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

Automated summary

This paper investigates the information-theoretic channel coding problem with input cost constraints in the wiretap channel (WTC). It is found that, compared to the WTC without cost constraints, two auxiliary variables are required to achieve capacity in the cost-constrained DM-WTC. This highlights the essential role of superposition coding in cost-constrained WTCs.