Reduced-complexity LDPC decoding
View Patent ↗Methods and systems for reduced-complexity decoding of low-density parity-check (LDPC) information. An encoded input stream is received. The received stream is decoded with one or more reduced-complexity min-sum or a posteriori probability LDPC decoders. A v-node update rule in the reduced complexity decoder is omitted.
1. A method for decoding low-density parity-check (LDPC) information, comprising:
receiving an encoded input stream; and
decoding the encoded input stream with one or more reduced-complexity min-sum LDPC decoders comprising:
initializing variable-nodes based on channel reliabilities;
performing attenuated check-node updates for one or more check nodes based on said variable-node reliabilities using a processor;
skipping variable-node updates to improve decoding performance; and
improving decoder performance based on additional attenuated check-node updates.
2. The method of claim 1 , wherein decoding the encoded input stream further comprises testing for convergence by checking whether
zH T =0,
where z is a vector of hard decisions and H is a LDPC parity check matrix.
3. The method of claim 1 , wherein decoding the encoded input stream further comprises computing messages L c→v to be sent from the check-nodes to the variable-nodes as
L
c
→
v
=
⊕
N
(
c
)
\
{
v
}
L
v
→
c
,
where
L
1
⊕
L
2
=
α
∏
k
=
1
2
sign
(
L
k
)
min
(
L
1
,
L
2
)
,
α is an attenuation factor, N(c)\{v} is the neighborhood of check-node c excluding variable-node v, and L v→c are the messages to be sent from variable-node v to check-node c.
4. A method for decoding low-density parity-check information, comprising:
receiving an encoded input stream; and
decoding the encoded input stream with one or more reduced-complexity a posteriori probability low-density parity-check (LDPC) decoders comprising:
initializing hard decisions and variable-node magnitudes based on channel reliabilities;
performing attenuated check-node updates for one or more check nodes based on said hard decisions and magnitudes;
skipping variable-node updates to improve decoding performance; and
improving decoder performance based on additional attenuated check-node updates.
5. The receiver of claim 4 , wherein decoding the encoded input stream further comprises testing for convergence by checking whether
zH T =0,
where z is a vector of hard decisions and H is a LDPC parity check matrix.
6. The method of claim 4 , wherein performing check-node updates comprises computing magnitudes to be sent from check-node c to variable-node v as:
m
c
->
v
=
α
(
min
N
(
c
)
\
{
v
}
m
v
)
,
where α is an attenuation factor, N(c)\{v} is the neighborhood of c excluding v, and m v is the magnitude of v.
7. The method of claim 4 , wherein performing check-node updates comprises computing hard decisions from check-node c to variable-node v as:
z
c
->
v
=
(
∑
N
(
c
)
\
{
v
}
z
v
)
mod
2
,
where α is an attenuation factor, N(c)\{v} is the neighborhood of c excluding v, and z v is the hard decision of v.
8. The method of claim 4 , wherein performing check-node updates comprises updating variable-node magnitudes as
m
v
=
L
ch
(
v
)
+
∑
N
(
c
)
(
1
-
2
z
c
->
v
)
m
c
->
v
,
where L ch (v) is the channel log-likelihood ratio for variable node v, N(c) is the neighborhood of check-node c, z c→v is the hard decision from c to v, and m c→v is the magnitude from c to v.
9. A receiver, comprising:
a detector configured to receive an input stream and produce a stream of samples corresponding to encoded bits; and
one or more reduced-complexity min-sum low-density parity-check (LDPC) decoders configured to initialize variable-nodes based on channel reliabilities, to perform attenuated check-node updates for one or more check nodes based on said variable-node reliabilities to decode the encoded bits, to skip variable-node updates to improve decoding performance, and to perform additional attenuated check-node updates to improve decoder performance.
10. The receiver of claim 9 , wherein the one or more decoders are further configured to test for convergence by checking whether
zH T =0,
where z is a vector of hard decisions and H is a LDPC parity-check matrix.
11. The receiver of claim 9 , wherein the one or more decoders are further configured to compute messages L c→v to be sent from the check-nodes to the variable-nodes as
L
c
->
v
=
⊕
N
(
c
)
\
{
v
}
L
v
->
c
,
where
L
1
⊕
L
2
=
α
∏
k
=
1
2
sign
(
L
k
)
min
(
L
1
,
L
2
)
,
α is an attenuation factor, N(c)\{v} is the neighborhood of check-node c excluding variable-node v, and L v→c are the messages to be sent from variable-node v to check-node c.
12. A receiver, comprising:
a detector configured to receive an input stream and produce the samples that correspond to encoded bits;
one or more reduced-complexity a posteriori probability (APP) low-density parity-check (LDPC) decoders configured to initialize hard decisions and variable-node magnitudes based on channel reliabilities, to perform attenuated check-node updates for one or more check nodes based on said hard decisions and variable-node magnitudes to decode the encoded bits, to skip variable-node updates to improve decoding performance, and to perform additional attenuated check-node updates to improve decoder performance.
13. The receiver of claim 12 , wherein the one or more decoders are further configured to test for convergence by checking whether
zH T =0,
where z is a vector of hard decisions and H is a LDPC parity check matrix.
14. The receiver of claim 12 , wherein the one or more decoders are further configured to compute magnitudes to be sent from check-node c to variable-node v as:
m
c
->
v
=
α
(
min
N
(
c
)
\
{
v
}
m
v
)
,
where α is an attenuation factor, N(c)\{v} is the neighborhood of check-node c excluding variable-node v, and m v is the magnitude of variable-node v.
15. The receiver of claim 12 , wherein the one or more decoders are further configured to compute hard decisions from check-node c to variable-node v as:
z
c
->
v
=
(
∑
N
(
c
)
\
{
v
}
z
v
)
mod
2
,
where α is an attenuation factor, N(c)\{v} is the neighborhood of c excluding variable-node v, and z v is the hard decision of v.
16. The receiver of claim 12 , wherein the one or more decoders are further configured to update variable-node magnitudes as
m
v
=
L
ch
(
v
)
+
∑
N
(
c
)
(
1
-
2
z
c
->
v
)
m
c
->
v
,
where L ch (v) is the channel log-likelihood ratio for variable node v, N(c) is the neighborhood of check-node c, z c→v is the hard decision from c to v, and m c→v is the magnitude from c to v.