I'd like to use my living space as a deduction, I don't pay rent.
In general, tax deductions can only be used to offset specific expenses or income. If there is no expense, then you can't deduct it. Similarly, if you paid only $1 in rent, then you could deduct at most $1 for a room deduction. Note this also explains why if you donate your time to a charity, you cannot deduct that either (because there is no income to offset).
Note that tax credits work differently, as they reduce your tax bill, and can sometimes cause you to receive a tax refund even if you have no income. Credits are typically a special case and do not apply here.
In addition to TTT's excellent and accurate answer, you also can't deduct rent for your living space - even if you paid any - because living space isn't a business expense. You need your living space even if you weren't running a business, so it isn't a business cost.
There are some ways to make it work, primarily involving having part of your 'home' solely dedicated to work, but the tax office investigates them very thoroughly and they are very strict, because it's such an easy thing to fiddle.