Display posts from category in monthly archives

Hi,

I can’t really figure this out myself.
I would like to display posts grouped by categories on my monthly archive like this:

Category name link
Category description
-post title link1
-post title link2
-post title link3

Category name link 2
Category description
-post title link1
-post title link2
-post title link3

The catch is that I want to exclude categories with posts not created in the month the archive is displaying.
Since WP doesn’t store the category publish/creation date the idea of using the oldest posts publish date would be the best starting point. I just don’t know how.

If you have any clue how to code it – please share!