Can. 916 Anyone who is conscious of grave sin may not celebrate Mass or receive the Body of the Lord without previously having been to sacramental confession, unless there is a grave reason and there is no opportunity to confess; in this case the person is to remember the obligation to make an act of perfect contrition, which includes the resolve to go to confession as soon as possible.
This appears in the front cover of the OCP hymnal "Breaking Bread" (which I had my first introduction to last week on vacation). It is a Canon I am familiar with, and one that I have seen people misinterpret to mean they can receive Communion in a state of (grave/mortal) sin as long as they go to confession right after Mass. I know people in my own church who follow this practice of receiving Communion and going to confession right after Mass, using this Canon as their rationale for doing so.
An act of perfect contrition (which is required in this case) is being sorry for offending God with your sins because you love Him above all things, and an act of imperfect contrition (which isn't enough in this case) is being sorry for your sins because you dread the pains of hell.
Canon 916 requires a grave reason to exist for the application of receiving Communion without confession. What I see people using as grave reason are 1) not having confession scheduled prior to Mass, and 2) arriving at Mass too late to ask the priest hear your confession. My gut feeling on this is that neither of these qualify as grave reasons to receive Holy Communion as outlined by Canon 916 if you are conscious of mortal sin.
It takes a certain degree of humility to stay in your seat and abstain from Communion when everyone else is receiving Communion. Maybe I'm being scrupulous here, but neither of the two situations I outlined above seem to be qualify as grave matter. What would you do?