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..

Effect of microstructural morphology on the mechanical properties of titanium alloys

Different morphologies of α+β microstructures were obtained in a commercial Ti-6Al-4V alloy by cooling at different rates from the single β-phase region into the two phase region. The effect of such morphologies on mechanical properties was studied using hot compression tests in a Gleeble thermomechanical simulator. A variety of complex morphologies could be obtained since the cooling rate has a significant influence on the β to α phase transformation and the resulting morphological development. While most of the β phase transformed to colonies of α at high cooling rates, it was possible to obtain a complex mixture of a colonies, grain boundary a and lamellar structure by decreasing the cooling rate. These complex morphologies each exhibited distinctive mechanical properties and characteristic dynamic phase transformation behaviour during deformation as a function of strain rate