom.com
ahmed.zeddam@francetelecom.com
Abstract: In this paper, we take a new look at the single-carrier modulation technique for VDSL system. Using
powerful coding techniques can further increase the performance of a Quadrature Amplitude Modulation (QAM)
system. This paper investigates an implementation of the trellis coding in a single-carrier modulation (SCM) VDSL
system intended for transmissions over short copper cables. The suggested code is a 4-dimensional 16-state trellis
coder; it gains typically 4dB over uncoded transmissions in an AWGN environment. For suitable values of the
truncation length of the Viterbi decoder, the results of the simulations carried out showed that the trellis coding
implemented over the SCM-VDSL system, introduces an important gain in either the range of the twisted copper-pair,
or in channel capacity.
Key words: twisted copper pair cable, xDSL, Quadrature Amplitude Modulation (QAM), Trellis Coded Modulation
(TCM), Crosstalk.
1 VDSL Overview
Figure 1 shows a simplified VDSL system
deployment (M.D. Nava & C. Del-Toso, 2002). In this
general architecture, fiber links connect the optical
line termination unit (OLT) at the central office (CO)
to the optical network unit (ONU) at the local
exchanges and street cabinets. The network
termination unit (NT) provides the necessary protocol
adaptation at the customer site.
CO
AN
OLT
Local
Exchange
ONU
VTU-O
FTTEx
Liaison VDSL
Customer
Premises
NT
VTU-R
the customer premises are close to the local exchange
and can be served directly from it. This is suitable for
business service. In the second configuration, FTTCab
or FTTC, the residential premises can be served from
the street cabinet.
The subscriber loop is a very hostile medium and
suffers from many impairments, such as the
attenuation of the twisted pair, the crosstalk, and the
thermal noise.
1. Attenuation of the twisted pair: the line attenuation
increases with both frequency and wire length (Figure
2). This results in potentially lower bit rate capacity
when considering long loops and broadband signals
like VDSL.
Other
xDSL
Optical Fiber
Cabinet
ISDN
HDSL
ADSL
Customer
Premises
ONU
VTU-O
Liaison VDSL
NT
VTU-R
Distribution
Cable
FTTCab
Figure 1. Typical VDSL deployment scenarios
As shown in this figure, there are two
configurations that connect the ONU to the CO: Fiber
to the exchange (FTTEx) and Fiber to the cabinet/curb
(FTTCab/FTTC). In the first configuration, FTTEx,

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20Log10(|H(f)|
0
−10
−20
−30
−40
−50
−60
−70
1300m
Channel Attenuation
500m
1000m
270-1 v2.0.6 part1, 2002), we will deal with the
32QAM constellation shown in Figure 4 we used in
our simulations. This constellation is invariant to 90°
rotations. Therefore, to make the system transparent to
90° phase offsets, when mapping bits into
constellation points:
1. 3 bits (Q3n, Q4n and Q5n) are assigned to points
within a quadrant so that a 90° rotation leaves them
unchanged, as shown in the constellation of Figure 4.
2. The two first bits (Q1n and Q2n) are differentially
encoded to specify the quadrant, i.e., bits Q1n and
Q2n will determine the change in quadrant from
symbol to symbol using the rules listed in table 1.
−80
0 0.5 1 1.5 2 2.5
Freq (Hz)
3 3.5 4 4.5
x 10 6
xx111
xx011
xx110
xx010
Figure 2. Signal attenuation for a 500m, 1000m and 1300m
wire length
2. Crosstalk: is noise caused by electromagnetic
radiation of other telephone lines physically located in
close proximity in the same cable binder. Such
coupling increases with frequency, so it is very
harmful for VDSL, which uses bandwidth up to 12
MHz. Practically, we can distinguish two types of
crosstalk: Near-End crosstalk (NEXT) caused by
signals traveling in opposite directions in the same
cable binder, and Far-End crosstalk (FEXT) caused by
signals traveling in the same direction as shown in
Figure 3.
