HCCI engines are a really cool technology, but very hard to do.
Efficiency of internal combustion engines is related to the compression ratio - the ratio of the combustion chamber from largest to smallest capacity.
Gasoline engines usually have a compression ratio around 9:1. Higher, and the compressional heating combined with the heat off of the walls can cause "knocking," which detonation of pockets of fuel/air away from the flame front from the spark plug. Engines with premium gas can run higher compression ratios. Higher-octane fuels can be compressed more without burning, but of course there is no benefit to running it on engines rated for regular.
Diesel engines run ratios of around 17:1, resulting in much greater efficiency. Diesel engines of course don't have spark plugs. The fuel is injected just before top dead center, where the air is compressed maximally. This is in contrast to a gasoline engine, where it is well mixed with air before entering the combustion chamber. Due to compressional heating, it spontaneously combusts very quickly, much faster than the combustion in a spark-plug-ignited gas engine.
HCCI well-mixes the air and gas upon intake, but ignites by compression like diesel. This gives diesel efficiency. In addition to the better compression ratio, HCCI controls power by the amount of fuel injected, like a diesel. Gasoline engines use a throttle to choke off the air supply, which induces losses because the engine has to work harder to pull air at lower power. That's how engine braking works, and also why diesel trucks use a separate "jake brake" to use the engine to brake.
It must run under a leaner mixture. It's really hard to have complete burning of fuel, and avoid knocking. That's why it has to be very carefully computer controlled based on temperature and such.