1,501 research outputs found
On Computation of Groebner Bases for Linear Difference Systems
In this paper we present an algorithm for computing Groebner bases of linear
ideals in a difference polynomial ring over a ground difference field. The
input difference polynomials generating the ideal are also assumed to be
linear. The algorithm is an adaptation to difference ideals of our polynomial
algorithm based on Janet-like reductions.Comment: 5 pages, presented at ACAT-200
High-rate self-synchronizing codes
Self-synchronization under the presence of additive noise can be achieved by
allocating a certain number of bits of each codeword as markers for
synchronization. Difference systems of sets are combinatorial designs which
specify the positions of synchronization markers in codewords in such a way
that the resulting error-tolerant self-synchronizing codes may be realized as
cosets of linear codes. Ideally, difference systems of sets should sacrifice as
few bits as possible for a given code length, alphabet size, and
error-tolerance capability. However, it seems difficult to attain optimality
with respect to known bounds when the noise level is relatively low. In fact,
the majority of known optimal difference systems of sets are for exceptionally
noisy channels, requiring a substantial amount of bits for synchronization. To
address this problem, we present constructions for difference systems of sets
that allow for higher information rates while sacrificing optimality to only a
small extent. Our constructions utilize optimal difference systems of sets as
ingredients and, when applied carefully, generate asymptotically optimal ones
with higher information rates. We also give direct constructions for optimal
difference systems of sets with high information rates and error-tolerance that
generate binary and ternary self-synchronizing codes.Comment: 9 pages, no figure, 2 tables. Final accepted version for publication
in the IEEE Transactions on Information Theory. Material presented in part at
the International Symposium on Information Theory and its Applications,
Honolulu, HI USA, October 201
Oscillatory mixed difference systems
The aim of this paper is to discuss the oscillatory behavior of difference systems of mixed type. Several criteria for oscillations are obtained. Particular results are included in regard to scalar equations. Copyright © 2006 J. M. Ferreira and S. Pinelas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis-tribution, and reproduction in any medium, provided the original work is properly cited. 1
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