Line 1
Line i
NEXT
Line 1
Line i
Figure 3. NEXT and FEXT in cable binder
FEXT
3. Thermal or background noise: a convention in
standardization committees is to model background
noise as additive white Gaussian noise (AWGN) with
a fixed Power Spectral Density (PSD) level equal to -
140 dBm/Hz as defined in (ETSI TS 101 270-1 v2.0.6
part1, 2002)(ETSI TS 101 270-2 v2.0.3 part2, 2002).
qi
Serial to
Parallel
Converter
xx010
xx110
xx011
xx101
xx100
xx001
xx111 xx101 xx100
Q5n
Q4n
Q3n
Q2n
Q1n
xx010
xx001
xx100
xx101
xx111
xx000 xx000 xx001 xx011
xx000 xx000 xx100 xx110
xx110
xx001 xx101 xx010
xx011
Table 2.1
xx111
Y2n−1
D
Y1n−1
D
Differential Encoder
Figure 4. Symbol Mapper
Y5n
Y4n
Y3n
Y2n
Y1n
Complex
Symbol
Mapper
Inputs Previous Outputs Current Outputs
Q1n Q2n Y1n-1 Y2n-1 Y1n Y2n
1 0 0 0 0 1
1 0 0 1 1 0
Cn
2 Trellis Coding in AWGN Passband
Channels
Trellis Coded Modulation using four-dimensional
constellations have a better performance in terms of
complexity and coding gain over the usual twodimensional
schemes (Lee-Fang Wei, 1987).
Actual SCM-VDSL systems use the twodimensional
Differential Quadrature Amplitude
Modulation (DQAM) scheme (ETSI TS 101 270-1
v2.0.6 part1, 2002). In this section, we demonstrate
that using the 4-dimensional Trellis Coded Modulation
as a function of the truncation length of the Viterbi
decoder can further increase the performance of this
DQAM system, from a coding gain and cable range
viewpoints.
2.1 DQAM Principe
To fully understand the DQAM (ETSI TS 101
1 0 1 0 1 1
1 0 1 1 0 0
Table 1. Differential QAM Coding table
2.2 Trellis Coded Modulation: A modified WEI 16-
State 4D Code
An inherent cost of the coded schemes is that the
size of the 2D constellation is doubled over uncoded
schemes. This is due to the fact that a redundant bit is
added every signaling interval. Otherwise, the coding
gain of those coded schemes would be 3 dB greater.
Using multidimensional (>2) constellations with a
trellis code of rate m/m+1 (Lee-Fang Wei, 1987) can
reduce that cost because fewer redundant bits are
added for each 2D signaling interval. Furthermore,
multidimensional encoding provides more flexibility
than 2D encoding in that it can use a fractional
number of bits per symbol.

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We will focus, now, on the case where the number
Q of information bits transmitted per signaling interval
is equal to 5. These five information bits arriving in
the current signaling interval n are denoted as I1n,
I2n… and I5n.
A 2/3 rate, 16-state code with a 4D rectangular
constellation of 211 points and a Minimum Square
Euclidean Distance (MSED) d 2 0 is shown in Figure 5.
The 4D constellation is constructed from a 48-point
2D constellation partitioned into eight subsets with
enlarged MSED equal to 4d 2 0 , as explained in (Lee-
Fang Wei, 1987).
I5_n+1
I4_n+1
I3_n+1
I2_n+1
I1_n+1
I5_n
I4_n
I3_n
I2_n
I1_n
DIFFERENTIAL
ENCODING
I3_n’
I2_n’
W2n
2T
W3n
2T
Trellis ENCODER
W1n
2T
W4n
2T
I3_n’
I2_n’
I1_n
Y0_n
BIT
CONVERTOR
T
2 T
Z10_n
Z9_n
Z8_n
Z7_n
Z6_n
Z5_n
Z4_n
Z1_n+1
Z0_n+1
Z1_n
Z0_n
Exlusive OR
Signaling Interval
Delay Element
Figure 5. 16-State code with 4D Rectangular constellation
If we denote the current and next states of the
trellis encoder as W1pW2pW3pW4p, p=n and n+2, the
corresponding 16-state trellis diagram is shown in
Figure 6.
CURRENT
NEXT
STATE STATE
10log
2
⎛ 4d0
⎜
⎜ 31.33d
⎜ 2
d0
⎜
2
⎝ 20d0
⎞
⎟
2
0 ⎟
10
=
⎟
⎟
⎠
4.0713
dB
Where 31.33 d 2
0 is the average power of the 4D
constellation, and 20d 2 0 is the average power of the
32QAM.
