76 research outputs found
Block-avoiding point sequencings
Let and be positive integers. Recent papers by Kreher, Stinson and
Veitch have explored variants of the problem of ordering the points in a triple
system (such as a Steiner triple system, directed triple system or Mendelsohn
triple system) on points so that no block occurs in a segment of
consecutive entries (thus the ordering is locally block-avoiding). We describe
a greedy algorithm which shows that such an ordering exists, provided that
is sufficiently large when compared to . This algorithm leads to improved
bounds on the number of points in cases where this was known, but also extends
the results to a significantly more general setting (which includes, for
example, orderings that avoid the blocks of a design). Similar results for a
cyclic variant of this situation are also established.
We construct Steiner triple systems and quadruple systems where can be
large, showing that a bound of Stinson and Veitch is reasonable. Moreover, we
generalise the Stinson--Veitch bound to a wider class of block designs and to
the cyclic case.
The results of Kreher, Stinson and Veitch were originally inspired by results
of Alspach, Kreher and Pastine, who (motivated by zero-sum avoiding sequences
in abelian groups) were interested in orderings of points in a partial Steiner
triple system where no segment is a union of disjoint blocks. Alspach~\emph{et
al.}\ show that, when the system contains at most pairwise disjoint blocks,
an ordering exists when the number of points is more than . By making
use of a greedy approach, the paper improves this bound to .Comment: 38 pages. Typo in the statement of Theorem 17 corrected, and other
minor changes mad
On Perfect Difference Families and their Applications to Radar Arrays
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Self-Synchronizing Pulse Position Modulation With Error Tolerance
Pulse position modulation (PPM) is a popular signal modulation technique which converts signals into M-ary data by means of the position of a pulse within a time interval. While PPM and its variations have great advantages in many contexts, this type of modulation is vulnerable to loss of synchronization, potentially causing a severe error floor or throughput penalty even when little or no noise is assumed. Another disadvantage is that this type of modulation typically offers no error correction mechanism on its own, making them sensitive to intersymbol interference and environmental noise. In this paper, we propose a coding theoretic variation of PPM that allows for significantly more efficient symbol and frame synchronization as well as strong error correction. The proposed scheme can be divided into a synchronization layer and a modulation layer. This makes our technique compatible with major existing techniques such as standard PPM, multipulse PPM, and expurgated PPM as well in that the scheme can be realized by adding a simple synchronization layer to one of these standard techniques. We also develop a generalization of expurgated PPM suited for the modulation layer of the proposed self-synchronizing modulation scheme. This generalized PPM can also be used as stand-alone error-correcting PPM with a larger number of available symbols
Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)
The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), SaarbrĀØucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), WĀØurzburg (1993), Caen (1994), MĀØunchen (1995), Grenoble (1996), LĀØubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
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