In order to understand an optical communication channel I need to find the dominat term of this
$$ \frac{1}{n}\log\left(\sum_{q=0}^{\lceil\frac{n}{d+1}\rceil}\binom{n-(q-1)d}{q}\right), $$ where $d$ is a fixed positive integer.
using the Stirling formula $k!\sim \left(\frac{k}{e}\right)^k\sqrt{2\pi k}$ and this $\binom{n}{k}\sim\frac{n^k}{k!}$ I get this:
$$ \frac{1}{n}\log\left(\sum_{q=0}^{\lceil\frac{n}{d+1}\rceil}\frac{(e(n-(q-1)d))^q}{q^q\sqrt{2\pi q}}\right), $$
But I still have no idea of how to get the dominant terms.