scholarly journals Trapping Sets of Quantum LDPC Codes

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 562
Author(s):  
Nithin Raveendran ◽  
Bane Vasić
Keyword(s):  
Finite Length ◽  
Parity Check ◽  
Error Floor ◽  
Hardware Complexity ◽  
Trapping Sets ◽  
Iterative Decoders ◽  
Syndrome Decoding ◽  
Systematic Methodology ◽  
Code Graph ◽  
Definition Of

Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles, detrimental graphical configurations known as trapping sets (TSs) present in a code graph as well as symmetric degeneracy of errors. These factors significantly degrade the decoder decoding probability performance and cause so-called error floor. In this paper, we establish a systematic methodology by which one can identify and classify quantum trapping sets (QTSs) according to their topological structure and decoder used. The conventional definition of a TS from classical error correction is generalized to address the syndrome decoding scenario for QLDPC codes. We show that the knowledge of QTSs can be used to design better QLDPC codes and decoders. Frame error rate improvements of two orders of magnitude in the error floor regime are demonstrated for some practical finite-length QLDPC codes without requiring any post-processing.

Assessment of Influence of Land Use–Transportation System on Travel Behavior

1997 ◽  
Vol 1607 (1) ◽  
pp. 105-115 ◽  
Author(s):  
Michael G. McNally ◽  
Anup Kulkarni
Keyword(s):  
Land Use ◽  
Travel Behavior ◽  
Transportation System ◽  
Transportation Systems ◽  
Neighborhood Design ◽  
Preliminary Assessment ◽  
Modeling Framework ◽  
Systematic Methodology ◽  
Definition Of ◽  
Planned Unit Development

An empirical assessment of the interaction between the land use–transportation system and travel behavior is presented. A methodology for identifying a range of land use–transportation systems by a clustering technique with network and land use inputs was developed. Twenty neighborhoods from Orange County, California, were considered in this process. Three groups, or themes, were found to best represent the neighborhoods in the sample area: one each associated with the conventional definition of traditional and neotraditional neighborhood design (TND) and planned unit development (PUD) neighborhoods and one representing neighborhoods that blend characteristics of TND and PUD. Conventional measures of individual travel behavior were compared with an analysis of variance between the themes to identify significant differences, controlling for socioeconomic characteristics. Research results include the development of (a) a systematic methodology to identify a more explicit land use–transportation dimension, (b) an estimate of the potential effectiveness of design-oriented solutions to reduce automobile congestion by using the developed themes, and (c) a preliminary assessment of the extent to which development themes can be used to improve the current modeling framework.

Mass and charge conservation check in dynamic models: application to the new ADM1 model

2006 ◽  
Vol 53 (1) ◽  
pp. 225-240 ◽  
Author(s):  
M. de Gracia ◽  
L. Sancho ◽  
J.L. García-Heras ◽  
P. Vanrolleghem ◽  
E. Ayesa
Keyword(s):  
Organic Matter ◽  
Anaerobic Digestion ◽  
Dynamic Models ◽  
Nitrogen Release ◽  
Mass Fluxes ◽  
Systematic Methodology ◽  
Mass Fractions ◽  
Model Components ◽  
Definition Of ◽  
Elemental Mass

This paper proposes a systematic methodology for the analysis of the mass and charge balances in dynamic models expressed using the Petersen matrix notation. This methodology is based on the definition of the model components via elemental mass fractions and in the estimation of the COD as a function of the redox equations associated with these elements. This approach makes the automatic calculation of all the stoichiometric coefficients under different measuring units and the study of COD, charge or mass fluxes easier. As an example of its application this methodology was applied to the ADM1 in order to illustrate its usefulness for the analysis of organic matter characterisation, nitrogen release or biogas composition in anaerobic digestion. The application of the methodology for a rigorous integration of different IWA models is proposed for further study.

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