Hybrid LDPC codes and iterative decoding methods - i3s

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Hybrid LDPC codes and iterative decoding methods - i3s

122Chapitre 4 : Two-Bit Message Passing Decoders for LDPC Codes Over the Binary Symmetric Channel

Table 4.3 : Update rule for the two-bit decoder defined by (C,S,W) = (2,2,1).

# −S # −W # W # S

mess. mess. mess. mess.

r v = 1 0 0 2 1

w j (v, c) = W 0 0 3 0

0 1 0 2

r v = 1 0 0 0 3

w j (v, c) = S 0 0 1 2

r v = 0 2 1 0 0

w j (v, c) = −S 3 0 0 0

0 3 0 0

r v = 0 1 2 0 0

w j (v, c) = −W 2 0 1 0

0 2 0 1

0 2 1 0

0 3 0 0

1 0 2 0

1 1 0 1

r v = 1 1 1 1 0

w j (v, c) = −S 1 2 0 0

2 0 0 1

2 0 1 0

2 1 0 0

3 0 0 0

0 1 1 1

r v = 1 0 1 2 0

w j (v, c) = −W 1 0 0 2

1 0 1 1

0 2 1 0

r v = 0 1 1 0 1

w j (v, c) = W 1 1 1 0

2 0 0 1

0 0 0 3

0 0 1 2

0 0 2 1

0 0 3 0

r v = 0 0 1 0 2

w j (v, c) = S 0 1 1 1

0 1 2 0

0 2 0 1

1 0 0 2

1 0 1 1

1 0 2 0

this configuration converges to the correct codeword at the end of the first iteration.

Case 2: Consider the error configuration shown in Figure 4.1(b) and Figure 4.2.

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