Cryptography Reference
In-Depth Information
The data paths of the VNPs and PNPs are both of the total sum type, with
a serial implementation. From time
T
1
,
d
c
=4
messages
L
j,p
enter serially into
the PNP. After a computation latency of
T
2
−
T
1
, the messages
Z
j,p
calculated
are sent back, again serially, to the VNPs which are controlled in distributed
mode. But in this case, the update of the information is immediate. This is
translated by using a single block of
Lacc
memory. Thus, the sum of the extrinsic
information of the
j
bits is updated as soon as a new input
Z
j,p
arrives.
Parameters
Values
Message propagation architecture
(
α
p
=
d
c
=4
,
α
v
=
d
v
=3
,
P
=3
)
Position of the interconnection network
4
Control
Compact
VNP
Data path
Totalsum,serial
Control
Distributed, immediate update
PNP
Data path
Totalsum,serial
Table 9.6 - Values of the parameters characterizing vertical interleaving architecture.
9.2.6 Sub-optimal decoding algorithm
In order to reduce the complexity of the LDPC decoder, many "sub-optimal" de-
coding algorithms have been proposed. These algorithms are based on the same
principle: reduction in complexity and in memory of the (parity or variable)
node processors, by replacing the individual computation of the
d
output mes-
sages (with
d
the degree of the node) by the computation of
Δ
(
Δ
<d
)distinct
values. Of course, using a sub-optimal algorithm generally degrades the perfor-
mance of the code. A compromise thus has to be found between performance
and complexity.
Single message decoding algorithm (
Δ=1
)
This is the simplest algorithm since all the outputs of the (variable or parity)
node processor are assigned a same single value at each step in the iterative
process.
VNP with
Δ=1
In this technique, the VNP simply returns
L
j
to the parity constraints to
which it is connected. Thus, it is no longer necessary to memorize the
Z
j,p
mes-
sages since the latter are no longer used by the VNP. There results a significant
economy in memory. This algorithm, APP algorithm, was first proposed by
Fossorier
et al.
in [9.20] , and taken up again by E. Yeo
et al.
in [9.66].
Note that the hypothesis of independence between the messages leaving
and entering a parity node is absolutely not verified. That is why the iterative
