Contribution of Multidimensional Trellis Coding in VDSL Systems

SETIT2005
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.