Computer Science – Information Theory
Scientific paper
2010-04-26
Computer Science
Information Theory
5 pages, to appear in ISIT 2010, Austin, Texas
Scientific paper
This paper extends the "single crossing point" property of the scalar MMSE function, derived by Guo, Shamai and Verd\'u (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.
Bustin Ronit
Palomar Daniel P.
Payaró Miquel
Shamai Shlomo
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