Abstract
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.
Highlights
Physical-layer security (PLS), rooted in informationtheoretic principles, dates back to Wyner’s landmark 1975 paper [1], where the wiretap channel (WTC) was introduced
We proved optimality of superposition wiretap coding under a cost constraint, and provided a WTC example for which single-layer coding is strictly suboptimal
This stands in contrast to the classic WTC secrecy-capacity result without a cost constraint, that is characterized using a single auxiliary random variable
Summary
Physical-layer security (PLS), rooted in informationtheoretic principles, dates back to Wyner’s landmark 1975 paper [1], where the wiretap channel (WTC) was introduced. In many information-theoretic communication problems, adding an input cost constraint amounts to restricting the optimization domain in the capacity expression (e.g., the set of feasible PV,X in (1)). We show that this reasoning is not valid for cost-constrained (CC) WTCs. To do so, we characterize the CC secrecy-capacity using two auxiliary variables and prove that a single-auxiliary formula is strictly suboptimal. To the best of our knowledge, the WTC is the only point-to-point communication scenario for which the capacity formula itself changes due to the addition of an input cost constraint
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