Similar to realization 5, this decoder has four redundant parity checks. However, as starting point the realization 2 with the hidden states has been taken. The parity check matrix is the same as for realization 5:
| | 1 1 1 0 1 0 0 0 | |
| | 1 1 0 1 0 1 0 0 | |
| | 1 0 1 1 0 0 1 0 | |
| | 0 1 1 1 0 0 0 1 | |
| H' |
| | 0 0 1 1 1 1 0 0 | |
| | 0 1 1 0 0 1 1 0 | |
| | 1 1 0 0 0 0 1 1 | |
| | 1 0 0 1 1 0 0 1 | |
Thus, the added parity checks are
u2 + u3 + x4 + x5 = 0
u1 + u2 + x5 + x6 = 0
u0 + u1 + x6 + x7 = 0
u3 + u0 + x7 + x4 = 0.
The hidden states are the same as in realization 2:
s2 = u0 + u1
s3 = u1 + u2
s0 = u2 + u3
s1 = u3 + u0,
and when combining those with the redundant parity checks, we get
s0 + x4 + x5 = 0
s3 + x5 + x6 = 0
s2 + x6 + x7 = 0
s1 + x7 + x4 = 0.
This yields the following realization: