The Secrecy Capacity of Cost-Constrained Wiretap Channels

In many information-theoretic channel coding problems, adding an input cost constraint to the operational setup amounts restricting optimization domain in capacity formula. This paper shows that, contrast common belief, such a simple modification does not hold for cost-constrained (CC) wiretap (WTC). The secrecy-capacity of discrete memoryless (DM) WTC without constraints is described by single auxiliary random variable. For CC DM-WTC, however, we show that two auxiliaries are necessary achieve capacity. Specifically, first derive formula, proving direct part via superposition coding. Then, provide example DM-WTC whose cannot be achieved using auxiliary. establishes fundamental role over WTCs.