328 research outputs found
Finite Dimensional Infinite Constellations
In the setting of a Gaussian channel without power constraints, proposed by
Poltyrev, the codewords are points in an n-dimensional Euclidean space (an
infinite constellation) and the tradeoff between their density and the error
probability is considered. The capacity in this setting is the highest
achievable normalized log density (NLD) with vanishing error probability. This
capacity as well as error exponent bounds for this setting are known. In this
work we consider the optimal performance achievable in the fixed blocklength
(dimension) regime. We provide two new achievability bounds, and extend the
validity of the sphere bound to finite dimensional infinite constellations. We
also provide asymptotic analysis of the bounds: When the NLD is fixed, we
provide asymptotic expansions for the bounds that are significantly tighter
than the previously known error exponent results. When the error probability is
fixed, we show that as n grows, the gap to capacity is inversely proportional
(up to the first order) to the square-root of n where the proportion constant
is given by the inverse Q-function of the allowed error probability, times the
square root of 1/2. In an analogy to similar result in channel coding, the
dispersion of infinite constellations is 1/2nat^2 per channel use. All our
achievability results use lattices and therefore hold for the maximal error
probability as well. Connections to the error exponent of the power constrained
Gaussian channel and to the volume-to-noise ratio as a figure of merit are
discussed. In addition, we demonstrate the tightness of the results numerically
and compare to state-of-the-art coding schemes.Comment: 54 pages, 13 figures. Submitted to IEEE Transactions on Information
Theor
Outage Capacity and Optimal Transmission for Dying Channels
In wireless networks, communication links may be subject to random fatal
impacts: for example, sensor networks under sudden power losses or cognitive
radio networks with unpredictable primary user spectrum occupancy. Under such
circumstances, it is critical to quantify how fast and reliably the information
can be collected over attacked links. For a single point-to-point channel
subject to a random attack, named as a \emph{dying channel}, we model it as a
block-fading (BF) channel with a finite and random delay constraint. First, we
define the outage capacity as the performance measure, followed by studying the
optimal coding length such that the outage probability is minimized when
uniform power allocation is assumed. For a given rate target and a coding
length , we then minimize the outage probability over the power allocation
vector \mv{P}_{K}, and show that this optimization problem can be cast into a
convex optimization problem under some conditions. The optimal solutions for
several special cases are discussed.
Furthermore, we extend the single point-to-point dying channel result to the
parallel multi-channel case where each sub-channel is a dying channel, and
investigate the corresponding asymptotic behavior of the overall outage
probability with two different attack models: the independent-attack case and
the -dependent-attack case. It can be shown that the overall outage
probability diminishes to zero for both cases as the number of sub-channels
increases if the \emph{rate per unit cost} is less than a certain threshold.
The outage exponents are also studied to reveal how fast the outage probability
improves over the number of sub-channels.Comment: 31 pages, 9 figures, submitted to IEEE Transactions on Information
Theor
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