IEEE Solid-State Circuits Magazine - Fall 2016 - 60
messages it is going to send to the connected check nodes. As an example, to
compute the message for m = 0, the
(0)
variable node only processes R 1 " 3 and
(1)
(0)
R 2 " 3 to calculate Q 3 " 0 [Figure 3(d)]. To
(1)
compute the message for m = 1, Q 3 " 1,
(0)
the variable node only processes R 0 " 3
(0)
and R 2 " 3 [Figure 3(e)]; to calculate the
(1)
message for m = 2, Q 3 " 2, the variable
(0)
(0)
node only processes R 0 " 3 and R 1 " 3
[Figure 3(f)].
In updating the information of one
check node, using its own messages
from iterations is avoided to eliminate
the possibility of feeding back any
error introduced by this node. For this
reason, one check node only "trusts"
the information updated in the variable node that processed the messages coming from its neighbors-in
other words, the extrinsic information.
Significant work has been done in constructing
practical LDPC codes to reduce the complexity
of the decoding algorithm and the
decoder hardware.
based on the channel information from
the initialization and the extrinsic
information from all the neighboring
check nodes. The process is repeated
until it converges to a valid code word
or until a time limit is reached (a maximum number of iterations).
Figure 3 shows, the process for
one code with three check nodes and
seven variable nodes. This example
is focused on the fourth bit (n = 3)
and the second check node (m = 1) .
First [Figure 3(a)], the variable node is
initialized with the LLR for the variable
m=0
node n = 3, i.e., L 3 . This variable
node sends the information to the
connected check nodes. The message
(0)
sent to the check node m = 0 is Q 3 " 0 .
For check node m = 1, the message
(0)
is Q 3 " 1; for check node m = 2, the
(0)
message is Q 3 " 2 [Figure 3(b)]. Each
check node updates its messages
and sends them back to the variable
(0)
(0)
nodes. The messages are R 0 " 3, R 1 " 3,
(0)
and R 2 " 3 [Figure 3(c)].
In the second iteration, the
variable node n = 3 only uses the
extrinsic information to update the
m=2
m=1
m=0
m=1
Q (0)
Q (0)
3->1
3->0
3->2
n=1
n=2
n=3
L3
n=4
n=5
n=6
n=0
n=1
n=2
Channel Detector
(a)
(b)
m=1
m=0
m=2
R (0)
R (0)
0->3
m=1
2->3
n=2
n=3
n=4
n=5
n=6
n=0
n=1
n=2
n=1
fa l l 2 0 16
n=4
(d)
m=1
m=0
m=2
(0)
R 2->3
m=1
n=2
n=3
n=5
n=6
m=2
Q (1)
R (0)
0->3
3->2
R (0)
1->3
n=4
n=5
n=6
n=0
n=1
n=2
n=3
n=4
Channel Detector
Channel Detector
(e)
(f)
Figure 3: (a)-(f) The six steps of a message-passing algorithm, as described in the text.
60
n=3
Channel Detector
Q (0)
3->1
n=0
2->3
(c)
R (0)
0->3
n=6
m=2
Channel Detector
m=0
n=5
R (0)
Q (1)
3->0
(0)
R 1->3
n=1
n=4
Channel Detector
m=0
n=0
n=3
(0)
R 1->3
n=0
m=2
Q (0)
3->2
IEEE SOLID-STATE CIRCUITS MAGAZINE
n=5
n=6
Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Fall 2016
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