B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

13.6 Practical Communication Systems in Light of Shannon's Equation 773
the introduction of turbo codes and the rediscovery of the low-density parity check (LDPC)
codes would completely alter the landscape. We shall introduce these codes in Chapter 14.
13.6 PRACTICAL COMMUNICATION SYSTEMS IN
LIGHT OF SHANNON'S EQUATION
It would be instructive to determine the ideal law for the exchange between the SNR and
the transmission bandwidth by using the channel capacity equation. Consider a message of
bandwidth B that is used for modulation (or coding), with the resulting modulated signal of
bandwidth By. This signal is received at the input of an ideal demodulator with signal and noise
powers of Si and Ni, respectively* (Fig. 13.9). The demodulator output bandwidth is B, and the
SNR is S 0 /N 0 • Because an SNR S/N and a bandwidth B can transmit ideally Blog ( l + S/N)
bits of information, the ideal information rates of the signals at the input and the output of the
demodulator are By log (1 + Si/Ni) bits and Blog (1 + S 0 /N 0 ) bits, respectively. Because the
demodulator neither creates nor destroys information, the two rates should be equal, that is,
and
( Si ) ( So )
By log 1 + N i
= B log 1 + N o
In practice, for the majority of systems, S 0 /N0 as well as Si/Ni » I, and
( 13.70a)
(13.70b)
Also,
Hence, Eqs. ( 13.70) become
S
No
Br/B
( )
By/B
Br/B
)
By/B
___!!__ = 1 + -y- - 1
:::: (-y
(13.71a)
(13.7 1b)
figure 13.9
Ideal exchange
between SNR
and bandwidth.
Bandwidth Br
Ideal
demodulator
Bandwidth B
* An additive white Gaussian channel noise is assumed.