Design and Performance of Rate Compatible

Design and Performance of
Rate Compatible-SCCC
Alexandre Graell i Amat†‡, Guido Montorsi‡, Francesca Vatta*
† Universitat Pompeu Fabra. Barcelona, Spain
‡ Politecnico di Torino. Torino, Italy
* Università di Trieste. Trieste, Italy
NEWCOM, Department 1-SPW1 meeting
ENSEA, April 28th, 2005
Motivations
■ Standard SCCC for high-rates:
Outer
Encoder
P
Inner
Encoder
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Motivations
■ Standard SCCC for high-rates:
High-rate
Encoder
■
■
P
Inner
Encoder
If the interleaver size is fixed
different
information block sizes for different rates
For very high rates, the increasing value of the
outer code rate causes an interleaver gain penalty
error floor
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Motivations
■ Standard Rate-compatible SCCC:
Outer
Encoder
P
Inner
Encoder
Pi
■
Rate-compatibility restricts puncturing to the inner
encoder
■
In general, the rate of the inner encoder is restricted
to be Ri  1
the overall code rate is at most Ro
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A new class of SCCC
RC-SCCC
u
Outer
Encoder
Po
P
Inner
Encoder
Psi
Ppi
M
U
X
■ The inner code may be punctured beyond the unitary
rate
RSCCC may be greater than the outer code
rate
■ Puncturing is split between systematic and parity bits:
rs : systematic permeability
rp : parity permeability
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A new class of SCCC
■ Performance depend on puncturing patterns Po,Psi,Ppi
rs and rp should be properly selected
■ We propose design criteria of this new class of SCCC
by deriving the upper bounds to the error probability
Outer
Encoder
C’’o
C’o
Po
P
Psi
C’i
Inner
Encoder
M
U
X
Ppi
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Upper bounds to the error probability
■ We obtain:
■ The dominant contribution to the error probability for
(asymptotic with N) is the largest exponent of N, aM.
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Upper bounds to the error probability
■ For recursive inner encoder:
and
■
h(aM): weight associated to the highest exponent of N
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Upper bounds to the error probability
■ We obtain:
■
■
■
■
do’f: free distance of C’o
do’’(do’f): minimum weight of C’’o code sequences
corresponding to a C’o code sequence of weight do’f
di’f,eff: effective free distance of C’i
h(3)m: minimum weight of C’i sequences generated by weight 3
input sequences
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Upper bounds to the error probability
Outer
Encoder
C’o
Po
C’’o
P
Psi
C’i
Inner
Encoder
■
■
■
■
M
U
X
Ppi
do’f: free distance of C’o
do’’(do’f): minimum weight of C’’o code sequences
corresponding to a C’o code sequence of weight do’f
di’f,eff: effective free distance of C’i
h(3)m: minimum weight of C’i sequences generated by weight 3
input sequences
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Upper bounds to the error probability
■ We obtain:
■
■
■
■
do’f: free distance of C’o
do’’(do’f): minimum weight of C’’o code sequences
corresponding to a C’o code sequence of weight do’f
di’f,eff: effective free distance of C’i
h(3)m: minimum weight of C’i sequences generated by weight 3
input sequences
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Upper Bound to the error probability
■ Then, Pb(e) (asymptotic with respect to N):
do’f even
do’f odd
■ For large Eb/N0 BER performance is given by:
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Upper Bound to the error probability
■ Design considerations:
Po should be chosen to optimize C’o distance spectrum
■ Psi and Ppi should be chosen so that h(am ) and hm are
maximized
■ Ppi must be optimized to yield the best C’i IOWEF
■ Psi must be selected to optimize do’’(do’f )
Psi turns out to be interleaver dependent
■
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Rate-compatible SCCC
■ We designed well-performing rate-compatible SCCC
following the aforementioned considerations
■
■
■
Psi to optimize do’’(do’f )
Ppi to optimize Ci’ IOWEF
We used a searching algorithm that works incrementally,
fulfilling the rate-compatible restriction, so that the
punctured positions for a given outer rate are also
punctured for all higher rates.
