Signal Space Coding over Rings

Chapter 2: Combined coding and modulation techniques 12
r / 2 Hertz. Usually in practice transmission is done at a rate r symbols per second
over a channel of bandwidth r .
2.2.3 Shannon limit
The bandpass noise power at the output of a bandlimited channel of bandwidth B is
N B 0
= N B , where N 0 is the noise power spectral density. Then the channel capacity
relationship can be written as:
Cch B
P
log 2 1 bits / s
N 0B
⎟ ⎛ ⎞
=
⎜ +
(2.3)
⎝ ⎠
An equivalent expression for the above equation is:
B
Eb
C
log 2 1
bits / s
N 0 B ⎟ ⎛ ⎞
=
⎜ +
(2.4)
⎝ ⎠
Cch ch
and finally:
E
N
0
B
=
C
b ch
8
7
6
5
4
3
2
1
ch
C / B ( 2 −1)
B/Cch,
Hz/bits/s
Practical
systems
Eb/N0, dB
0
-5
-1.59 dB
0 5 10 15 20
Figure 2.1 B / Cch
ratio as a function of Eb / N 0
(2.5)