NEWCOM, Department 1-SPW1 meeting ENSEA , April 28th, 2005

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

Politecnico di Torino – Universitat Pompeu Fabra 2

Motivations

■ Standard SCCC for high-rates:

Outer Encoder Inner

Encoder

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Motivations

■ Standard SCCC for high-rates:

High-rate Encoder 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:

■ 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

Outer Encoder Inner

Encoder Pi

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A new class of SCCC

RC-SCCC

■ 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:

s : systematic permeability

p : parity permeability

Outer Encoder

u Inner EncoderPo

MUX

Psi

Ppi

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A new class of SCCC

■ Performance depend on puncturing patterns Po,Psi,Pp

i

s and p 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 Po

Inner Encoder

MUX

Ppi

Psi

C’oC’’o

C’i

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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, M.

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Upper bounds to the error probability

■ For recursive inner encoder:

and

■ h(M): 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 Po

Inner Encoder

MUX

Ppi

Psi

C’oC’’o

C’i

■ 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):

■ For large Eb/N0 BER performance is given by:

do’f odd

do’f even

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Upper Bound to the error probability

■ Design considerations:■ Po should be chosen to optimize C’o distance spectrum

■ Psi and Pp

i should be chosen so that h(m ) 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■ Ps

i 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

Rate-1/24 state

u Rate-1/24 state

Fix punct.

MUX

Psi

Ppi

do’f=3

do’f=4

outer code puncturingconstituent codes

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Performance Bounds

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9Eb/N0

FE

R

Bounds of Rate-2/3 SCCC for several p N=200. Po,1

p =2/30

p =4/30

p =6/30

p =8/30

p =10/30

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Performance Bounds

Bounds of Rate-2/3 SCCC for several p N=200. Po,2

p =2/30

p =4/30

p =6/30

p =8/30

p =10/30

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9Eb/N0

FER

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Simulation Results

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9

Eb/N0

FER

Performance of Rate-2/3 SCCC for several p N=200. Po,1

p=2/30. Simulation

p =2/30. Bound

p =4/30. Simulation

p =4/30. Bound

p =8/30. Simulation

p =8/30. Bound

p =10/30. Simulation

p =10/30. Bound

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Simulation Results

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8 9 10

Eb/N0

FE

R

p=2/30. Simulation

p =2/30. Bound

p =4/30. Simulation

p =4/30. Bound

p =8/30. Simulation

p =8/30. BoundUMTS PCCCSCCC (VTC’01)

Performance of Rate-2/3 SCCC for several p N=2000. Po,1

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Simulation Results

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

2 3 4 5 6 7 8 9 10Eb/N0

FE

R

p =4/222. Simulation

p =4/222. Bound

p =10/222. Simulation

p =10/222. Bound

p =16/222. Simulation

p =16/222. BoundUMTS PCCC

Performance of Rate-9/10 SCCC for several p N=2000. Po,1

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Simulation Results

Performance versus p for several Eb/N0 . R=9/10. N=2000. Po,1

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

200 202 204 206 208 210 212 214 216 218 220

Router

FE

R

Eb/N0=4dB

4.2dB

4.4dB

4.6dB

4.8dB

5dB

5.4dB

5.2dB

5.6dB

5.8dB 6dB

6.2dB 6.4dB

Eb/N0=6.8dB

6.6dB

22/222 20/222 18/222 16/222 14/222 12/222 10/222 8/222 6/222 4/222 2/222

p

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Simulation Results

FER Performance comparison. N=428

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 1 2 3 4 5 6 7 8Eb/N0

FER

R=1/3 R=5/6

R=9/10

SCCC (10 it.)PCCC (8 it.)LDPC (50 it.)

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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!!!