2.3 Simulation Results
Bit Error Rates (BER) for the two different
systems have been simulated, the uncoded system (32
DQAM), and the 4D 16-state code TCM system with
a Viterbi decoder using a truncation length equal to K.
In this stage of simulation, the system is simulated
only with the AWGN disturbance.
The results of the BER simulations, for 105
information bits sent, are shown in Figure 7. This
figure shows the BER values for different Signal-to-
Noise Ratios (SNR) and for different values of the
truncation length K. Both systems have the same
information rate (5 information bits/symbol period).
Table 2 shows that the BER decreases with K.
However, the BER values become very similar for the
values of K that exceed 125.
BER
10 −1
10 −2
10 −3
32QAM non codée
MCT:Tronc 10
MCT:Tronc 40
MCT:Tronc 125
MCT:Tronc 500
MCT:Tronc 5000
MCT:No Tronc
4D SUBSET
0 2 1 3
4 6 5 7
2 0 3 1
W1n W2n W3n W4n W1n+2 W2n+2 W3n+2 W4n+2
0 0 0 0
0
0 0 0 0
2
0 0 0 1
3
1
0 0 0 1
0 0 1 0
0 0 1 0
6 4 7 5
1 3 0 2
0 0 1 1
0 1 0 0
0 0 1 1
0 1 0 0
10 0 SNR (dB)
10 −4
10 −5
0 5 10 15 20 25
5 7 4 6
3 1 2 0
7 5 6 4
2 0 3 1
6 4 7 5
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
Figure 7. 4D TCM performance in AWGN channel
As shown in Figure 7, asymptotically, the system
employing 4D TCM code gains approximately 4 dB of
SNR over the uncoded system.
0 2 1 3
1 0 1 0
1 0 1 0
4 6 5 7
3 1 2 0
7 5 6 4
1 3 0 2
5 7 4 6
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Figure 6. Trellis Diagram of 16-State code of Figure 5
The coding gain of the trellis coded modulation
over the uncoded 32QAM therefore is:
SNR = 18
K 10 20 40 125
BER 0.0171 0.0096 0.0065 0.004
K 500 5000 No Trunc
BER 0.0051 0.0031 0.0039
SNR = 19
K 10 20 40 125
BER 0.0054 0.0026 0.0018 5.6e-4
K 500 5000 No Trunc
BER 3e-4 2e-4 2.7e-4

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SNR = 20
K 10 20 40 125
BER 0.0013 3.3e-4 1.5e-4 0
K 500 5000 No Trunc
BER 0 0 0
Table 2. Effect of truncation length on the performance of
the 4D TCM Code
3 Trellis Coding in Twisted Copper-Pair
Passband Channels
As specified in ANSI and ETSI (ETSI TS 101
270-1 v2.0.6 part1, 2002)(ETSI TS 101 270-2 v2.0.3
part2, 2002) functional documents, SCM-VDSL
systems don’t use convolutional coding. In what
follows, we will study the contribution of the TCM in
the SCM-VDSL systems. The achievable gains for
systems using the scheme consisting of 4D Trellis
Coded Modulation have been analyzed in the previous
section, and are typically equal to 4 dB for an AWGN
channel.
3.1 SCM-VDSL system
Figure 8 presents the SCM-VDSL system (T. Starr &
M. Sorbara & J.M. Cioffi & P.J. Silverman, 2003) we
used in our simulations. For the sake of simplification,
the Reed-Solomon coding and interleaving functions,
whose main purpose is to protect the data from
Impulse Noise, have not been introduced in that
system because the purpose of our study is not to
investigate the impact of Impulse Noise on VDSL
transmission, but to demonstrate the advantage of
using the TCM rather than the DQAM modulation.
fractionally spaced equalizer (MMSE) at a new
sampling rate equal to 2×symbolrate because the input
is now a baseband signal. The received symbols are
decoded and compared to the originally transmitted
data in order to compute the errors caused by the noise
burst, and consequently, to compare the DQAM and
TCM modulations.
3.2 Impairment Generator
The impairment generator produces the noise that
is injected into the simulation set. It includes both
crosstalk noise and background noise.
