CONSTELLATIONS MULTIDIMENSIONNELLES POUR MODULATION PAR CODAGE EN TREILLIS AVEC CONCATENATION EN PARALLELE

MULTI-DIMENSIONAL CONSTELLATIONS FOR PARALLEL CONCATENATED TRELLIS CODED MODULATION

Abrégé anglais

Parallel Concatenated Convolution Codes (PCCC) were presented as a promising
candidate for improving the performance of G.lite.bis and G.dmt.bis. This
contribution
shows preliminary simulation results which were not able to confirm the coding
gain of
[BM-087] and [NG-097].

Description

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MULTI-DIMENSIONAL CONSTELLATIONS FOR
PARALLEL CONCATENATED TRELLIS CODED MODULATION
Background of Invention:
There have been several proposals to apply powerful turbo coding /decoding
technique to
G.lite and G.dmt to improve transmission rate and loop reach. Particularly,
Alcatel
proposal (the text of which follows in the Reference section below) of
Parallel
Concatenated Trellis Coded Modulation (PCTCM), also called as Parallel
Concatenated
Convolution Codes (PCCC), has shown some promising preliminary simulation
results
[NT-112]. As shown in Figure 1, parallel bit streams go through two parallel
convolutional encoders with an interleaver in between and two sets of coded
bits are
mapped into a constellation point independently, which are sent out
alternatively, e.g.,
one constellation point is punctured out at a given dmt symbol.
gel
One drawback of such configuration is that it can only support minimum
constellation of
size eight, i.e., it can not map to bins with smaller constellation of size
four or two. It
may become a major problem as loop reach becomes longer and SNR becomes lower,
in
which case, a powerful coding scheme is more desirable.
Description of invention
The invention to be disclosed is to enhance above configuration by
incorporating a multi-
dimensional constellation construction function block such that smaller
constellations can
be grouped together to accommodate a minimum of 3 coded bits. The enhanced
configuration diagram is shown in figure 2 immediately below. A new function
block
(tone ordering bin grouping) is introduced to order the tones based on
constellation sizes
and group them accordingly to form mufti-dimensional constellations, which
interfaces
with the Signal Mapper to control the bits-to-point mapping.
Figure 1 Alcatel's Proposal of PCTCM

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Figure 2 Enhance PTCM diagram
To Channel
Signal
Encoder Mapper
1
v'9~e ~i':deri~g~ ,
:B~r ~r~upfng . : :
Signal
Encoder ~ Mapper
2
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The Bin grouping can be flexible enough to handle different bin loading
scenarios. The
following table lists some possible mufti-dimensional constellation
construction scenarios
for small constellations.
Table 1 Bin Group Summary
Case Grou in Scenario Constellation Dimension
1 four b=1 bins 4
2 two B=1 bin and one b=2 bin 4
Two b=2 bins 4
NOTE: b is the number of bits that a bin (subchannel) carries.
It is not intended here to define specific mapping schemes to map coded bits
into
constellation points due to the fact that there exist many different mapping
alternatives.
The general guideline, thought, is that for a given encoder, the mapping
scheme should
give roughly the same error protection for each constellation dimension. One
mapping
example is for Case 3, one of three coded bits from the encoders, say the
bottom one, can
be used to select one of the two bins and the remaining two bits can be used
to select
4QAM points in each bin.
In summary, what is claimed in this invention disclosure is an added function
block on
Alcatel's proposal of PCTCM to construct mufti-dimensional constellation with
small
constellation of size two and four. The benefit of this enhancement is that
powerful turbo
code technique can still be applied to low SNR environment, which is critical
to extend
loop reach.

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The constituent convolutional encoder is represented in figure 2.
Figure 2 : Constituent convolutional encoder
The PCTCM scheme simulated uses a 64 QAM constellation. Given the rate of the
code
5/6 , it achieves a spectral efficiency of 5 bits/s/Hz. The Line Code Capacity
limit for
such a modulation is at SNR per bit Eb/No= 9.2 dB. The Shannon capacity is
situated at
8.2 dB but is not attainable.
The characteristics of the PCTCM scheme that we have investigated are
summarized
below
~ 64 QAM modulation
~ r)=5 bits/s/Hz
~ Spread interleaver
~ 8-state encoder (depicted in fig 2)
~ Soft In Soft Out (SISO) algorithm
In addition, one of the most important parameter is the interleaver block
size. As a
starting point, we have considered an interleaver of 6 DMT symbols consisting
of 204
Garners. It results in a delay of l.Sms. Let note that such a delay is the
time to fill the
interleaver.
Performance of the PCTCM configuration with an interleaver size of 1224
symbols is
depicted in figure 3. The different curves corresponds to 1, 2, 3, 4, 5, 6, 7
iterations.

