Reliability and Secrecy Functions of the Wiretap Channel under Cost Constraint
This work addresses security and reliability tradeoffs in communication systems, particularly for wiretap channels, but appears incremental as it builds on existing frameworks with new analytical tools.
The paper tackles the problem of analyzing and designing efficient wiretap channel systems under cost constraints by introducing reliability and security functions, demonstrating that these functions allow control over the tradeoff between reliability and security with exponentially decreasing rates as block length increases.
The wiretap channel has been devised and studied first by Wyner, and subsequently extended to the case with non-degraded general wiretap channels by Csiszar and Korner. Focusing mainly on the Poisson wiretap channel with cost constraint, we newly introduce the notion of reliability and security functions as a fundamental tool to analyze and/or design the performance of an efficient wiretap channel system. Compact formulae for those functions are explicitly given for stationary memoryless wiretap channels. It is also demonstrated that, based on such a pair of reliability and security functions, we can control the tradeoff between reliability and security (usually conflicting), both with exponentially decreasing rates as block length n becomes large. Two ways to do so are given on the basis of concatenation and rate exchange. In this framework, the notion of the δ secrecy capacity is defined and shown to attain the strongest security standard among others. The maximized vs. averaged security measures is also discussed.