Secrecy Capacity per Unit Cost

The concept of channel capacity per unit cost was introduced by Verdu in 1990 to study the limits of cost-efficient wide-band communication. It was shown that orthogonal signaling can achieve the channel capacity per unit cost of memoryless stationary channels with a zero-cost input letter. This paper introduces a concept of secrecy capacity per unit cost to study cost-efficient wide-band secrecy communication. For degraded memoryless stationary wiretap channels, it is shown that an orthogonal coding scheme with randomized pulse position and constant pulse shape achieves the secrecy capacity per unit cost with a zero-cost input letter. For general memoryless stationary wiretap channels, the performance of orthogonal codes is studied, and the benefit of further randomizing the pulse shape is demonstrated via a simple example.