Method and system for computing log-likelihood ratios for coded quadrature amplitude modulated signals
According to an embodiment of the invention, a method and system is disclosed for determining log-likelihood ratios for a coded set of individual bits ( 40 ) of a quadrature amplitude modulation (QAM) codeword. In the method at most two constant values ( 33,35 ) may be determined to perform a set of predetermined functions, the output of each of function is based on the constant values and at least one received component corresponding to the codeword, to determine log-likelihood ratios ( 37 ) for each individual bit of the set of individual bits of the codeword. The QAM codeword may correspond to at least a portion of a signal of a wireless device, such as a mobile third-generation device operating according to a Wideband Code-Division Multiple Access (WCDMA) standard.
1. A method for determining log-likelihood ratios for quadrature amplitude modulation (QAM) signals of a set of bits of a QAM codeword, the method comprising:
determining, by a computer system, an offset constant Δ given by
8
a
2
E
S
N
o
,
and a pre-scale constant k given by
4
a
E
S
N
0
,
where Es=coded symbol energy, N 0 =noise power spectral density, and a=a normalization constant; and
determining, by the computer system, a log-likelihood ratio for each bit of the set of the bits of the codeword using a set of functions based on said offset constant and said pre-scale constant.
2. A method according to claim 1 wherein the codeword is a turbo coded codeword.
3. A method according to claim 1 , wherein the codeword corresponds to at least a portion of a signal transmitted in a wireless system.
4. A method according to claim 3 , wherein the wireless system is a mobile third-generation cellular system.
5. A method according to claim 3 , wherein the wireless system operates according to a Code-Division Multiple Access (CDMA) standard.
6. A method according to claim 3 , wherein the wireless system operates according to a High-Speed Downlink Packet Access (HSDPA) portion of the Wireless Code-Division Multiple Access (WCDMA) standard.
7. A method according to claim 1 , wherein the codeword is a 16-QAM codeword.
8. A method according to claim 7 , wherein a set of individual bits of the codeword comprises four information bits mapped to the 16-QAM codeword.
9. A method according to claim 1 , further comprising determining a log-likelihood ratio Λ for an individual bit i I , given that the at least one received component is r I , and a scaled received component r′ I is defined as r I multiplied by the pre-scale constant k, and for the offset constant Δ, in accordance with the function:
Λ i 1 ( r′ I )= r′ I +max*( r′ I ,Δ)−max*(− r′ I ,Δ)
where the function max* is defined as max*(x, y)=max (x, y)+ln(1+exp[−|x−y|]).
10. A method according to claim 1 , further comprising determining a log-likelihood ratio (Λ) for an individual bit i 2 , given that the at least one received component is r I , and a scaled received component r′ I is defined as r I multiplied by the pre-scale constant k, and for the offset constant Δ, in accordance with the function:
Λ i 2 ( r′ I )=−max $ (− r′ I −Δ,r′ I −Δ)
where the function max is defined by:
max
$
(
x
,
y
)
=
max
(
x
,
y
)
+
ln
[
1
+
exp
[
-
x
-
y
]
-
exp
[
-
x
-
y
2
]
]
.
11. A method according to claim 1 , further comprising determining a log-likelihood ratio (Λ) for an individual bit q I , given that the at least one received component is r Q , and a scaled received component r′ Q is defined as r Q multiplied by the pre-scale constant k, and for the offset constant Δ, in accordance with the function:
Λ q 1 ( r′ Q )= r′ Q +max*( r′ Q ,Δ)−max*(− r′ Q ,Δ)
where the function max* is defined as max* (x, y)=max(x, y)+ln(1+exp[−|x−y|]).
