Evidently, there is a characteristic odor that comes when a woman in natural labor is close to giving birth -- and it's lovely. http://blogs.babble.com/being-pregnant/2011/10/03/what-does-birth-smell-like/
According to this article on Babble.com:
It’s a ‘deep’ scent… not musky, necessarily, but primal and vaguely familiar …” Maybe birth smells like the opposite of death? The opposite of decay.