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This paper extends the single crossing point property of the scalar MMSE function, derived by Guo, Shamai and Verdu (first presented in ISIT 2008), to the parallel degraded MIMO scenario. It is shown that the matrix Q(t), which is the difference between the MMSE assuming a Gaussian input and the MMSE assuming an arbitrary input, has, at most, a single crossing point for each of its eigenvalues. Together with the I-MMSE relationship, a fundamental connection between Information Theory and Estimation Theory, this new property is employed to derive results in Information Theory. As a simple application of this property we provide an alternative converse proof for the broadcast channel (BC) capacity region under covariance constraint in this specific setting.
The scalar additive Gaussian noise channel has the single crossing point property between the minimum-mean square error (MMSE) in the estimation of the input given the channel output, assuming a Gaussian input to the channel, and the MMSE assuming an
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 wire
This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance
We examine codes, over the additive Gaussian noise channel, designed for reliable communication at some specific signal-to-noise ratio (SNR) and constrained by the permitted minimum mean-square error (MMSE) at lower SNRs. The maximum possible rate is
The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition for the eq