Entropy amplification by aperiodic noise and side information problems

A subset of an Abelian group has unique differences if for all nonzeros. when viewed as additive noise, sets with unique differences amplify the output entropy as much as possible for a large class of input distributions, which is known as entropy amplification property. Aperiodic (noise) distributions arise as extreme cases in the investigation of the rate loss in side information problems such as channel coding with additive interference known at the encoder and lossy source coding with side information at the decoder. The decoder outputs a reconstruction, which is required to satisfy a distortion constraint. Reconstructing the clean source with some distortion is equivalent to reconstructing the encrypted source with the same distortion. Using the EAP, the rate loss can be arbitrarily large and arbitrarily close to 100%.