Page 18 - Introduction to Information Optics

1.1. Information Transmission 3

language should be properly (temporally) encoded; for instance, as transmitted
through an optical fiber, which represents a temporal communication channel.
Needless to say, at this receiving end a temporally decoding process is required
before the temporal coded language is sent to the user. Viewing a television
show, for example, represents a one-way spatial-temporal transmission. It is
interesting to note that temporal and spatial information can be traded for
information transmission. For instance, television signal transmission is a
typical example of exploiting the temporal information transmission for spatial
information transmission. On the other hand, a movie sound track is an
example of exploiting spatial information transmission for temporal informa-
tion transmission.
Information transmission has two basic disciplines: one developed by
Wiener [1.1, 1.2], and the other by Shannon [1.3, 1.4]. Although both Wiener
and Shannon share a common interest, there is a basic distinction between
their ideas. The significance of Wiener's work is that, if a signal (information)
is corrupted by some physical means (e.g., noise, nonlinear distortion), it may
be possible to recover the signal from the corrupted one. It is for this purpose
that Wiener advocates correlation detection, optimum prediction, and other
ideas. However, Shannon carries his work a step further. He shows that the
signal can be optimally transferred provided it is properly encoded; that is, the
signal to be transferred can be processed before and after transmission. In other
words, it is possible to combat the disturbances in a communication channel
by properly encoding the signal. This is precisely the reason that Shannon
advocates the information measure of the signal, communication channel
capacity, and signal coding processes. In fact, the main objective of Shannon's
theory is the efficient utilization of the information channel.
A fundamental theorem proposed by Shannon may be the most surprising
result of his work. The theorem can be stated approximately as follows: Given
a stationary finite-memory information channel having a channel capacity C,
if the binary information transmission rate R (which can be either spatial or
temporal) of the signal is smaller than C, there exists a channel encoding and
decoding process for which the probability of error per digit of information
transfer can be made arbitrarily small. Conversely, if the formation trans-
mission rate R is larger than C, there exists no encoding and decoding
processes with this property; that is, the probability of error in information
transfer cannot be made arbitrarily small. In other words, the presence of
random disturbances in an information channel does not, by itself, limit
transmission accuracy. Rather, it limits the transmission rate for which arbit-
rarily high transmission accuracy can be accomplished.
To conclude this section, we note that the distinction between the two
communication disciplines are that Wiener assumes, in effect, that the signal in
question can be processed after it has been corrupted by noise. Shannon
suggests that the signal can be processed both before and after its transmission