The crosstalk noise power level varies with the
frequency, the length of the cable loop, and the
transmit direction (Upstream or Downstream). The
crosstalk model (ETSI TS 101 270-2 v2.0.3 part2,
2002) applied according to the test scenarios we
choose is described below.
Figure 9 defines a functional diagram of the
composite impairment noise. This diagram has the
following elements:
1. The three impairment "generators" G1, G2, and G3
generate noise as defined in (T. Starr & M. Sorbara &
J.M. Cioffi & P.J. Silverman, 2003).
2. The transfer function H 1 (f, d) models the length
and frequency dependency of the NEXT impairment
as specified in (T. Starr & M. Sorbara & J.M. Cioffi &
P.J. Silverman, 2003).
3. The transfer function H 2 (f, d) models the length
and frequency dependency of the FEXT impairment as
specified in (T. Starr & M. Sorbara & J.M. Cioffi &
P.J. Silverman, 2003).
NEXT noise
Independent noise
Generators
G1
Crosstalk transfer
functions
H1(f,d)
S1
FEXT noise
G2
H2(f,d)
S2
FSAN SUM
Background noise
Cable independent
G3
S3
Figure 9. Functional diagram of the impairment noise
composition
Figure 8. VDSL Transmission Chain
To satisfy the sampling theorem, the QAM
symbols x k are over-sampled at the sampling rate
4×symbolrate, and are shaped using a raised cosine
filter ϕ
p
(t)
before being sent through the channel.
Inter-Symbol Interference (ISI), Additive White
Gaussian Noise (AWGN), and crosstalk impair singlecarrier
transmission over the copper pairs. After being
modulated and sent through the channel, an Additive
White Gaussian and crosstalk Noises are
superimposed to the channel output in the time
domain. After crossing the whitening filter g(t), the
data, brought back to the baseband, are sent through a
low-pass filter in order to eliminate the whitened noise
situated out of the frequency band. After that, they are
sent through a finite minimum-mean-square-error
Several deployment scenarios have been identified
to achieve VDSL simulations. Each scenario (noise
model) results in a length dependant PSD description
of noise. Some of the three individual impairment
generators G1, G2, and G3, are used more once in the
same noise model.
We denote six models, Type "A", Type "B", and
Type "C" for cabinet modeling and Type "D", Type
"E", and Type "F" for exchange modeling (ETSI TS
101 270-2 v2.0.3 part2, 2002). In our simulations, we
chose Type "A" as the impairment modeling.
Type "A" models (Cabinet) are intended to
represent a mixed scenario including full ADSL where
the VDSL system is placed in a distribution cable (up
to ten of wire pairs) that is filled with many other
transmission systems: 10 ADSL, 4 HDSL, and 20
ISDN interferers.

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3.3 Simulation Results
The VDSL system shall operate with a bit error
ratio < 1 erroneous bit through 10 7 bits sent when
operated over any loop with the noise models and
simulation conditions specified in this section.
Because of computer restrictions, we carried our
simulations with a BER level equal to 10 -5 .
Simulation defaults: We have simulated the 4D
TCM method in the VDSL system described in Figure
8 with three configurations of the truncation length K
of the Viterbi decoder: K = 10, K = 125, and without
truncation.
The set of default parameters used in the
simulations is listed below:
• Number of Feed-Forward Equalizer (FFE)
taps=32.
• Roll-off factor: α = 0. 2 .
• Number of information bits per signaling
interval=5.
• Symbol rate: f baud = 2.16 MHz.
• Carrier frequency: f c = 2.2275 MHz.
• Sampling rate: f s = 4f baud = 8.64 MHz.
• The sampling rate at the input of the MMSE-FSE
equalizer is L x f baud with L = 2.
• Transmitted constellations = 32QAM for noncoded
transmission, and 48QAM for trellis coded
transmission.
• The noise is additive, colored, and Gaussian
ACGN. When whitened, its power spectral density
(PSD) level is fixed to typically -140 dBm/Hz, which
usually corresponds to the reference noise floor in the
VDSL system.
• As specified in the functional requirement
documents (ETSI TS 101 270-1 v2.0.6 part1,
2002)(ETSI TS 101 270-2 v2.0.3 part2, 2002), the
PSD of the transmitted modulated signal is typically
equal to -60 dBm/Hz.
