2,531 research outputs found
Constructing Sobol' sequences with better two-dimensional projections
Direction numbers for generating Sobol' sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49–57]. However, these Sobol' sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol' sequences in d dimensions as (t, d)-sequences and then optimizing the t-values of the two-dimensional projections. Our target dimension is 21201
Embedded Rank Distance Codes for ISI channels
Designs for transmit alphabet constrained space-time codes naturally lead to
questions about the design of rank distance codes. Recently, diversity embedded
multi-level space-time codes for flat fading channels have been designed from
sets of binary matrices with rank distance guarantees over the binary field by
mapping them onto QAM and PSK constellations. In this paper we demonstrate that
diversity embedded space-time codes for fading Inter-Symbol Interference (ISI)
channels can be designed with provable rank distance guarantees. As a corollary
we obtain an asymptotic characterization of the fixed transmit alphabet
rate-diversity trade-off for multiple antenna fading ISI channels. The key idea
is to construct and analyze properties of binary matrices with a particular
structure induced by ISI channels.Comment: Submitted to IEEE Transactions on Information Theor
Improved bounds for the number of forests and acyclic orientations in the square lattice
In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice . The authors gave the following bounds for the asymptotics of , the number of forests of , and , the number of acyclic orientations of : and .
In this paper we improve these bounds as follows: and . We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices
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