Design of Duo-Binary Turbo Convolution Code

Design of Duo-Binary Turbo Convolution Code Debasish Bera Tata Consultancy Services, Kolkata

0.1

Systematic Part

A

1

+ 1

B

+

S2

S3

0.01

2

BER

Interleaver

+

S1

C O D E

2

W O R D

+ +

CRSC W 1 or 2

'itr_1.dat' 'itr_2.dat' 'itr_4.dat' 'itr_5.dat' 'itr_8.dat'

0.001

0.0001

Y 1 or 2 Y

Puncturing

1e-005

W

1

1.5

2

Redundancy Part

Turbo Encoder Data path

Duo-binary CRSC encoder with memory length = 3

For 1st decoder, in r‐th iteration, Λ 011e ( r ) (d t ) = Λ 011 ( r ) (d t ) − 2 d t , b

For 2nd decoder, in r‐th iteration, Λ 012 e( r ) (d t

~ − Λ 012e( r − 1 ) ( d t )

~ Λ111e( r ) (d t ) = Λ111 ( r ) (d t ) − 2 ( d t ,b + d t , a ) − Λ112e( r −1) ( d t )

A′k B′k

SISO Decoder 1 (SOVA-1)

Y1′k

W1′k

L01e1 ( d k ) L10e1 ( d k ) L ( dk ) 11 e1

Deinterleaver_01 Deinterleaver_10 Deinterleaver_11

Interleaver_01 Interleaver_10 Interleaver_11

3

3.5

BER  performance  of  bi‐directional  SOVA  with  code  rate  =  1/3,  number  of  iteration  is  5  and  frame  lengths  110  bytes  (Intl_len_440),  188  bytes  (Intl_len_752) and 212 bytes (Intl_len_848). Prologue decoding is performed  in  alternate  iteration.  Performance  improves  as  the  frame  length increases.  Eb/N0 is in dB. 1

'Intl_len_440.txt' 'Intl_len_752.txt' 'Intl_len_848.txt'

0.1

L01e 2 ( dk )

0.01

L10e 2 ( d k ) L11e 2 ( d k )

L012 ( d k )

BER

L101 ( d k ) L111 ( d k )

~ Λ 012 ( r ) (d t ) − 2 d t , b − Λ 011e ( r ) ( d t )

~ Λ 102 e( r ) (d t ) = Λ 102 ( r ) (d t ) − 2 d t , a − Λ 101e( r ) ( d t ) ~ Λ112e( r ) (d t ) = Λ112 ( r ) (d t ) − 2 ( d t ,b + d t , a ) − Λ111e( r ) ( d t )

~ Λ 101e ( r ) (d t ) = Λ 101 ( r ) (d t ) − 2 d t , a − Λ 102 e( r − 1 ) ( d t )

L011 ( d k )

)=

Eb/N0 2.5

L102 ( d k ) L112 ( d k )

0.001 0.0001

Lsoft1(dk | x)

Interleaver_Sys

A#k B#k

SISO Decoder 2 (SOVA-2)

Y1′k W2′k

1e-005 DEINTERLEAVER Lsoft2(dk | x)

1e-006

P/O

A′k = Received systematic bit corresponds to A B′k = Received systematic bit corresponds to B Y1′k = Received parity bit corresponds to Y1 W1′k = Received parity bit corresponds to W1 W2′k = Received parity bit corresponds to W2 Y2′k = Received parity bit corresponds to Y2 A#k = Interleaved systematic received bit corresponds to A′k # B k = Interleaved systematic received bit corresponds to B′k Lije1 ( d k )= Extrinsic info. from SISO # 1for symbol ij, Lije 2 ( d k )= Extrinsic info from SISO # 2 for symbol ij

1e-007

Lsoft1(dk | x) =

Soft value i.e. a posteriori information from SISO # 1 Soft value i.e. a posteriori information from SISO # 2

Duo-binary SOVA based Turbo Decoder

0.5

1

1.5 Eb/N0

2

2.5

3

BER performance of bi‐directional SOVA decoding with variable number of  iteration for duo‐binary CRSC code (interleaver length = 12 bytes, code rate =  1/3). Performance increases as number of iteration increases. Itr_i.dat: BER  curve for i‐th iteration. Eb/N0 in dB.

ij = 01, 10, 11

Lsoft2(dk | x) =

0

Turbo Decoder Data path