Generating soft q-ary channel information
A probability is determined, including by obtaining a set of probability ratios, wherein each probability ratio in the set is a ratio of a first probability to a second probability. A probability P(E m =z) that an m th error symbol E m has a level of z is determining based at least in part on one or more dominant error patterns.
1. A method for determining a probability, comprising:
obtaining a set of probability ratios, wherein each probability ratio in the set is a ratio of a first probability to a second probability; and
determining, using a processor, a probability P(E m =z) that an m th error symbol E m has a level of z based at least in part on one or more dominant error patterns.
2. The method of claim 1 , wherein the second probability is a probability that the m th error symbol E m has a level of z that corresponds to an error-free level.
3. The method of claim 2 , wherein the error-free level includes all 0's when expressed in bits.
4. The method of claim 1 , wherein the one or more dominant error patterns include(s) a pattern that includes all 1's when expressed in bits.
5. The method of claim 1 , wherein obtaining includes obtaining from a bank of error event correlators.
6. The method of claim 1 further comprising passing the determined probability to an error correction decoder configured to input q-ary symbol level soft information.
7. The method of claim 6 , wherein the error correction decoder includes at least one of the following: a q-ary low density parity check (LDPC) decoder or a soft-input Reed-Solomon decoder.
8. The method of claim 1 , wherein determining includes using
P
(
E
m
=
0
)
∑
[
e
j
(
i
)
]
mp
(
m
+
1
)
p
-
1
=
z
R
(
e
j
(
i
)
)
and/or
P
(
E
m
=
0
)
∑
(
i
,
j
)
∈
A
(
m
,
z
)
R
i
,
j
to determine P(E m =z).
9. The method of claim 1 , wherein determining includes using
∏
i
P
(
E
m
=
z
i
)
to determine P(E m =z).
10. The method of claim 1 , wherein determining includes using
1
/
(
1
+
∑
(
i
,
j
)
∈
A
(
m
,
z
)
R
i
,
j
)
to determine P(E m =0).
11. The method of claim 1 , wherein determining includes decomposing a composite error event into two or more dominant single error events.
12. The method of claim 11 , wherein decomposing includes using one or more independent error events separated by i zeros when E m includes i consecutive 0's.
13. The method of claim 1 , wherein determining includes operating, at least partially, on log-domain information.
14. The method of claim 1 , wherein the probability P(E m =z) is part of a probability mass function (PMF) and the method further includes performing PMF truncation that includes evenly distributing a residual probability amongst q−q′ levels.
15. A system for determining a probability, comprising:
an interface configured to obtain a set of probability ratios, wherein each probability ratio in the set is a ratio of a first probability to a second probability; and
a hardware processor configured to determine a probability P(E m =z) that an m th error symbol E m has a level of z based at least in part on one or more dominant error patterns.
16. The system of claim 15 , wherein the processor is configured to determine by using
P
(
E
m
=
0
)
∑
[
e
j
(
i
)
]
mp
(
m
+
1
)
p
-
1
=
z
R
(
e
j
(
i
)
)
and/or
P
(
E
m
=
0
)
∑
(
i
,
j
)
∈
A
(
m
,
z
)
R
i
,
j
to determine P(E m =z).
17. The system of claim 15 , wherein the processor is configured to determine by using
∏
i
P
(
E
m
=
z
i
)
to determine P(E m =z).
18. The system of claim 15 , wherein the processor is configured to determine by using
1
/
(
1
+
∑
(
i
,
j
)
∈
A
(
m
,
z
)
R
i
,
j
)
to determine P(E m =0).
19. The system of claim 15 , wherein the processor is configured to determine by decomposing a composite error event into two or more dominant single error events.
20. The system of claim 15 , wherein the probability P(E m =z) is part of a probability mass function (PMF) and the processor is further configured to perform PMF truncation that includes evenly distributing a residual probability amongst q−q′ levels.