Sleep disordered breathing (SDB) is a frequent comorbidity for heart failure patients. Its prevalence varies according to the seriousness of the condition of the patients, but it is present in approximately 50% of patients. Screening patients for SDB and managing them by providing adapted ventilation therapy should improve their quality of life or even their prognosis. Moreover, SDB lowers nocturnal cardiovascular recovery abilities and leads to an increase in fatigability and, as a result, exercise intolerance in patients with heart failure. Physical training as part of a cardiac rehabilitation programme provides many benefits, including improving patients' exercise capacities. Our hypothesis is that adapted sleep disordered breathing therapy during rehabilitation will lead to an improvement in rehabilitation results.

Controlled, randomised, multicentre study. Patients will be assessed prior to starting the rehabilitation programme with regard to exercise tolerance parameters (cardiopulmonary exercise test, 6 minute walk test), ultrasound parameters and biological parameters (Na, Hb, BNP).

The cardiac rehabilitation programme will include education, secondary prevention and physical training components in each of the two groups. The physical training component will include a minimal "base" of activities that is identical for both groups. The nocturnal therapy device will be adapted to the type of SDB specific to each patient (central, mixed, obstructive). The randomisation will be stratified by centre according to predictive factors for performance improvement during rehabilitation.

The main objective is to evaluate the improvement in physical performance resulting from adapted ventilation on SDB compared to physical training alone in patients with heart failure.

Inclusion Criteria:

• Patients who have NYHA class II to IIIb heart failure, operated or not, ischemic or not, without significant valve pathology.
• Referred to cardiac rehabilitation
• With an EF < 40%
• And an apnea-hypopnea index > 15/h (determined by a nasal flow recording method)
• Have signed the consent document to participate in the study.

Exclusion Criteria:

• Patients who have been stabilised for less than 10 days (inotropic drugs or modification of the anticipated resynchronisation or PM parameters)
• Patients who already use sleep disordered breathing devices
• Resting SBP < 80 mmHg (averaged over 3 separate measurements)
• Recent angioplasty (within the last 10 days)
• Infarction within the last 10 days
• Heart surgery within the last 15 days
• Valve dysfunction requiring surgery
• Uncontrolled high blood pressure (BP > 180 and/or 110 mmHg)
• Anaemia (Hb < 9g/dl)
• Haemodialysis
• Patient receiving circulatory assistance
• Severe chronic respiratory failure (FEV1 < 1000) or hypercapnia greater than 46 mmHg
• Patient incapable of performing a 6 minute walk test and an exercise test
• Absolute contraindication for an exercise test and/or physical training according to the recommendations of the French Society of Cardiology
• Evolving myopericarditis
• Severe ventricular rhythm disorders that do not stabilise with treatment