Multiple-Input Multiple-Output Gaussian Broadcast Channels with Confidential Messages

This paper considers the problem of secret communication over a two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel. The transmitter has two independent messages, each of which is intended for one of the receivers but needs to be kept asymptotically perfectly secret from the other. It is shown that, surprisingly, under a matrix power constraint both messages can be simultaneously transmitted at their respective maximal secrecy rates. To prove this result, the MIMO Gaussian wiretap channel is revisited and a new characterization of its secrecy capacity is provided via a new coding scheme that uses artificial noise and random binning.

💡 Research Summary

This paper addresses the problem of confidential communication over a two‑receiver multiple‑input multiple‑output (MIMO) Gaussian broadcast channel. The transmitter, equipped with multiple antennas, wishes to send two independent messages: W₁ intended for receiver 1 and W₂ intended for receiver 2. Each message must remain asymptotically perfectly secret from the unintended receiver, i.e., the mutual information between W₁ and the observations at receiver 2 (and vice‑versa) must vanish as the block length grows. The channel model is linear Gaussian: Y₁ = H₁X + Z₁ and Y₂ = H₂X + Z₂, where H₁ and H₂ are the respective channel matrices, Z₁ and Z₂ are independent unit‑variance Gaussian noise vectors, and X is the transmitted vector subject to a matrix power constraint Tr(K_X) ≤ P, with K_X = E