Phase transitions of subset sum and Shannonʹs limit in source coding

We consider statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. After introducing the statistical mechanical treatment of the problem, the phase transition behaviors are discussed. We also introduce a source coding scheme which is based on the idea of the subset sum. It is shown that the phase transitions in the subset sum is related to Shannonʹs limit for source coding.