On MMSE Properties of Codes for the Gaussian Broadcast and Wiretap Channels

TL;DR

This paper analyzes the MMSE behavior of capacity-achieving codes in Gaussian multi-user channels, exploring their impact on unintended receivers and the trade-offs between capacity and disturbance constraints.

Contribution

It provides new insights into the MMSE properties of codes in Gaussian broadcast and wiretap channels, including effects on capacity regions and secrecy capacity.

Findings

MMSE behavior influences unintended receivers in multi-user channels

Explicit trade-offs between capacity and MMSE disturbance constraints

Characterization of secrecy capacity regions under MMSE constraints

Abstract

This work concerns the behavior of "good" (capacity achieving) codes in several multi-user settings in the Gaussian regime, in terms of their minimum mean-square error (MMSE) behavior. The settings investigated in this context include the Gaussian wiretap channel, the Gaussian broadcast channel (BC) and the Gaussian BC with confidential messages (BCC). In particular this work addresses the effects of transmitting such codes on unintended receivers, that is, receivers that neither require reliable decoding of the transmitted messages nor are they eavesdroppers that must be kept ignorant, to some extent, of the transmitted message. This work also examines the effect on the capacity region that occurs when we limit the allowed disturbance in terms of MMSE on some unintended receiver. This trade-off between the capacity region and the disturbance constraint is given explicitly for the Gaussian BC and the secrecy capacity region of the Gaussian BCC.