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


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


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


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


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


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.



■ For recursive inner encoder:

and

■ h(M): weight associated to the highest exponent of N



■ 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



Outer Encoder Po

Inner Encoder

MUX

Ppi

Psi

C’oC’’o

C’i






input sequences



■ We obtain:






input sequences


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


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


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.


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


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


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


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


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)



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. Bound


p =10/222. Bound


p =16/222. BoundUMTS PCCC



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


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.)


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


Open Problems

■ Convergence analysis EXIT charts and Density Evolution Techniques are difficult to apply

■ We are open to cooperations with other groups!!!

Documents

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