![](https://csdnimg.cn/release/download_crawler_static/10931614/bg13.jpg)
Information 3
characters, with each character being one of 45 or so different characters (26 letters,
10 digits, and punctuation marks), then there is a very large but finite number of
possible messages. Moreover, only a very small fraction of these messages are intel-
ligible English, so the size of the set of possible messages – defined as intelligible
English messages of 1,000 characters or less – is further reduced. It is less clear
that the sound waves generated by an orchestra playing Beethoven’s Fifth can be
conceived of as coming from a finite set of messages. That is why Shannon chose
this as his second example. It serves to illustrate the generality of his theory.
In the telegraphy example, the telegraph system is the transmitter of the mes-
sages. The signals are the short current pulses in the telegraph wire, which travel
from the sending key to the sounder at the receiving end. The encoder is the tele-
graph operator. The code generally used is the Morse code. This code uses pulses
of two different durations to encode the characters – a short mark (dot), and a
long mark (dash). It also uses four different inter-pulse intervals for separations
– an intra-character gap (between the dots and dashes within characters), a short
gap (between the letters), a medium gap (between words), and a long gap (between
sentences).
In the orchestral example, the broadcast system transmitting radio signals from
the microphone to your radio is the transmitter. The encoder is the electronic device
that converts the sound waves into electromagnetic signals. The type of code is likely
to be one of three different codes that have been used in the history of radio (see
Figure 1.2), all of which are in current use. All of them vary a parameter of a high-
frequency sinusoidal carrier signal. The earliest code was the AM (amplitude
modulated) code. In this code, the encoder modulates the amplitude of the carrier
signal so that this amplitude of the sinusoidal carrier signal varies in time in a way
that closely follows the variation in time of the sound pressure at the microphone’s
membrane.
When the FM (frequency modulated) code is used, the encoder modulates the
frequency of the carrier signal within a limited range. When the digital code is used,
as it is in satellite radio, parameters of the carrier frequency are modulated so as
to implement a binary code, a code in which there are only two characters, cus-
tomarily called the ‘0’ and the ‘1’ character. In this system, time is divided into
extremely short intervals. During any one interval, the carrier signal is either low
(‘0’) or high (‘1’). The relation between the sound wave arriving at the microphone
with its associated encoding electronics and the transmitted binary signal is not
easily described, because the encoding system is a sophisticated one that makes use
of what we have learned about the statistics of broadcast messages to create efficient
codes. The development of these codes rests on the foundations laid by Shannon.
In the history of radio broadcasting, we see an interesting evolution (Figure 1.2):
We see first (historically) in Figure 1.2a a code in which there is a transparent (eas-
ily comprehended) relation between the message and the signal that transmits it
(AM). The code is transparent because variation in the amplitude of the message
is converted into variation in the amplitude of the carrier signal that transmits
the message. This code is, however, inefficient and highly vulnerable to noise. It
is low tech. In Figure 1.2b, we see a code in which the relation is somewhat less
transparent, because variation in the amplitude of the message is converted into
9781405122870_4_001.qxd 23/1/09 11:18 AM Page 3