New coding theorems for fixed-length source coding and Shannon's cipher system with a general source

Abstract

This paper is concerned with new coding theorems for (a) fixed-length coding of a general source, and (b) coding of Shannon's cipher system with a general source, under the condition that the decoding error probability vanishes as the blocklength goes to infinity. The converse theorems consist of inequalities that include the limit inferior in probability. In addition, the converse theorems are valid for the class of stochastic encoders. The direct theorems are proved under the assumptions that are slightly stronger than the consequences of the converse theorems. We can obtain known coding theorems from the obtained results.