Page 71 - Introduction to Information Optics

56 1. Entropy Information and Optics

which corresponds to physical entropy of

AS = /(y4; B)kln2. (1.191)

This result can be interpreted as follows: the microstate of the channel acts as
the transmission of information through the channel. It is noted that I(A; B) is
derived under a strictly stationary ergodic assumption. In practice, however,
the output signal should be time limited, and the channel should have some
memory. In view of the second law of thermodynamics, the physical entropy
of the channel should be higher than that of the actual information transfer:

AS > I(A; B)kln2. (1.1.92)

1.8.1. CAPACITY OF A PHOTON CHANNEL

Let us denote the mean quantum number of the photon signal by m(v), and
the mean quantum number of a noise by n(v). We have assumed an additive
channel; thus, the signal plus noise is

Since the phonton density (i.e., the mean number of photons per unit time
per frequency) is the mean quantum number, the signal energy density per unit
time can be written as

E s(v) — m(v)/n>,

where h is Planck's constant. Similarly, the noise energy density per unit time is

E N(v) = h(v)hv.

Due to the fact that the mean quantum noise (blackbody radiation at
temperature T) follows Planck's distribution (also known as the Bose-Einstein
distribution),

TT
exp(/iv//cT) —