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

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