Generation of soft bit metrics for differentially encoded quadrature phase shift keying (QPSK)
View Patent ↗A computer implemented method for generating soft bit metric information of telecommunications systems employing differential encoding of data.
1. A computer implemented method for generating soft bit metrics in a telecommunications system employing modulation with differential encoding comprising the steps of:
a) identifying, from the signs of received coordinates, a subset of coordinates that significantly contribute to a logarithmic likelihood ratio (LLR) of each bit;
b) determining dominant terms of the LLR; and
c) outputting an indicia of the soft bit metrics;
wherein the subsets so identified are represented by (x1, x2), (y1, y2), (x1,y2), and (x2, Y1), with the coordinates x1, x2, y1 and y2 corresponding to in-phase and quadrature components of two successively received symbols produced by a modulator performing the differential encoding;
wherein the identification step includes comparing coordinate magnitudes within a subset to generate a magnitude of the LLR.
2. The computer implemented method of claim 1 wherein the LLR for a bit includes a correction factor that depends on a coordinate that was determined to contribute significantly to the LLR of another bit.
3. The computer implemented method of claim 2 wherein the LLR for a bit exhibits a sign that is different from that obtained by a hard decision decoding.
4. The computer implemented method of claim 3 wherein the hard decision decoding output is used to change the sign of the LLR.
5. The computer implemented method of claim 4 wherein said soft bit metrics pertain to differentially encoded optical signals.
6. The computer implemented method of claim 5 wherein said soft bit metrics pertain to turbo codes, turbo product codes and convolutional codes.
7. The computer implemented method of claim 1 wherein said differentially encoding is one selected from the group consisting of QPSK, 16 QAM, and 64 QAM.
8. The computer implemented method of claim 1 wherein the dominant terms of the LLR are determined according to the following relationships:
llr
(
b
1
)
=
log
(
P
(
α
,
β
❘
C
1
,
C
2
)
+
P
(
α
,
γ
❘
C
1
,
C
2
)
+
P
(
β
,
γ
❘
C
1
,
C
2
)
+
P
(
β
,
δ
❘
C
1
,
C
2
)
P
(
α
,
δ
❘
C
1
,
C
2
)
+
P
(
α
,
α
❘
C
1
,
C
2
)
+
P
(
β
,
α
❘
C
1
,
C
2
)
+
P
(
β
,
β
❘
C
1
,
C
2
)
…
P
(
γ
,
δ
❘
C
1
,
C
2
)
+
P
(
γ
,
α
❘
C
1
,
C
2
)
+
P
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δ
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❘
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1
,
C
2
)
+
P
(
δ
,
β
❘
C
1
,
C
2
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P
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γ
,
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❘
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1
,
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2
)
+
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1
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C
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+
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+
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;
wherein LLR is of bit b i , and P(μ,ν|C 1 C 2 ) represents the a posteriori probability of transitioning from transmitted symbol in setμ to a transmitted symbol in set ν given channel outputs C 1 and C 2 ; and
| p ˜k 1 |+| p ˜k 2 |<min(| p k 1 |, |p k 2 |)
wherein C 1 and C 2 and p k 1 , p k 2 are defined in the following table:
Conditions
p 1 1 and p 1 2 ,
p 2 1 and p 2 2 ,
C 1 and C 2 are
C 1 is in the 1st
x 1 , x 2
y 1 , y 2
in adjacent
or 3rd quadrant
quadrants
C 1 is in the 2nd
y 1 , y 2
x 1 , x 2
or 4th quadrant
C 1 and C 2 are
C 1 is in the
y 1 , x 2
x 1 , y 2
not in adjacent
1st or 3rd
quadrants
quadrant
C 1 is in the 2nd
x 1 , y 2
y 1 , x 2 .
or 4th quadrant