Incremental redundancy schemes based on LDPCs for transmission over Gaussian block-fading channels

½

! "

# $ %

! #

! ! !

" "#

! #!" # &' &'

!

!

# !" #

# ( ! )*+

" !

, - .&",-.&

!

/ 0

1 /

!

$ 2

3

4

1

!

# % #!

3

3

3 5

# Æ $

6 / (

!

$ # #!

3

$ # % !

! " # 7!

# 6 )

+ 3 1

!8 "/

% # 9

3 3

3 !#

# #

!

$ #

# "

#

#! # $ !

" # " ! ,

#

# " )* +

" # #

#! 2

$!

# #!#

½

#

&' "

/

/

# !

&' /"

/

!

# !#

½

¾

&':&'

# "

#

# #

# ,3

3

#"

! #

:

,

#! 2/

# )* + ! /

Æ # #

#6 !

3

;

<

#

# 1

#

# #! Æ

# # .

9 !# #

! # $#/

=6#!

3

>

$!

3 $ #

# 6)>?*+

! @ 3

: #

3 A :

$

3 )+

*

!

!

92 ! 3

# 9

!

3 .

31 B

2

3.

3 1

C

= *

3

1

14

?

9!#

9!

3 . D

3

# %

1

3 .

1A

<

#!

3 1

#

1 4!

!

¾

"

6 11

E !!

1A

!

#!

#3 1

#

15

# # #

/# (

/ ( & 8 0 # (

!

1

$

%

1;

$ %

! 0 #

& 8 !

!

) F&+

1>

F& 3

!

# #

/ # #

#3!

#1 5

8 ! #

3 AG 1AG ! # 3

#!!! ! ( & 8

31A AG! $& 8

( ! $

!# #

/ !

/ )A 1A 5+ : !

131 5A

3A 1 13513A 5#"

! 15 5; ! A 1A 5

5 J3 54'

' 1 $

! $8!#!

)B +

! " !

#!# G.# $

G G. #

" # !-

)C + $/ @

" # 2 G

! !

)C + < G 6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

rate of the code R

p(m)

m=1 m=3 m=5 m = 7

m=9

m=10

m=2 m=4 m=6 m=8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rate of the code R

p(m) ^m=10

m=9

m=7 m=5

m=3 m=1 m=2

m=4

m=6

m=8

!

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rate of the code R

Tput

Chernoff Bound

Gaussian Approximation Convolutions

"

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Rate of the code R

Tput

Chernoff Bound

Gaussian Approximation

Convolutions

#

#

#!G G.

# 6

! # G

6 9 !

# !

= #

2

3.

G

A

1*

G

G G. (

!

9 G. #

- )C+ & ,-.&

2 # #% &

) - * #

" + # "

,+

! #

#"

#! #! #

# 6

+ ( > ! ?

#

-

# ( / @ #

(

)C ;+ 2

##G.$

(

! # %

$ " # !

# # G. %!

" #! # = !

#)1 + / !

#

92 !, #!

! # #"

, ! 3 1 , -

! .

! #! $

- #!

-. , 3

1

-., 3 1B

( /

-K.,33/1$4

#/ $

!> #+ #

" = #

# # "

(#!

3

1

0

1C

2

01

3

&

1

41

#

# #"

(1

2

"

/ )5 + 9/ "

!

1

1 =

" #/

/

31

/1

1

1?

$ # #

#" (

#!

310

1

A

1D

G ## % 1C 1D

3

1

0

10

1

A

5A

3A

#Æ $

! #G/

5A %2/ 31 $

M2 2 2)A1 51

2 #

M2

3 1

0

10

12A

!7 &

3.

M

2 A A

2 2)A1

# #

#

# * B #

# ,-.&

$,-.&! #

# ! #

6

9( )C + 9! ,-.&

#!

# #C

! 3 A 1A ;::=6 9

# #

# /

# 3 A 15 3 A 1 #

A *A *D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rate of the code R

Tput

LDPC Codes

RB Codes Convolutions

$ %&' ( ( () '

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5

Rate of the code R

tput

LDPC Codes

RB Codes Convolutions

* %&' ( ( () '

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Rate of the code R

tput

LDPC Codes Binary code

+ %& ' ( (

",)

-. / (0&(1( 12 1%' 3

&(' ( &4

!

-!. / 5 &( 06( &('( /) & '3

7 '(&(/')4

!

-". /5&( 89' ( ( 9 : ( 07(

/)3'%'(3%( 3&'&

:( ; (7<) (4

!

-#. =07(2('( (273

' (4 >*?

-$. & ; (% ((0@379A

' ; (&(& ((4

!

-*. 9; ; 03%( 3&'&4

!>*"

-+. 8 9' ( ( 9 : ( 0& ' 3

%( 3&' & :( 3 ( %'3

(4 !

-?. BC ( 9 9 9 06( : 9( 3

( 7( 79A '4

>>*