  In this note, we show that the operator theoretic concept of Kolmogorov
numbers and the number of degrees of freedom at level $\epsilon$ of a
communication channel are closely related. Linear communication channels may be
modeled using linear compact operators on Banach or Hilbert spaces and the
number of degrees of freedom of such channels is defined to be the number of
linearly independent signals that may be communicated over this channel, where
the channel is restricted by a threshold noise level. Kolmogorov numbers are a
particular example of $s$-numbers, which are defined over the class of bounded
operators between Banach spaces. We demonstrate that these two concepts are
closely related, namely that the Kolmogorov numbers correspond to the "jump
points" in the function relating numbers of degrees of freedom with the noise
level $\epsilon$. We also establish a useful numerical computation result for
evaluating Kolmogorov numbers of compact operators.
