It depends. First, cedar chips take a very long time to
decompose, and will affect the soil and water, but not
significantly differently than the decomposition of cedar in the
forests which occurs naturally. However, I suggest that you
avoid trying to decompose them with other materials such as
garden waste or household vegetable matter. I assume by
"Household Compost" you are talking about vegetable/fruit waste
from inside the home. In this case, the important thing is to
ensure that the composting is done in a container that is fully
protected from rats in particular. Some things, like red worms,
significantly improve the efficiency of composting these wastes.
It is best that you have good drainage to ensure the composted
material dries out fairly well. It is a good idea to turn it
once in a while, i.e. mix it up. There is a neat tool which
makes this quit easy. Done properly, this will not adversly
affect the water or soil. The one thing that I would NOT include
in my compost pile is evergreen clippings, n