• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.7C
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• pp.594-597
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• 2010

This paper estimates belief-propagation (BP) decoding performance of moderate-length irregular low-density parity-check (LDPC) codes with sphere bounds. We note that for moderate-length($10^3{\leq}N{\leq}4\times10^3$) irregular LDPC codes, BP decoding performance, which is much worse than maximum likelihood (ML) decoding performance, is well matched with one of loose upper bounds, i.e., sphere bounds. We introduce the sphere bounding technique for particular codes, not average bounds. The sphere bounding estimation technique is validated by simulation results. It is also shown that sphere bounds and BP decoding performance of irregular LDPC codes are very close at bit-error-rates (BERs) $P_b$ of practical importance($10^{-5}{\leq}P_b{\leq}10^{-4}$).

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.319-326
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• 2003

In this paper, we obtain the optimal condition of the curvature bounds guaranteeing that Euclidean cones over Aleksandrov spaces of curvature bounded above preserve the curvature bounds, by considering the Euclidean cone CS$_{r}$ $^{n}$ over n-dimensional sphere S$_{r}$ $^{n}$ of radius r. More precisely, we show that for r<1, the Euclidean cone CS$_{r}$ $^{n}$ of S$_{r}$ $^{n}$ is a CBB(0) space, but not a CBA($textsc{k}$)-space for any real $textsc{k}$$\in$R.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.2
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• pp.243-246
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• 2006

This study investigates the improvement in the theoretical success rate of the integer ambiguity resolution in GPS/GNSS carrier-phase positioning by using many visible satellites. It estimates the dependence of the rate on the baseline length in relative positioning under the condition of the use of double/triple-frequency navigation signals. The calculation results show that the use of 14 navigation satellites (i.e., seven GPS and seven Galileo ones) remarkably improves the success rate under the condition of very short baseline length, compared with the use of seven GPS ones. The numerical reliability of the calculated success rates is strictly tested by examining the tightness of the union and minimum-distance bounds to the rate. These bounds are also shown to be effective to investigate the realization of the high success rates.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.771-788
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• 2015

In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the $L^p$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.3
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• pp.910-932
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• 1996

A problem of determining the effective conductivity of a useful model of sphere-matrix type, disordered three-phase composite media is considered. Specifically, a three-phase media in which two-phase composite spheres, consisting of spheres of conductivity $k_2$((phase 2) and concentric shells of conductivity $k_3$(phase 3), are randomly distributed in a matrix of conductivity $k_1$( (phase 1) is considered. As for the structure models configuring three-phase composite media, three different structure models of PCS, PS-1 and PS-2 models are defined, which are analogous to well-established PCS, PS structure models of two-phase composite media. Futhermore, a generalized PS-PCS structure model is proposed to incorporate thesee three different models in one. Effective condectivity $k^{\ast}$of multiphaes composite media is greatly influenced by the phase connectivity of each disspersed phase material, as well as phase conductivities and phase volume fractions. Phase connectivity of three-phase PCS, PS-1, PS-2 composite media is quantified by the impentrability parameter $\lambda$. Mathematically rigorous first-order cluster bounds on $k^{\ast}$ are derived for these models of three-phase composite media, and as computation examples, first-order cluster bounds on $k^{\ast}$ for three-phase composites consisting of largely different phase conductivities are computed and compared as function of concnectivity parpmeter $\lambda$. Results and discussions are given.