33,370 research outputs found
Low-Density Parity-Check Codes From Transversal Designs With Improved Stopping Set Distributions
This paper examines the construction of low-density parity-check (LDPC) codes
from transversal designs based on sets of mutually orthogonal Latin squares
(MOLS). By transferring the concept of configurations in combinatorial designs
to the level of Latin squares, we thoroughly investigate the occurrence and
avoidance of stopping sets for the arising codes. Stopping sets are known to
determine the decoding performance over the binary erasure channel and should
be avoided for small sizes. Based on large sets of simple-structured MOLS, we
derive powerful constraints for the choice of suitable subsets, leading to
improved stopping set distributions for the corresponding codes. We focus on
LDPC codes with column weight 4, but the results are also applicable for the
construction of codes with higher column weights. Finally, we show that a
subclass of the presented codes has quasi-cyclic structure which allows
low-complexity encoding.Comment: 11 pages; to appear in "IEEE Transactions on Communications
Planar 3-dimensional assignment problems with Monge-like cost arrays
Given an cost array we consider the problem -P3AP
which consists in finding pairwise disjoint permutations
of such that
is minimized. For the case
the planar 3-dimensional assignment problem P3AP results.
Our main result concerns the -P3AP on cost arrays that are layered
Monge arrays. In a layered Monge array all matrices that result
from fixing the third index are Monge matrices. We prove that the -P3AP
and the P3AP remain NP-hard for layered Monge arrays. Furthermore, we show that
in the layered Monge case there always exists an optimal solution of the
-3PAP which can be represented as matrix with bandwidth . This
structural result allows us to provide a dynamic programming algorithm that
solves the -P3AP in polynomial time on layered Monge arrays when is
fixed.Comment: 16 pages, appendix will follow in v
Testing of random matrices
Let be a positive integer and be an
\linebreak \noindent sized matrix of independent random variables
having joint uniform distribution \hbox{Pr} {x_{ij} = k \hbox{for} 1 \leq k
\leq n} = \frac{1}{n} \quad (1 \leq i, j \leq n) \koz. A realization
of is called \textit{good}, if its each row and
each column contains a permutation of the numbers . We present and
analyse four typical algorithms which decide whether a given realization is
good
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