9 research outputs found
On mutual information, likelihood-ratios and estimation error for the additive Gaussian channel
This paper considers the model of an arbitrary distributed signal x observed
through an added independent white Gaussian noise w, y=x+w. New relations
between the minimal mean square error of the non-causal estimator and the
likelihood ratio between y and \omega are derived. This is followed by an
extended version of a recently derived relation between the mutual information
I(x;y) and the minimal mean square error. These results are applied to derive
infinite dimensional versions of the Fisher information and the de Bruijn
identity. The derivation of the results is based on the Malliavin calculus.Comment: 21 pages, to appear in the IEEE Transactions on Information Theor
Mutual Information and Minimum Mean-square Error in Gaussian Channels
This paper deals with arbitrarily distributed finite-power input signals
observed through an additive Gaussian noise channel. It shows a new formula
that connects the input-output mutual information and the minimum mean-square
error (MMSE) achievable by optimal estimation of the input given the output.
That is, the derivative of the mutual information (nats) with respect to the
signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input
statistics. This relationship holds for both scalar and vector signals, as well
as for discrete-time and continuous-time noncausal MMSE estimation. This
fundamental information-theoretic result has an unexpected consequence in
continuous-time nonlinear estimation: For any input signal with finite power,
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 0 and SNR
Power allocation and signal labelling on physical layer security
PhD ThesisSecure communications between legitimate users have received considerable
attention recently. Transmission cryptography, which introduces
secrecy on the network layer, is heavily relied on conventionally to secure
communications. However, it is theoretically possible to break the
encryption if unlimited computational resource is provided. As a result,
physical layer security becomes a hot topic as it provides perfect secrecy
from an information theory perspective. The study of physical layer
security on real communication system model is challenging and important,
as the previous researches are mainly focusing on the Gaussian
input model which is not practically implementable.
In this thesis, the physical layer security of wireless networks employing
finite-alphabet input schemes are studied. In particular, firstly, the secrecy
capacity of the single-input single-output (SISO) wiretap channel
model with coded modulation (CM) and bit-interleaved coded modulation
(BICM) is derived in closed-form, while a fast, sub-optimal power
control policy (PCP) is presented to maximize the secrecy capacity performance.
Since finite-alphabet input schemes achieve maximum secrecy
capacity at medium SNR range, the maximum amount of energy that
the destination can harvest from the transmission while satisfying the
secrecy rate constraint is computed. Secondly, the effects of mapping
techniques on secrecy capacity of BICM scheme are investigated, the secrecy
capacity performances of various known mappings are compared on
8PSK, 16QAM and (1,5,10) constellations, showing that Gray mapping
obtains lowest secrecy capacity value at high SNRs. We propose a new
mapping algorithm, called maximum error event (MEE), to optimize the
secrecy capacity over a wide range of SNRs. At low SNR, MEE mapping
achieves a lower secrecy rate than other well-known mappings, but
at medium-to-high SNRs MEE mapping achieves a significantly higher
secrecy rate over a wide range of SNRs. Finally, the secrecy capacity and
power allocation algorithm (PA) of finite-alphabet input wiretap channels
with decode-and-forward (DF) relays are proposed, the simulation
results are compared with the equal power allocation algorithm