3,632 research outputs found
Efficient Two-Stage Group Testing Algorithms for Genetic Screening
Efficient two-stage group testing algorithms that are particularly suited for
rapid and less-expensive DNA library screening and other large scale biological
group testing efforts are investigated in this paper. The main focus is on
novel combinatorial constructions in order to minimize the number of individual
tests at the second stage of a two-stage disjunctive testing procedure.
Building on recent work by Levenshtein (2003) and Tonchev (2008), several new
infinite classes of such combinatorial designs are presented.Comment: 14 pages; to appear in "Algorithmica". Part of this work has been
presented at the ICALP 2011 Group Testing Workshop; arXiv:1106.368
Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
The concept of group divisible codes, a generalization of group divisible
designs with constant block size, is introduced in this paper. This new class
of codes is shown to be useful in recursive constructions for constant-weight
and constant-composition codes. Large classes of group divisible codes are
constructed which enabled the determination of the sizes of optimal
constant-composition codes of weight three (and specified distance), leaving
only four cases undetermined. Previously, the sizes of constant-composition
codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table
New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes
This paper presents several new construction techniques for low-density
parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on
specific classes of combinatorial designs, the improved code design focuses on
high-rate structured codes with constant column weights 3 and higher. The
proposed codes are efficiently encodable and exhibit good structural
properties. Experimental results on decoding performance with the sum-product
algorithm show that the novel codes offer substantial practical application
potential, for instance, in high-speed applications in magnetic recording and
optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications
Frame difference families and resolvable balanced incomplete block designs
Frame difference families, which can be obtained via a careful use of
cyclotomic conditions attached to strong difference families, play an important
role in direct constructions for resolvable balanced incomplete block designs.
We establish asymptotic existences for several classes of frame difference
families. As corollaries new infinite families of 1-rotational
-RBIBDs over are
derived, and the existence of -RBIBDs is discussed. We construct
-RBIBDs for , whose
existence were previously in doubt. As applications, we establish asymptotic
existences for an infinite family of optimal constant composition codes and an
infinite family of strictly optimal frequency hopping sequences.Comment: arXiv admin note: text overlap with arXiv:1702.0750
Generalized Balanced Tournament Packings and Optimal Equitable Symbol Weight Codes for Power Line Communications
Generalized balance tournament packings (GBTPs) extend the concept of
generalized balanced tournament designs introduced by Lamken and Vanstone
(1989). In this paper, we establish the connection between GBTPs and a class of
codes called equitable symbol weight codes. The latter were recently
demonstrated to optimize the performance against narrowband noise in a general
coded modulation scheme for power line communications. By constructing classes
of GBTPs, we establish infinite families of optimal equitable symbol weight
codes with code lengths greater than alphabet size and whose narrowband noise
error-correcting capability to code length ratios do not diminish to zero as
the length grows
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