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Abstract
This thesis represents an addition to the theory of information transmission, signal estimation,
nonlinear filtering, and multiuser detection over channels with Gaussian noise. The
work consists of two parts based on two problem settings—single-user and multiuser—which
draw different techniques in their development.
The first part considers canonical Gaussian channels with an input of arbitrary but fixed
distribution. An “incremental channel” is devised to study the mutual information increase
due to an infinitesimal increase in the signal-to-noise ratio (SNR) or observation time. It
is shown that the derivative of the input-output mutual information (nats) with respect
to the SNR is equal to half the minimum mean-square error (MMSE) achieved by optimal
estimation of the input given the output. This relationship holds for both scalar and vector
signals, as well as for discrete- and continuous-time models. This information-theoretic
result has an unexpected consequence in continuous-time estimation: The causal filtering
MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE
achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between |
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创芯大讲堂
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发表于 2009-3-24 12:22:37
