1,034 research outputs found
Prefix Codes for Power Laws with Countable Support
In prefix coding over an infinite alphabet, methods that consider specific
distributions generally consider those that decline more quickly than a power
law (e.g., Golomb coding). Particular power-law distributions, however, model
many random variables encountered in practice. For such random variables,
compression performance is judged via estimates of expected bits per input
symbol. This correspondence introduces a family of prefix codes with an eye
towards near-optimal coding of known distributions. Compression performance is
precisely estimated for well-known probability distributions using these codes
and using previously known prefix codes. One application of these near-optimal
codes is an improved representation of rational numbers.Comment: 5 pages, 2 tables, submitted to Transactions on Information Theor
Correcting Charge-Constrained Errors in the Rank-Modulation Scheme
We investigate error-correcting codes for a the
rank-modulation scheme with an application to flash memory
devices. In this scheme, a set of n cells stores information in the
permutation induced by the different charge levels of the individual
cells. The resulting scheme eliminates the need for discrete
cell levels, overcomes overshoot errors when programming cells (a
serious problem that reduces the writing speed), and mitigates the
problem of asymmetric errors. In this paper, we study the properties
of error-correcting codes for charge-constrained errors in the
rank-modulation scheme. In this error model the number of errors
corresponds to the minimal number of adjacent transpositions required
to change a given stored permutation to another erroneous
one—a distance measure known as Kendall’s τ-distance.We show
bounds on the size of such codes, and use metric-embedding techniques
to give constructions which translate a wealth of knowledge
of codes in the Lee metric to codes over permutations in Kendall’s
τ-metric. Specifically, the one-error-correcting codes we construct
are at least half the ball-packing upper bound
The Physics of Living Neural Networks
Improvements in technique in conjunction with an evolution of the theoretical
and conceptual approach to neuronal networks provide a new perspective on
living neurons in culture. Organization and connectivity are being measured
quantitatively along with other physical quantities such as information, and
are being related to function. In this review we first discuss some of these
advances, which enable elucidation of structural aspects. We then discuss two
recent experimental models that yield some conceptual simplicity. A
one-dimensional network enables precise quantitative comparison to analytic
models, for example of propagation and information transport. A two-dimensional
percolating network gives quantitative information on connectivity of cultured
neurons. The physical quantities that emerge as essential characteristics of
the network in vitro are propagation speeds, synaptic transmission, information
creation and capacity. Potential application to neuronal devices is discussed.Comment: PACS: 87.18.Sn, 87.19.La, 87.80.-y, 87.80.Xa, 64.60.Ak Keywords:
complex systems, neuroscience, neural networks, transport of information,
neural connectivity, percolation
http://www.weizmann.ac.il/complex/tlusty/papers/PhysRep2007.pdf
http://www.weizmann.ac.il/complex/EMoses/pdf/PhysRep-448-56.pd
The impact of spike timing variability on the signal-encoding performance of neural spiking models
It remains unclear whether the variability of neuronal spike trains in vivo arises due to biological noise sources or represents highly precise encoding of temporally varying synaptic input signals. Determining the variability of spike timing can provide fundamental insights into the nature of strategies used in the brain to represent and transmit information in the form of discrete spike trains. In this study, we employ a signal estimation paradigm to determine how variability in spike timing affects encoding of random time-varying signals. We assess this for two types of spiking models: an integrate-and-fire model with random threshold and a more biophysically realistic stochastic ion channel model. Using the coding fraction and mutual information as information-theoretic measures, we quantify the efficacy of optimal linear decoding of random inputs from the model outputs and study the relationship between efficacy and variability in the output spike train. Our findings suggest that variability does not necessarily hinder signal decoding for the biophysically plausible encoders examined and that the functional role of spiking variability depends intimately on the nature of the encoder and the signal processing task; variability can either enhance or impede decoding performance
Construction of Codes for Network Coding
Based on ideas of K\"otter and Kschischang we use constant dimension
subspaces as codewords in a network. We show a connection to the theory of
q-analogues of a combinatorial designs, which has been studied in Braun, Kerber
and Laue as a purely combinatorial object. For the construction of network
codes we successfully modified methods (construction with prescribed
automorphisms) originally developed for the q-analogues of a combinatorial
designs. We then give a special case of that method which allows the
construction of network codes with a very large ambient space and we also show
how to decode such codes with a very small number of operations
Population coding by globally coupled phase oscillators
A system of globally coupled phase oscillators subject to an external input
is considered as a simple model of neural circuits coding external stimulus.
The information coding efficiency of the system in its asynchronous state is
quantified using Fisher information. The effect of coupling and noise on the
information coding efficiency in the stationary state is analyzed. The
relaxation process of the system after the presentation of an external input is
also studied. It is found that the information coding efficiency exhibits a
large transient increase before the system relaxes to the final stationary
state.Comment: 7 pages, 9 figures, revised version, new figures added, to appear in
JPSJ Vol 75, No.
Punctured Binary Simplex Codes as LDPC codes
Digital data transfer can be protected by means of suitable error correcting
codes. Among the families of state-of-the-art codes, LDPC (Low Density
Parity-Check) codes have received a great deal of attention recently, because
of their performance and flexibility of operation, in wireless and mobile radio
channels, as well as in cable transmission systems. In this paper, we present a
class of rate-adaptive LDPC codes, obtained as properly punctured simplex
codes. These codes allow for the use of an efficient soft-decision decoding
algorithm, provided that a condition called row-column constraint is satisfied.
This condition is tested on small-length codes, and then extended to
medium-length codes. The puncturing operations we apply do not influence the
satisfaction of the row-column constraint, assuring that a wide range of code
rates can be obtained. We can reach code rates remarkably higher than those
obtainable by the original simplex code, and the price in terms of minimum
distance turns out to be relatively small, leading to interesting trade-offs in
the resulting asymptotic coding gain
- …