Statistical Mechanics of Low-Density Parity Check Error-Correcting Codes over Galois Fields

A variation of low density parity check (LDPC) error correcting codes defined over Galois fields ($GF(q)$) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of $C$ nonzero elements per column. We examine the dependence of the code performance on the value of $q$, for finite and infinite $C$ values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different $q$-dependencies in the cases of C=2 and $C \ge 3$; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.Comment: 7 pages, 1 figur

Temperature effect on the coupling between coherent longitudinal phonons and plasmons in n- and p-type GaAs

The coupling between longitudinal optical (LO) phonons and plasmons plays a fundamental role in determining the performance of doped semiconductor devices. In this work, we report a comparative investigation into the dependence of the coupling on temperature and doping in n- and p-type GaAs by using ultrafast optical phonon spectroscopy. A suppression of coherent oscillations has been observed in p-type GaAs at lower temperature, strikingly different from n-type GaAs and other materials in which coherent oscillations are strongly enhanced by cooling. We attribute this unexpected observation to a cooling-induced elongation of the depth of the depletion layer which effectively increases the screening time of surface field due to a slow diffusion of photoexcited carriers in p-type GaAs. Such an increase breaks the requirement for the generation of coherent LO phonons and, in turn, LO phonon-plasmon coupled modes because of their delayed formation in time.Comment: 18 pages, 4 figure

Superconductivity in BaPtSb with an Ordered Honeycomb Network

Superconductivity in BaPtSb with the SrPtSb-type structure (space group $P\bar{6}m2$, $D_{3h}^1$, No. 187) is reported. The structure consists of a PtSb ordered honeycomb network that stacks along the $c$-axis so that spatial inversion symmetry is broken globally. Electrical resistivity and specific-heat measurements revealed that the compound exhibited superconductivity at 1.64 K. The noncentrosymmetric structure and the strong spin-orbit coupling of Pt and Sb make BaPtSb an attractive compound for studying the exotic superconductivity predicted for a honeycomb network.Comment: 3 pages, 2 figure

Spectrally resolved detection in transient-reflectivity measurements of coherent optical phonons in diamond

Coherent optical phonons in bulk solid system play a crucial role in understanding and designing light-matter interactions and can be detected by the transient-reflectivity measurement. In this paper, we demonstrate spectrally resolved detection of coherent optical phonons in diamond from ultrashort infrared pump-probe measurements using optical band-pass filters. We show that this enhances the sensitivity approximately 35 times in measuring the coherent oscillations in the transient reflectivity compared with the commonly used spectrally integrated measurement. To explain this observation, we discuss its mechanism.Comment: 8 pages, 4 figure