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  1. In this paper, we examine variable node (VN) doping to mitigate the error propagation problem in sliding window decoding (SWD) of spatially coupled LDPC (SC-LDPC) codes from the point of view of the encoding process. More specifically, in order to simplify the process of generating an encoded sequence with some number of doped code bits, we propose to employ systematic encoding and to limit doping to systematic bits only. Numerical results show that doping of systematic bits only achieves comparable performance to employing general (nonsystematic) encoding and full doping of all the code bits at each doping position, while benefiting from a much simpler encoding process. We then show that the inherent rate loss due to doping can be reduced by doping only a fraction of the variable nodes at each doping position with only a minor impact on performance.
    Free, publicly-accessible full text available June 26, 2023

    The seismic quality factor (Q) of the Earth’s mantle is of great importance for the understanding of the physical and chemical properties that control mantle anelasticity. The radial structure of the Earth’s Q is less well resolved compared to its wave speed structure, and large discrepancies exist among global 1-D Q models. In this study, we build a global data set of amplitude measurements of S, SS, SSS and SSSS waves using earthquakes that occurred between 2009 and 2017 with moment magnitudes ranging from 6.5 to 8.0. Synthetic seismograms for those events are computed in a 1-D reference model PREM, and amplitude ratios between observed and synthetic seismograms are calculated in the frequency domain by spectra division, with measurement windows determined based on visual inspection of seismograms. We simulate wave propagation in a global velocity model S40RTS based on SPECFEM3D and show that the average amplitude ratio as a function of epicentral distance is not sensitive to 3-D focusing and defocusing for the source–receiver configuration of the data set. This data set includes about 5500 S and SS measurements that are not affected by mantle transition zone triplications (multiple ray paths), and those measurements are applied in linear inversions to obtainmore »a preliminary 1-D Q model QMSI. This model reveals a high Q region in the uppermost lower mantle. While model QMSI improves the overall datafit of the entire data set, it does not fully explain SS amplitudes at short epicentral distances or the amplitudes of the SSS and SSSS waves. Using forward modelling, we modify the 1-D model QMSI iteratively to reduce the overall amplitude misfit of the entire data set. The final Q model QMSF requires a stronger and thicker high Q region at depths between 600 and 900 km. This anelastic structure indicates possible viscosity layering in the mid mantle.

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  3. In this paper, we introduce two new methods of mitigating decoder error propagation for low-latency sliding window decoding (SWD) of spatially coupled low-density parity-check (SC-LDPC) codes. Building on the recently introduced idea of check node (CN) doping of regular SC-LDPC codes, here we employ variable node (VN) doping to fix (set to a known value) a subset of variable nodes in the coupling chain. Both of these doping methods have the effect of allowing SWD to recover from error propagation, at a cost of a slight rate loss. Experimental results show that, similar to CN doping, VN doping improves performance by up to two orders of magnitude compared to un-doped SC-LDPC codes in the typical signal-to-noise ratio operating range. Further, compared to CN doping, VN doping has the advantage of not requiring any changes to the decoding process. In addition, a log-likelihood-ratio based window extension algorithm is proposed to reduce the effect of error propagation. Using this approach, we show that decoding latency can be reduced by up to a significant fraction without suffering any loss in performance.