Is a person's freedom of choice compromised by the illegalization of euthanasia?
Clearly, a person's freedom of choice is reduced by laws that make euthanasia illegal. Killing yourself is clearly a choice that only you can make and a law that says you cannot do that compromises your freedom of choice.
The more important question is probably something like "does making euthanasia illegal excessively compromise a person's freedom of choice?" All laws reduce our freedom of choice, but in some cases it is important to do so. My own feeling is that euthanasia should not be banned, but that it needs to be strictly regulated to ensure that it is being done by choice and not on a whim or due to coercion.
I would argue that choice of living or dying is a very personal choice and that the government should not be involved in deciding whether a person may make that choice.