An I-MMSE based graphical representation of rate and equivocation for the Gaussian broadcast channel

In this work a graphical representation of rate and equivocation for the scalar Gaussian broadcast channel is provided. This representation builds on the fundamental relationship between information theory and estimation theory, the so-called I-MMSE relationship, and the natural properties of the minimum mean-square error (MMSE) function. The approach is then applied to the recent problem of “secrecy outside a bounded range” to provide both a graphical representation of the problem as well as additional insights into the increase in the completely secure rate.