From Cages to Trapping Sets and Codewords: A Technique to Derive Tight Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of LDPC Codes

Cages, defined as regular graphs with minimum number of nodes for a given girth, are well-studied in graph theory. Trapping sets are graphical structures responsible for error floor of low-density parity-check (LDPC) codes, and are well investigated in coding theory. In this paper, we make connections between cages and trapping sets. In particular, starting from a cage (or a modified cage), we construct a trapping set in multiple steps. Based on the connection between cages and trapping sets, we then use the available results in graph theory on cages and derive tight upper bounds on the size of the smallest trapping sets for variable-regular LDPC codes with a given variable degree and girth. The derived upper bounds in many cases meet the best known lower bounds and thus provide the actual size of the smallest trapping sets. Considering that non-zero codewords are a special case of trapping sets, we also derive tight upper bounds on the minimum weight of such codewords, i.e., the minimum distance, of variable-regular LDPC codes as a function of variable degree and girth

Energy, economic, and environmental analysis of converging air-based photovoltaic-thermal (air/PV-T) systems: A yearly benchmarking

Two converging channel configurations of photovoltaic-thermal (PV-T) systems, i.e., inlet and outlet at different sides (Case 1) and the inlet at the middle and outlets at the sides (Case 2), are investigated numerically. The results reveal that Case 1 features a nearly uniform and lower temperature distribution (up to 7 °C) for practical air flows, and the appropriate convergence ratio is 2:1 (inlet to outlet channel height) for which the PV surface temperature is lower by 8 °C than that of a similar conventional collector. Meanwhile, energy analyses based on the so called ‘rate of extra energy gain per PV surface area..

The algebraic hyperstructure of elementary particles in physical theory

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.Comment: 13 page