3,930 research outputs found
The price of certainty: "waterslide curves" and the gap to capacity
The classical problem of reliable point-to-point digital communication is to
achieve a low probability of error while keeping the rate high and the total
power consumption small. Traditional information-theoretic analysis uses
`waterfall' curves to convey the revolutionary idea that unboundedly low
probabilities of bit-error are attainable using only finite transmit power.
However, practitioners have long observed that the decoder complexity, and
hence the total power consumption, goes up when attempting to use sophisticated
codes that operate close to the waterfall curve.
This paper gives an explicit model for power consumption at an idealized
decoder that allows for extreme parallelism in implementation. The decoder
architecture is in the spirit of message passing and iterative decoding for
sparse-graph codes. Generalized sphere-packing arguments are used to derive
lower bounds on the decoding power needed for any possible code given only the
gap from the Shannon limit and the desired probability of error. As the gap
goes to zero, the energy per bit spent in decoding is shown to go to infinity.
This suggests that to optimize total power, the transmitter should operate at a
power that is strictly above the minimum demanded by the Shannon capacity.
The lower bound is plotted to show an unavoidable tradeoff between the
average bit-error probability and the total power used in transmission and
decoding. In the spirit of conventional waterfall curves, we call these
`waterslide' curves.Comment: 37 pages, 13 figures. Submitted to IEEE Transactions on Information
Theory. This version corrects a subtle bug in the proofs of the original
submission and improves the bounds significantl
Physics of Microswimmers - Single Particle Motion and Collective Behavior
Locomotion and transport of microorganisms in fluids is an essential aspect
of life. Search for food, orientation toward light, spreading of off-spring,
and the formation of colonies are only possible due to locomotion. Swimming at
the microscale occurs at low Reynolds numbers, where fluid friction and
viscosity dominates over inertia. Here, evolution achieved propulsion
mechanisms, which overcome and even exploit drag. Prominent propulsion
mechanisms are rotating helical flagella, exploited by many bacteria, and
snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and
algae. For artificial microswimmers, alternative concepts to convert chemical
energy or heat into directed motion can be employed, which are potentially more
efficient. The dynamics of microswimmers comprises many facets, which are all
required to achieve locomotion. In this article, we review the physics of
locomotion of biological and synthetic microswimmers, and the collective
behavior of their assemblies. Starting from individual microswimmers, we
describe the various propulsion mechanism of biological and synthetic systems
and address the hydrodynamic aspects of swimming. This comprises
synchronization and the concerted beating of flagella and cilia. In addition,
the swimming behavior next to surfaces is examined. Finally, collective and
cooperate phenomena of various types of isotropic and anisotropic swimmers with
and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics
(to appear
Rigidity of spherical codes
A packing of spherical caps on the surface of a sphere (that is, a spherical
code) is called rigid or jammed if it is isolated within the space of packings.
In other words, aside from applying a global isometry, the packing cannot be
deformed. In this paper, we systematically study the rigidity of spherical
codes, particularly kissing configurations. One surprise is that the kissing
configuration of the Coxeter-Todd lattice is not jammed, despite being locally
jammed (each individual cap is held in place if its neighbors are fixed); in
this respect, the Coxeter-Todd lattice is analogous to the face-centered cubic
lattice in three dimensions. By contrast, we find that many other packings have
jammed kissing configurations, including the Barnes-Wall lattice and all of the
best kissing configurations known in four through twelve dimensions. Jamming
seems to become much less common for large kissing configurations in higher
dimensions, and in particular it fails for the best kissing configurations
known in 25 through 31 dimensions. Motivated by this phenomenon, we find new
kissing configurations in these dimensions, which improve on the records set in
1982 by the laminated lattices.Comment: 39 pages, 8 figure
- …