21,503 research outputs found
Erasure List-Decodable Codes from Random and Algebraic Geometry Codes
Erasure list decoding was introduced to correct a larger number of erasures
with output of a list of possible candidates. In the present paper, we consider
both random linear codes and algebraic geometry codes for list decoding erasure
errors. The contributions of this paper are two-fold. Firstly, we show that,
for arbitrary ( and are independent),
with high probability a random linear code is an erasure list decodable code
with constant list size that can correct a fraction
of erasures, i.e., a random linear code achieves the
information-theoretic optimal trade-off between information rate and fraction
of erasure errors. Secondly, we show that algebraic geometry codes are good
erasure list-decodable codes. Precisely speaking, for any and
, a -ary algebraic geometry code of rate from the
Garcia-Stichtenoth tower can correct
fraction of erasure errors with
list size . This improves the Johnson bound applied to algebraic
geometry codes. Furthermore, list decoding of these algebraic geometry codes
can be implemented in polynomial time
Fuzzy approach to multimedia faulty module replacement
For non-real time multimedia systems, we present a fuzzy approach to replacing the faulty module. After analyzing the nature of the random and pseudo-random test sequences applied to a module under test, we obtain the aliasing fault coverage between the random and pseudo-random sequences. The activity probability features of intermittent faults in the module under test are discussed based on the Markov chain model. Results on real examples are presented to demonstrate the effectiveness of the proposed fuzzy replacement approac
Gradient-based estimation of Manning's friction coefficient from noisy data
We study the numerical recovery of Manning's roughness coefficient for the
diffusive wave approximation of the shallow water equation. We describe a
conjugate gradient method for the numerical inversion. Numerical results for
one-dimensional model are presented to illustrate the feasibility of the
approach. Also we provide a proof of the differentiability of the weak form
with respect to the coefficient as well as the continuity and boundedness of
the linearized operator under reasonable assumptions using the maximal
parabolic regularity theory.Comment: 19 pages, 3 figure
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