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Introduction   ::   Codes   ::   Bounds

Achievability of the bound

It can also be shown (with a lot of work!) that for an $\cdot/M/1$ queue, the upper bound can be achieved when the input process is Poisson with rate λ.

Thus

 \begin{displaymath}
C = e^{-1} \mu \text{ nats/s}.
\end{displaymath}

 

Information-bearing channels

We now generalize to the case where each packet actually carries some kind of information (e.g., bits). I will mostly summarize the results. Let the channel have information-bearing capacity C 0 in nats/sec.


Observe that if C 0 is sufficiently large, then the λ that maximizes capacity is equal to μ, so no information is carried in the timing. Combining some theorem, we find:

\begin{theorem}
\begin{displaymath}
C_I \geq
\begin{cases}
\mu e^{-1} \e...
...\\
\mu C_0 & \text{otherwise}.
\end{cases}
\end{displaymath}
\end{theorem}  \begin{displaymath}
C_I = 2 \mu e^{-1} \text{ nats/sec } = 1.06 \mu \text{
bits/second}.
\end{displaymath}

 

Pretty cool!
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 17). Bits and Queues. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture12_4.htm. This work is licensed under a Creative Commons License Creative Commons License