Page 24 - Introduction to Information Optics

1.3. Communication Channel 9

1.3. COMMUNICATION CHANNEL

An optical communication channel can be represented by an input-output
block diagram, for which an input event a can be transferred into an output
event fr, as described by a transitional probability p(b/a}. Thus, the input-
output transitional probability P(B/A) describes the random noise disturban-
ces in the channel.
Information channels are usually described according to the type of input-
output ensemble and are considered discrete or continuous. If both the input
and output of the channel are discrete events (discrete spaces), then the channel
is called a discrete channel. But if both the input and output of the channel are
represented by continuous events, the channel is called a continuous channel.
However, a channel can have a discrete input and a continuous output, or vice
versa. Accordingly, the channel is then called a discrete-continuous or continu-
ous-discrete channel.
We note again that the terminology of discrete and continuous com-
munication channels can also be extended to spatial and temporal domains.
This concept is of particular importance for optical communication
channels.
A communication channel can, in fact, have multiple inputs and multiple
outputs. If the channel possesses only a single input terminal and a single
output terminal, it is a one-way channel. However, if the channel possesses two
input terminals and two output terminals, it is a two-way channel. It is trivial.
One can have a channel with n input and m output terminals.
Since a communication channel is characterized by the input-output
transitional probability distribution P(B/A), if the transitional probability
distribution remains the same for all successive input and output events, then
the channel is a memoryless channel. However, if the transitional probability
distribution changes with the preceding events, whether at the input or the
output, then the channel is a memory channel. Thus, if the memory is finite; that
is, if the transitional probability depends on a finite number of preceding
events, the channel is a finite-memory channel. Furthermore, if the transitional
probability distribution depends on stochastic processes and the stochastic
processes are assumed to be nonstationary, then the channel is a nonstationary
channel. Similarly, if the stochastic processes the transitional probability
depends on are stationary, then the channel is a stationary channel. In short, a
communication channel can be fully described by the characteristics of its
transitional probability distribution; for example, a discrete nonstationary
memory channel.
Since a detailed discussion of various communication channels is beyond the
scope of this chapter, we will evaluate two of the simplest, yet important,
channels in the following subsection.