Simulation results: In tables 3 and 4, we show the
cable range reaches and the channel capacity gains for
the 4D TCM VDSL system.
On one hand, Table 3 shows the difference in cable
range reaches if we vary the truncation length K. For
the values of K that exceed 125, the 4D TCM VDSL
cable range is typically constant. It is approximatively
equal to 1270 m.
On the other hand, the reach in the case of the
32QAM non-coded VDSL system is typically equal to
1180 m. In fact, the channel capacity associated for
this value of the cable range is equal to 4.9823 bits.
Beyond this value, the channel capacity becomes
lower than the number of bits we want to send each
signaling interval (b = 5). Thus, the 4D TCM VDSL
system gives a cable range gain of 90m with the
suitable value of K = 125.
Table 4 shows the channel capacity gain in terms
of number of bits we can send through the channel for
different values of cable ranges and K. We note that
the use of the trellis Coded Modulation rather than the
DQAM allows sending 5 bits/signaling interval, even
when the channel capacity (denoted bpsi in Table 4),
calculated without taking into account the gain
introduced by the TCM, is lower than 5. In our
simulations, for K = 125 and BER = 10 -5 , the gain
introduced by the TCM increases the channel capacity
by 0.957 bits per signaling interval, which corresponds
to 0.957 × 2.16 = 2.067 Mbps of rate gain.
Cable Length Erroneous Symbols BER
K = 10
1210 0 0
1220 0 0
1230 2 0.6e-5
1240 6 e-5
1250 6 1.2e-5
1260 27 5.3e-5
K = 125
1260 0 0
1270 0 0
1280 5 1.2e-5
1290 36 7e-5
1300 39 9.7e-5
Without Truncation
1270 0 0
1290 0 0
1300 20 4.3e-5
1400 247 5.22e-4
Table 3. TCM SCM-VDSL: Cable range reaches for
different values of the truncation length K
K
Cable
Length
Bpsi
Gain
10 1230 4.5822 0.4178
125 1270 4.043 0.957
No Trunc 1290 3.8172 1.1828
Table 4. Channel capacity gain for different values of K
Conclusion
The VDSL system is expected to be the solution to
provide broadband services to residential and business
on the existing copper plant.
In this paper, we demonstrated that the Trellis-
Coded Modulation with 4-dimensional rectangular
constellations is superior to using 2D constellations.
Using multi-dimensional rectangular constellations
not only reduces the size of the constituent 2D
constellations, but also improves the performance in
terms of both the coding gain and cable range reaches.

SETIT2005
The simulation model was based on the singlecarrier
modulation technique Quadrature Amplitude
Modulation (QAM). 4-Dimensional 16-state trellis
code with Viterbi decoding truncation length K was
has been suggested as a suitable coding scheme with a
value of K = 125. It has been evaluated in both
AWGN and twisted copper-pair channels and has
shown a coding gain of approximatively 4dB in the
AWGN channel. It has, also, shown a cable range gain
of approximatively 90m, and a channel capacity gain
of typically 0.95 bits/signaling interval for K = 125
and a BER level of 10-5, which corresponds to a rate
gain of 2.067 Mbps.
References
ETSI TS 101 270-1 v2.0.6 (2002-11). Transmission and
Multiplexing (TM); Access transmission systems on
metallic access cables; Very high speed Digital
Subscriber Line (VDSL); Part 1 : Functional
requirements.
ETSI TS 101 270-2 v2.0.3 (2002-10). Transmission and
Multiplexing (TM); Access transmission systems on
metallic access cables; Very high speed Digital
Subscriber Line (VDSL); Part 2 : Transceiver
Specification.
Lee-Fang. Wei. Trellis-coded modulation with
multidimensioanl constellations. IEEE Transactions on
Communications Theory, IT-33(4), July 1987.
Mario Diaz Nava and Christophe Del-Toso. A short
overview of the vdsl system requirements. IEEE
Communications Magazine, December 2002.
T. Starr, M. Sorbara, J.M. Cioffi, P.J. Silverman. DSL
Advances, Prentice Hall Inc., New Jersey, 2003.