12. A method according to claim 1 , further comprising determining a log-likelihood ratio (Λ) for an individual bit q 2 , given that the at least one received component is r Q , and a scaled received component r′ Q is defined as r Q multiplied by the pre-scale constant k, and for the offset constant Δ, in accordance with the function:
Λ q 2 ( r′ Q )=−max $ (− r Q −Δ,r′ Q −Δ)
where the function max $ is defined by:
max
$
(
x
,
y
)
=
max
(
x
,
y
)
+
ln
[
1
+
exp
[
-
x
-
y
]
-
exp
[
-
x
-
y
2
]
]
.
13. A method according to claim 1 , further comprising using a custom-coded instruction to configure a reconfigurable execution unit to perform at least a portion of a determination of a log-likelihood ratio for at least one of the individual bits, the determination comprising using at least one of the two constant values.
14. A method according to claim 13 , further comprising setting a value of an input of the reconfigurable execution unit based on the at least one constant value used in the log-likelihood ratio determination.
15. A method according to claim 13 , further comprising using the reconfigurable execution unit to complete a calculation of the log-likelihood ratio for the at least one individual bit in two cycles.
16. A method according to claim 13 , further comprising using the reconfigurable execution unit to complete a calculation of the log-likelihood ratio for the at least one individual bit in one cycle.
17. A method according to claim 13 , wherein the reconfigurable execution unit comprises a single instruction multiple data lane of a computer system.
18. A method according to claim 17 , wherein the computer system comprises a separate control execution path and a separate data execution path.
19. A method according to claim 18 , wherein the reconfigurable execution unit forms a portion of the separate data execution path.
20. A computer system, the system comprising:
a dedicated control execution path comprising a branch unit and a control execution unit; and
a dedicated data execution path comprising a reconfigurable execution unit, the control execution path being separate from the data execution path;
wherein the reconfigurable execution unit comprises a single instruction multiple data (SIMD) lane of the computer system, and wherein the reconfigurable execution unit is configured by a custom-coded instruction to perform at least a portion of a determination of a log-likelihood ratio for an individual bit of a quadrature amplitude modulation (QAM) codeword, wherein the log-likelihood ratio is determined based on determining an offset constant Δ given by
8
a
2
E
S
N
0
,
and a pre-scale constant k given by
4
a
E
S
N
0
,
where E S =coded symbol energy, N 0 =noise power spectral density, and a=a normalization constant.
21. A computer system according to claim 20 wherein the QAM codeword is a turbo coded codeword.
22. A computer system according to claim 20 , wherein the codeword corresponds to at least a portion of a signal transmitted in a wireless system.
23. A computer system according to claim 22 , wherein the wireless system is a mobile third-generation cellular system.
24. A computer system according to claim 22 , wherein the wireless system operates according to a Code-Division Multiple Access (CDMA) standard.
25. A computer system according to claim 22 , wherein the wireless device operates according to a High-Speed Downlink Packet Access Portion (HSDPA) of the Wireless Code-Division Multiple Access (WCDMA) standard.
26. A computer system according to claim 20 , wherein the codeword is a 16-QAM codeword.
27. A computer system according to claim 20 , wherein a set of individual bits of the codeword comprises four information bits mapped to the 16-QAM codeword.
28. A computer system according to claim 20 , wherein the determination of the determination of the log-likelihood ratio is made using a function, the output of the log-likelihood ratio is based on received signal characteristics corresponding to the codeword.
29. A computer system according to claim 28 wherein the received signal characteristics corresponding to the codeword comprise signal energy and noise power spectral density.
30. A computer system according to claim 28 , wherein an input value of the reconfigurable execution unit is determined based on at least one constant value used in the log-likelihood ratio determination.
31. A computer system according to claim 28 , wherein the reconfigurable execution unit is capable of calculating the log-likelihood ratio for the at least one individual bit in two cycles.
32. A computer system according to claim 28 , wherein the reconfigurable execution unit is capable of calculating the log-likelihood ratio for the at least one individual bit in one cycle.
33. A method according to claim 1 wherein the set of functions is stored in a look-up table.
34. A computer system according to claim 28 wherein the function is stored in a look-up table.