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Figure 3 : BER performance of PCTCM, 64 QAM, 5 bits/s/Hz
Figure 3 depicts typical BER curves for PCTCM. It turns out that the BER
decreases
when the number of iterations increases from 1 to 6 iterations but then it
saturates. The
BER starts to drop at a very low SNR.
Knowing that the Line Code Capacity limit for 64 QAM modulation is at 9.2 dB,
we can
see that PCTCM achieves a BER <_10~5 at about 1dB distance from the capacity
limit.
But the error floor significantly degrades the BER performance at lower BER. 2
additional dB's are required to achieve the target BER of 10-~. This
phenomenon was
also observed in [PO-071 ], although another type of encoder and different
interleaver
length was used, which confirms that this is a fundamental behaviour of PCTCM.
The remaining main task is to remove the error floor. Suppose, that some
technique could
lower the BER 10-5 to a BER of 10-~ without power penalty. Knowing that
uncoded 5
bps/Hz QAM modulation reaches a BER=lE-7 at Eb/No= 17.5 dB, this technique
would
correspond with a net coding gain of 7.3 dB.
In [BM-087] it was proposed to use a Reed Solomon as an outer code. From
[Vocal-1]
we learned that PCTCM interleaver size and block length used in [BM-087] and
[NG-
097] was 256 QAM symbols. For spectral efficiency of 5, this corresponds with
5*256 is
about 1250 bits per block or frame.
It is also well know that the error behaviour of the PCTCM decoder is very
bursty. The
number of errored frames is low, but if a frame is in error, a lot of bit
errors occur. Our
preliminary simulations for 256 symbols show that at a BER=1 e-5 (at
Eb/No=11.OdB)
the average number of bit-errors per errored-frame is about 50 bit-errors.
This number is
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only the average number and in practice the number of bit-errors will
sometimes be
higher. A probability distribution curve of the number of bit-errors per error-
frame would
give these probabilities. Because of computing- time constraints we were not
able to
produce these numbers in this contribution.
Taking the average number of 50 bit-errors per error-frame, for a byte
oriented RS
decoder this means that an average burst of 50 bytes have to be corrected.
The burst error correcting capability of the Reed Solomon decoder is known to
be R.D /2
= 0.5 x rs-overhead x rs-interleaver depth. If R=8 is assumed, D needs to be
>= 12.5,
which in practice means D=16.
Assuming a max allowed latency requirement of the 6.992.1 Performance
requirements
4 + (S-1)/2 + S.D/4 <= 12 msec, one can allow only S=1.
The power penalty of using an RS-overhead of R=8 and S=1 is shown to be 2...3
dB
[NG-097]. This would correspond with a reduction of the net coding gain from
7.3 dB
to 4.3...5.3 dB.
This corresponds with a net coding gain of 6.992.1 concatenated Trellis + Reed
Solomon only.
3. References:
[PO-071 ] "G.dmt: Inclusion of a Serial Concatenated Convolutional Code in the
G.992.1.bis". J. A. Tomes, V. Demjanenko. Sunriver, Oregon 18-22 January
1999
[BM-087] "G.gen: Comparison of simulation results for different Coding
Techniques
(Uncoded, Reed-Solomon, Reed-Solomon plus Trellis and Reed-Solomon
plus Parallel Concatenated Convolutional Codes) for G.992.1.bis and
G.992.2.bis". J. A. Tomes, Frederic Hirzel, Victor Demjanenko. Boston 10-14
May 1999.
[NG-097] "G.gen.bis: Considerations about the power penalty of Reed-Solomon
forward Error Correction in ADSL systems in regard to the use of inner
encoders". J. A. Tomes, Frederic Hirzel, Victor Demjanenko. Nuremberg
(Germany) 2-6 August 1999.
[Rob96] P. Robertson and T. Worz, "Bandwidth-efficient turbo trellis-coded
modulation using punctured component codes", IEEE J. Select Areas
Commun., vol. 18, no. 2, pp. 206-218 February 1998.
[Vocal_1] Private conversation 25/10/99.
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4. Summary:
This contribution showed preliminary simulation results. These results were
not able to
confirm the coding gain of [BM-087] and [NG-097].
Further it is shown that latency is a very important constraint. Complexity is
another
constraint not explored in this contribution.
Further study of Turbo Coding needs to be done to find a coding scheme with an
improved net coding gain under the constraint of latency and complexity.
This contribution addresses the following point of the G.dmt.bis issues list:
4.2 Open Shall G.dmt.bis specify Parallel ConcatenatedBM-087, NG-
Convolutional Codes as inner encoder 097
with
Reed-Solomon codes as outer encoder?
This contribution addresses the followin oint of the G.lite.bis issues list:
1.4.3 Open Should a multiple concatenated convolutional code NG-097, NG
8/2/99 ~ be made mandatory in the ATU-x transmitter? ~ 100
Further this contribution wants to add 2 new issues the of the G.dmt.bis and
the G.lite.bis
issues list
Agreed ~ Proposal for coding techniques shall present results
on Net Coding gain, Latency and Complexity.
Open ~ What is the maximum allowed latency for new
coding techniques ?
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