Quantized Mechanisms for Gaussian Multiple Access Wiretap Channels

Economic mechanisms have been widely studied for allocating network resources while accounting for the incentives of self-interested users. Indeed, the well known Vickrey-Clarke-Groves (VCG) mechanism provides an elegant solution to such problems with a strong incentive guarantee. However, VCG mechanisms can incur high communication costs. Recent work has shown that via quantization, one can reduce the communication costs of VCG while maintaining its incentive guarantees for allocating a single divisible resource. However, in many information theoretic settings, the underlying resource constraints are more complex. Here, we consider developing similar quantized mechanisms for one such setting: a Gaussian multiple access wiretap channel. Namely, we seek to allocate secure rates to a set of users assuming that all users employ a superposition coding scheme. This results in an achievable rate region that we show is a polymatroid. We utilize this characterization to design a quantized mechanism with strong incentive properties.