Cryptography Reference
In-Depth Information
i 2
000
001
010
011
100
101
110
111
j 0
000
j 1
001
j 2
010
011
j 3
i 1
j 4
100
101
j 5
j 6
110
j 7
111
(a)
i 2
000
001
010
011
100
101
110
111
j 0
j 1
000
j 2
j 3
j 4
001
j 5
j 6
j 7
010
011
j 8
j 9
j 10
i 1
j 11
j 12
j 13
100
101
j 14
j 15
j 16
j 17
j 18
j 19
110
j 20
j 21
111
(b)
Fig. 12.3. The illustrations of the nested index assignment in MDSQ for two chan-
nels with the codebook size L = 8. (a) With spread k = 0. (b) With spread k =1.
Because the conditional probability for transmitting j 3 is 1 given the received
conditions, we determine that the transmitted index is j 3 . If one of the chan-
nels breaks down, say, Channel 1, only i 2 = 011 is received. Using Fig. 12.3(a)
and calculating the conditional probability at the decoder as indicated in
Eq. (12.2), we visualize the column containing 011. We can then determine
that the transmitted scalar is j 3 with probability 1. This is the same as when
both descriptions are received. In this circumstance, the central distortion is
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