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The OMEGA laser system is being used to investigate several approaches to inertial confinement fusion: the traditional central-hot-spot (CHS) ignition, fast ignition (FI), and shock ignition (SI). To achieve ignition, CHS requires the highly uniform compression of a solid deuterium-tritium (DT)-layered target on a low adiabat (defined as the ratio of the pressure to the Fermi-degenerate pressure) and with an implosion velocity Vimp ≥ 3.5 × 107 cm/s. A laser pulse shape with triple pickets is used to produce this low adiabat by optimally timing multiple shocks launched by the pickets and the main laser. Cryogenic targets that imploded optimally with such pulses have demonstrated near-design compression with an areal density ρR ~ 290 mg/cm2 at Vimp = 3.1 × 107 cm/s. These are, by far, the highest DT areal densities demonstrated in the laboratory. SI experiments, where a shock is launched by a picket at the end of the laser pulse into the compressing capsule, have been performed on low-adiabat warm plastic targets. Both yield and areal density improve significantly when a spike is used at the end of the laser pulse, indicating that the energy from the shock is coupled into the compressing target. Integrated FI experiments have begun on the OMEGA/OMEGA EP laser system.