5,085 research outputs found
Dispersion of the Gilbert-Elliott Channel
Channel dispersion plays a fundamental role in assessing the backoff from capacity due to finite blocklength. This paper analyzes the channel dispersion for a simple channel with memory: the Gilbert-Elliott communication model in which the crossover probability of a binary symmetric channel evolves as a binary symmetric Markov chain, with and without side information at the receiver about the channel state. With side information, dispersion is equal to the average of the dispersions of the individual binary symmetric channels plus a term that depends on the Markov chain dynamics, which do not affect the channel capacity. Without side information, dispersion is equal to the spectral density at zero of a certain stationary process, whose mean is the capacity. In addition, the finite blocklength behavior is analyzed in the non-ergodic case, in which the chain remains in the initial state forever.National Science Foundation (U.S.) (Grant CCF-06-35154)National Science Foundation (U.S.) (Grant CNS-09-05398
Second-Order Coding Rates for Channels with State
We study the performance limits of state-dependent discrete memoryless
channels with a discrete state available at both the encoder and the decoder.
We establish the epsilon-capacity as well as necessary and sufficient
conditions for the strong converse property for such channels when the sequence
of channel states is not necessarily stationary, memoryless or ergodic. We then
seek a finer characterization of these capacities in terms of second-order
coding rates. The general results are supplemented by several examples
including i.i.d. and Markov states and mixed channels
On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime
As the mobile application landscape expands, wireless networks are tasked
with supporting different connection profiles, including real-time traffic and
delay-sensitive communications. Among many ensuing engineering challenges is
the need to better understand the fundamental limits of forward error
correction in non-asymptotic regimes. This article characterizes the
performance of random block codes over finite-state channels and evaluates
their queueing performance under maximum-likelihood decoding. In particular,
classical results from information theory are revisited in the context of
channels with rare transitions, and bounds on the probabilities of decoding
failure are derived for random codes. This creates an analysis framework where
channel dependencies within and across codewords are preserved. Such results
are subsequently integrated into a queueing problem formulation. For instance,
it is shown that, for random coding on the Gilbert-Elliott channel, the
performance analysis based on upper bounds on error probability provides very
good estimates of system performance and optimum code parameters. Overall, this
study offers new insights about the impact of channel correlation on the
performance of delay-aware, point-to-point communication links. It also
provides novel guidelines on how to select code rates and block lengths for
real-time traffic over wireless communication infrastructures
First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory
This article considers the performance of digital communication systems
transmitting messages over finite-state erasure channels with memory.
Information bits are protected from channel erasures using error-correcting
codes; successful receptions of codewords are acknowledged at the source
through instantaneous feedback. The primary focus of this research is on
delay-sensitive applications, codes with finite block lengths and, necessarily,
non-vanishing probabilities of decoding failure. The contribution of this
article is twofold. A methodology to compute the distribution of the time
required to empty a buffer is introduced. Based on this distribution, the mean
hitting time to an empty queue and delay-violation probabilities for specific
thresholds can be computed explicitly. The proposed techniques apply to
situations where the transmit buffer contains a predetermined number of
information bits at the onset of the data transfer. Furthermore, as additional
performance criteria, large deviation principles are obtained for the empirical
mean service time and the average packet-transmission time associated with the
communication process. This rigorous framework yields a pragmatic methodology
to select code rate and block length for the communication unit as functions of
the service requirements. Examples motivated by practical systems are provided
to further illustrate the applicability of these techniques.Comment: To appear in IEEE Transactions on Information Theor
The generalized gradient approximation kernel in time-dependent density functional theory
A complete understanding of a material requires both knowledge of the excited
states as well as of the ground state. In particular, the low energy
excitations are of utmost importance while studying the electronic, magnetic,
dynamical, and thermodynamical properties of the material. Time-Dependent
Density Functional Theory (TDDFT), within the linear regime, is a successful
\textit{ab-initio} method to access the electronic charge and spin excitations.
However, it requires an approximation to the exchange-correlation (XC) kernel
which encapsulates the effect of electron-electron interactions in the
many-body system. In this work we derive and implement the spin-polarized XC
kernel for semi-local approximations such as the adiabatic Generalized Gradient
Approximation (AGGA). This kernel has a quadratic dependence on the wavevector,
{\bf q}, of the perturbation, however the impact of this on the electron energy
loss spectra (EELS) is small. Although the GGA functional is good in predicting
structural properties, it generality overestimates the exchange spin-splitting.
This leads to higher magnon energies, as compared to both ALDA and experiment.
In addition, interaction with the Stoner spin-flip continuum is enhanced by
AGGA, which strongly suppresses the intensity of spin-waves.Comment: 11 pages, 7 figure
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