Obstructive sleep apnea, a sleep-related breathing disorder in which breathing stops for short periods during sleep, is a common condition in patients with atrial fibrillation. Studies have shown that up to 75% of atrial fibrillation patients undergoing catheter ablation procedure have obstructive sleep apnea. Obstructive sleep apnea increases the risk of atrial fibrillation recurrence after successful catheter ablation by 40%. However, whether treatment of obstructive sleep apnea with positive airway pressure (PAP, the current most effective treatment for obstructive sleep apnea that uses a machine to help breathe more easily) reduces the risk of atrial fibrillation recurrence is not fully understood. The purpose of this study, therefore, is to examine whether positive airway pressure therapy reduces atrial fibrillation recurrence after catheter ablation in patients with obstructive sleep apnea and atrial fibrillation.