Digital Signal Processing Reference
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of iterations (the current experience of iteration is 200 times). If the decoding values
meet the equation
Hx
T
D
z
, the decoding is successful; if it still cannot satisfy
the equation
Hx
T
D
z
when the number of iterations reaches to the limit, then the
decoding fails.
3.4.2
The Implementation of LDPC Slepian-Wolf Encoder
LDPC Slepian-Wolf encoder based on the syndrome encoding, the specific encod-
ing algorithm involves the following steps:
1. Let the input sequence
X
be multiplied by the parity matrix
H
, and the result is
the syndrome
S
,
S D X H
T
.
2. Send the syndrome
S
to the decoding end.
The syndrome
S
is received in the decoding end, and side information
Y
uses BP
algorithm of the modified version to find out
X
; the specific modification appears in
the following:
•
When the syndrome equals to zero, which indicates that the input codeword can
be directly decoded by the traditional method of BP.
•
If the associated type does not equal to zero (all nonzero syndromes are marked
on the corresponding parity nodes in the diagram), then we change the output
symbol of the parity node and then apply the BP algorithm. This is because the
inverse verification and inverse operation in log-domain mean sign change to the
parity nodes [
10
].
3.4.3
The Coding and Decoding Algorithms of LDPCA
Slepian-Wolf
Similar to turbo code, conducting puncturing and deleting for the syndrome after
LDPC Slepian-Wolf encoding in last section can also achieve adjustable bit rate
for Slepian-Wolf, but its performance is poor when the rate of compression is high
because the figure of LDPC structure includes noise node which is disconnected
or single connected [
10
]; these structures prevent the exchange of information in
BP iterative decoding algorithm. Therefore, Varodayan et al. [
10
] suggest that we
should use bit rate adaptive LDPCA to improve its performance; next, we will
introduce this method.
3.4.3.1
Encoding Algorithm
Figure
3.8
represents a coding structure of LDPCA; its encoding end consists of
an accumulator and an LDPC syndrome generator. First, according to the graph
