Information Theory - Digital Communication: Principles and System Modelling - page 173

⎡
⎣

⎤
⎦

3
4

1

4 000
00 3

2

| =

[ P ( Y X ) ]

3 0
00001

(8.23)

y 1

Fig. 8.4 Lossless channel

3 4

1 4

x 1

y 2

1 3

x 2 y 3

2 3

x 3 y 4

1

y 5

8.6.2 Deterministic Channel

Deterministic channel matrix holds only one and unique non-zero element at each
row as shown in the Fig. 8.5 . The channel matrix is given by

⎡ ⎤

100
100
010
010
001

⎣ ⎦

[ P ( Y | X ) ] = (8.24)

Fig. 8.5 Deterministic
channel

x 1

1

1

x 2 y 1

1

x 3 y 2

1

x 4 y 3

1

x 5

Since, the Eq. ( 8.24 ) says, summation of elements of each row must be unity, and
in deterministic channel, each row holds only one element, therefore the element
itself must be unity. The physical interpretation of the matrix is, 'if a symbol is
transmitted it must be received'.