3 research outputs found
A construction of UD -ary multi-user codes from -ary codes for MAAC
In this paper, we proposed a construction of a UD -ary -user coding
scheme for MAAC. We first give a construction of -ary -user UD code
from a -ary -user UD code and a -ary -user difference
set with its two component sets and {\em a
priori}. Based on the -ary -user difference set constructed
from a -ary UD code, we recursively construct a UD -ary -user
codes with code length of from initial multi-user codes of -ary,
-ary, \dots, -ary. Introducing multi-user codes with
higer-ary makes the total rate of generated code higher than that
of conventional code
Multi-Group Testing for Items with Real-Valued Status under Standard Arithmetic
This paper proposes a novel generalization of group testing, called
multi-group testing, which relaxes the notion of "testing subset" in group
testing to "testing multi-set". The generalization aims to learn more
information of each item to be tested rather than identify only defectives as
was done in conventional group testing. This paper provides efficient
nonadaptive strategies for the multi-group testing problem. The major tool is a
new structure, -ary additive -disjunct matrix, which is a
generalization of the well-known binary disjunct matrix introduced by Kautz and
Singleton in 1964.Comment: presented in part at 2nd Japan-Taiwan Conference of Combinatorics and
its Applications, Nagoya University, Japan, 201
Semi-Quantitative Group Testing: A Unifying Framework for Group Testing with Applications in Genotyping
We propose a novel group testing method, termed semi-quantitative group
testing, motivated by a class of problems arising in genome screening
experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary
pooling scheme that may be viewed as a concatenation of an adder channel and an
integer-valued quantizer. In its full generality, SQGT may be viewed as a
unifying framework for group testing, in the sense that most group testing
models are special instances of SQGT. For the new testing scheme, we define the
notion of SQ-disjunct and SQ-separable codes, representing generalizations of
classical disjunct and separable codes. We describe several combinatorial and
probabilistic constructions for such codes. While for most of these
constructions we assume that the number of defectives is much smaller than
total number of test subjects, we also consider the case in which there is no
restriction on the number of defectives and they may be as large as the total
number of subjects. For the codes constructed in this paper, we describe a
number of efficient decoding algorithms. In addition, we describe a belief
propagation decoder for sparse SQGT codes for which no other efficient decoder
is currently known. Finally, we define the notion of capacity of SQGT and
evaluate it for some special choices of parameters using information theoretic
methods