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

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.