Code design method for repeat-zigzag Hadamard codes
View Patent ↗A method for selecting a signal to noise ratio for a communications code includes obtaining extrinsic information transfer (EXIT) information for a repeat-zigzag Hadamard (RZH) code responsive to a Hadamard order and a signal to noise ratio, determining code parameters for an irregular repeat zigzag Hadamard (IRZH) code for a corresponding code rate in response to the obtained EXIT values, and repeating the step of obtaining the EXIT information for a different signal to noise ratio if the corresponding code rate is other than a selected rate. The corresponding code rate is related to a bit error rate. In a preferred embodiment, the step of obtaining EXIT information includes one of obtaining an EXIT curve for repeat-zigzag Hadamard code by Monte Carlo simulation using serial decoding or obtaining an EXIT function for parallel decoding of the repeat-zigzag Hadamard code by using equations.
1. A for selecting code parameter with minimum signal to noise ratio threshold for a communications code comprising:
obtaining, using an encoder, extrinsic information transfer (EXIT) information for a repeat-zigzag Hadamard (RZH) code responsive to a Hadamard order and a signal to noise ratio,
determining code parameters for an irregular repeat zigzag Hadamard (IRZH) code for a corresponding code rate in response to the obtained EXIT values, and
repeating the step of obtaining said EXIT information for a different said signal to noise ratio if said corresponding code rate is other than a selected rate.
2. The method of claim 1 , wherein said code parameters are a code ensemble for said irregular repeat zigzag Hadamard code.
3. The method of claim 1 , wherein said step of obtaining EXIT information comprises obtaining an EXIT curve for repeat-zigzag Hadamard code by Monte Carlo simulation using serial decoding.
4. The method of claim 3 , wherein said step of determining code parameters comprises an optimization of maximizing said code rate to determine said code parameters.
5. The method of claim 3 , wherein said step of obtaining said EXIT information for a different said signal to noise ratio comprises increasing said signal to noise ratio if said corresponding code rate is less than said target rate.
6. The method of claim 3 , wherein said step of obtaining said EXIT information for a different said signal to noise ratio comprises decreasing said signal to noise ratio if said corresponding code rate is greater than said target rate.
7. The method of claim 3 , wherein said corresponding code rate is related to a bit error rate.
8. The method of claim 3 , wherein a bit error rate is a function of said signal to noise ratio and said corresponding code rate.
9. The method of claim 1 , wherein said step of obtaining EXIT information comprises obtaining an EXIT function for parallel decoding of said repeat-zigzag Hadamard code by using equations.
10. The method of claim 9 , wherein said step of determining code parameters comprises minimizing a bit error rate BER corresponding to said code rate.
11. The method of claim 9 , wherein said step of obtaining said EXIT information for a different said signal to noise ratio comprises decreasing said signal to noise ratio if a bit error rate corresponding to said code rate is less than a target bit error rate.
12. The method of claim 9 , wherein said equations include for the information bits
I
E
,
d
BIAWGN
≅
1
-
1
ln
2
∑
g
=
0
1
∑
h
=
0
r
∑
j
=
0
m
-
1
∑
k
=
0
1
(
A
g
,
h
,
j
,
k
d
,
odd
-
A
g
,
h
,
j
,
k
d
,
even
)
∑
i
=
1
∞
1
(
2
i
)
(
2
i
-
1
)
·
Φ
i
g
(
m
q
)
Φ
i
h
(
m
d
)
Φ
i
j
(
m
p
)
Φ
i
k
(
m
p
m
)
,
for the connection bits
I
E
,
q
BIAWGN
≅
1
-
1
ln
2
∑
h
=
0
r
∑
j
=
0
m
-
1
∑
k
=
0
1
(
A
h
,
j
,
k
d
,
odd
-
A
h
,
j
,
k
d
,
even
)
∑
i
=
1
∞
1
(
2
i
)
(
2
i
-
1
)
·
Φ
i
h
(
m
d
)
Φ
i
j
(
m
p
)
Φ
i
k
(
m
p
m
)
,
and
for the last parity bit
I
E
,
p
m
BIAWGN
≅
1
-
1
ln
2
∑
g
=
0
1
∑
h
=
0
r
∑
j
=
0
m
(
A
g
,
h
,
j
p
m
,
odd
-
A
g
,
h
,
j
p
m
,
even
)
∑
i
=
1
∞
1
(
2
i
)
(
2
i
-
1
)
·
Φ
i
g
(
m
q
)
Φ
i
h
(
m
d
)
Φ
i
j
(
m
p
)
.
13. The method of claim 1 , wherein said step of obtaining EXIT information comprises determining a degree profile that has minimum bit error rate BER by using differential evolution.
14. The method of claim 13 , wherein said step of obtaining EXIT information comprises computing said bit error rate during differential evolution optimization by mutual information tracking.
15. A method for selecting code parameter with minimum signal to noise ratio threshold for a communications code comprising:
choosing a signal to noise ratio,
selecting a Hadamard code order,
obtaining, using an encoder, extrinsic information transfer (EXIT) information for one of a serial decoding and a parallel decoding of a irregular repeat-zigzag Hadamard (IRZH) code responsive to said Hadamard order and said signal to noise ratio,
determining a code ensemble for said irregular repeat zigzag Hadamard (IRZH) code for a related bit error rate in response to the obtained EXIT information, and
changing the signal to noise ratio for repeated said steps of obtaining said EXIT information and said determining a code ensemble for a different said signal to noise ratio if said related bit error rate is other than a target rate.
16. The method of claim 15 , wherein said EXIT information is a curve for said irregular repeat-zigzag Hadamard (IRZH) code obtained by Monte Carlo simulation using said serial decoding.
17. The method of claim 15 , wherein said EXIT information is a function for parallel decoding said irregular repeat-zigzag Hadamard (IRZH) code using equations.