## Question on calculating throughput [closed]

Here is the necessary information:

A file contains:

• A header of size of h bits
• Data component of size d bits
• There is a probability b that a bit will be dropped (ruining the file)
• The connection can support a maximum of c bits/second

I need to:

• Calculate the probability a file will be ruined. Already did this: b(h+d)
• Compute the throughput over the link. (h remains the same size, so what is the optimal value for d?)

I'm having problems coming up with a function to model the number of files being sent through. If I could do that, I think it would be simple to maximize it.

Any help is appreciated.

-
 MO isn't a good fit for this question (mathoverflow.net/faq#whatquestions). Please try math.stackexchange.com, stats.stackexchange.com or other math sites listed in the FAQ. – David Roberts Oct 10 2011 at 6:23

## closed as too localized by Andres Caicedo, Will Jagy, David Roberts, Ryan Budney, Scott Morrison♦Oct 11 2011 at 0:24

Your answer to the first part is wrong. Let $h+d=2$ and $b=\frac{1}{2}$ then you give a 100% probability that the file will be ruined, but it should be more like 75% if bits are dropped independently. This question is going to be closed.

-

Though it could be elementary for people who know information theory, its worth nontrivial question for others. So I would like to provide an answer.

What you have here is a binary erasure channel. Its capacity is $1-b$. By Shannon's channel coding theorem, so long as $(h+d)< c(1-b)$, we can send the file with error as small as we wish. That is, $d< c(1-b)-h$.

For the first part, it should be $1-(1-b)^{h+d}$.

-