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The SCCC Scheme
u
Rate-1/2
4 state
Fix
punct.
P
Rate-1/2
4 state
Psi
Ppi
M
U
X
do’f=3
do’f=4
constituent codes
outer code puncturing
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Performance Bounds
Bounds of Rate-2/3 SCCC for several rp N=200. Po,1
rp =2/30
rp =4/30
rp =6/30
rp =8/30
rp =10/30
1.E+00
1.E-01
1.E-02
FER
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
0
1
2
3
4
Eb/N0
5
6
7
8
9
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Performance Bounds
Bounds of Rate-2/3 SCCC for several rp N=200. Po,2
rp =2/30
rp =4/30
rp =6/30
rp =8/30
rp =10/30
1.E+00
1.E-01
1.E-02
FER
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
0
1
2
3
4
Eb/N0
5
6
7
8
9
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Simulation Results
Performance of Rate-2/3 SCCC for several rp N=200.
Po,1
1.E+00
1.E-01
1.E-02
FER
1.E-03
1.E-04
rp=2/30. Simulation
rp =2/30. Bound
rp =4/30. Simulation
rp =4/30. Bound
rp =8/30. Simulation
rp =8/30. Bound
rp =10/30. Simulation
rp =10/30. Bound
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
0
1
2
3
4
5
6
7
8
9
Eb/N0
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Simulation Results
Performance of Rate-2/3 SCCC for several rp N=2000. Po,1
1.E+00
rp=2/30. Simulation
rp =2/30. Bound
rp =4/30. Simulation
rp =4/30. Bound
rp =8/30. Simulation
rp =8/30. Bound
UMTS PCCC
SCCC (VTC’01)
1.E-01
1.E-02
1.E-03
FER
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
1.E-09
1.E-10
1.E-11
0
1
2
3
4
5
6
7
8
9
10
Eb/N0
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Simulation Results
Performance of Rate-9/10 SCCC for several rp N=2000. Po,1
1.E+00
rp =4/222. Simulation
rp =4/222. Bound
rp =10/222. Simulation
rp =10/222. Bound
rp =16/222. Simulation
rp =16/222. Bound
UMTS PCCC
1.E-01
1.E-02
FER
1.E-03
1.E-04
1.E-05
1.E-06
1.E-07
1.E-08
2
3
4
5
6
7
8
9
10
Eb/N0
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Simulation Results
Performance versus rp for several Eb/N0 . R=9/10. N=2000. Po,1
1.E+00
Eb/N0=4dB
4.2dB
1.E-01
4.4dB
4.6dB
1.E-02
4.8dB
FER
5dB
1.E-03
5.2dB
5.4dB
1.E-04
5.6dB
5.8dB
6.2dB
1.E-05
6dB
6.4dB
6.6dB
Eb/N0=6.8dB
1.E-06
22/222
200
20/222
202
18/222
204
16/222
206
14/222
208
12/222
210
rp
Router
10/222
212
8/222
214
6/222
216
4/222
218
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2/222
220
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Simulation Results
FER Performance comparison. N=428
1.E+00
SCCC (10 it.)
PCCC (8 it.)
LDPC (50 it.)
1.E-01
R=9/10
FER
1.E-02
1.E-03
1.E-04
R=5/6
R=1/3
1.E-05
1.E-06
0
1
2
3
4
5
6
7
8
Eb/N0
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Conclusions
■ Derived lower bound to the error probability of a new
class of SCCC
■ Derived suitable design guidelines
■ Derived optimal Rate-compatible SCCC families
■ The proposed scheme offers good performance for low
to moderate block lengths in a large range of rates
■
The interleaver gain for low rates is kept also in the case
of heavy puncturing
■ This code structure has been proposed as a candidate
coding scheme for ESA MHOMS
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Open Problems
■ Convergence analysis
EXIT charts and Density
Evolution Techniques are difficult to apply
■ We are open to cooperations with other groups!!!
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