Planting around Cedars

I'm in Zone 4. My yard is lined with Eastern Red Cedar trees. They are great because they provide wonderful privacy, but I have a lot of trouble growing grass in even the sunny spots in the middle of the yard, and growing anything at all in the shade of the cedars. Does anyone know if there is anything specific to cedar trees that causes this, and what I might plant near the trees that would survive?
Also, I've never done anything in terms of feeding or mulching them - again are there any suggestions?
Thanks much.
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