Degrees of Freedom Region of the Gaussian MIMO Broadcast Channel with Common and Private Messages

TL;DR

This paper characterizes the degrees of freedom region for the Gaussian MIMO broadcast channel with common and private messages, using novel outer bounds derived from parallel channel constructions and achievable schemes including DPC and ZF.

Contribution

It introduces a method to bound the DoF region of MIMO broadcast channels via parallel channel models and demonstrates that these bounds are tight with practical coding schemes.

Findings

Derived explicit outer bounds for the DoF region.

Showed that the bounds are achievable with DPC and ZF schemes.

Provided a unified approach for channels with common and private messages.

Abstract

We consider the Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and private messages. We obtain the degrees of freedom (DoF) region of this channel. We first show that a parallel Gaussian broadcast channel with unmatched sub-channels can be constructed from any given Gaussian MIMO broadcast channel by using the generalized singular value decomposition (GSVD) and a relaxation on the power constraint for the channel input, in a way that the capacity region of the constructed parallel channel provides an outer bound for the capacity region of the original channel. The capacity region of the parallel Gaussian broadcast channel with unmatched sub-channels is known, using which we obtain an explicit outer bound for the DoF region of the Gaussian MIMO broadcast channel. We finally show that this outer bound for the DoF region can be attained both by the achievable scheme that uses a classical Gaussian coding for the common message and dirty-paper coding (DPC) for the private messages, as well as by a variation of the zero-forcing (ZF) scheme.