The purpose of this trial is to evaluate the long-term effects and cost-effectiveness of adaptive servo-ventilation (ASV) on the mortality and morbidity of patients with stable heart failure due to left ventricular systolic dysfunction, already receiving optimal medical therapy, who have sleep disordered breathing (SDB) that is predominantly central sleep apnea. Assumptions: the intervention reduces the hazard rate by 20%. The event rate in the control group is 35% in the first year. It is assumed that the hazard rate is constant over time.