Question on calculating throughput - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-19T05:16:24Z http://mathoverflow.net/feeds/question/77660 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77660/question-on-calculating-throughput Question on calculating throughput Jeff Sanders 2011-10-10T05:11:38Z 2011-10-10T09:17:40Z <p>Here is the necessary information:</p> <p>A file contains:</p> <ul> <li>A header of size of <strong>h</strong> bits</li> <li>Data component of size <strong>d</strong> bits</li> <li>There is a probability <strong>b</strong> that a bit will be dropped (ruining the file) </li> <li>The connection can support a maximum of <strong>c</strong> bits/second</li> </ul> <p>I need to:</p> <ul> <li>Calculate the probability a file will be ruined. Already did this: <strong>b(h+d)</strong></li> <li>Compute the throughput over the link. (<strong>h</strong> remains the same size, so what is the optimal value for <strong>d</strong>?)</li> </ul> <p>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.</p> <p>Any help is appreciated.</p> http://mathoverflow.net/questions/77660/question-on-calculating-throughput/77664#77664 Answer by psd for Question on calculating throughput psd 2011-10-10T05:38:03Z 2011-10-10T05:38:03Z <p>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.</p> http://mathoverflow.net/questions/77660/question-on-calculating-throughput/77667#77667 Answer by Ashok for Question on calculating throughput Ashok 2011-10-10T06:42:13Z 2011-10-10T09:17:40Z <p>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.</p> <p>What you have here is a <a href="http://en.wikipedia.org/wiki/Binary_erasure_channel" rel="nofollow">binary erasure channel</a>. Its capacity is $1-b$. By Shannon's channel coding theorem, so long as $(h+d)&lt; c(1-b)$, we can send the file with error as small as we wish. That is, $d&lt; c(1-b)-h$.</p> <p>For the first part, it should be $1-(1-b)^{h+d}$.</p>