Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this rate, the optimal Bayesian estimator recovers the data perfectly, and above it the recovered data becomes uncorrelated. This study uses the replica method from the theory of spin glasses to show that this critical rate is the channel capacity. This interesting finding has a particular application to the problem of secure transmission: A strictly nonlinear Gaussian random field along with random binning can be used to securely encode a confidential message in a wiretap channel. Our large-system characterization demonstrates that this secure coding scheme asymptotically achieves the secrecy capacity of the Gaussian wiretap channel.
翻译:纯非线性高斯随机字段给出的基因模型显示全非无行为的反概率问题: 存在一种临界率, 巴伊西亚的推论显示一个阶段转换。 在此率下, 最佳的巴伊西亚估计器完美地恢复数据, 并且超过此率, 回收的数据变得不相干 。 本研究使用旋转眼镜理论的复制方法来显示这个临界速率是频道能力。 这个有趣的发现对安全传输问题特别适用: 一个严格的非线性高斯随机字段, 以及随机的宾宁可以用来安全地将机密信息编码在窃听频道。 我们的大型系统特征显示, 这个安全的编码方案在瞬间就能实现高斯电磁带的保密能力 。