No abstract

The performance of iterative decoding of Low Density Parity Check (LDPC) codes over Binary Erasure Channels can be completely characterized by the study of stopping sets. Therefore, the burst erasure correction capability of a given LDPC code can be readily quantified by searching for stopping sets within consecutive bit nodes. In this work we study the optimal permutation of the bit nodes that will result in the maximum possible burst erasure correction capability for a given LDPC code. Noting that this is essentially a combinatorial optimization problem that is highly likely to be NP-hard, we adopt a simulated annealing based approach for finding the optimal permutation. We present bounds based on stopping sets that limit the burst erasure correction capability. As part of our results, we provide interleavers that greatly improve the burst erasure correction capability of protograph quasi-cyclic LDPC codes used in the WiMax standard.

Transmission diffraction gratings operating at 1,565 nm based on multilayer porous silicon films are modeled, fabricated, and tested. Features down to 2 μm have been patterned into submicron-thick mesoporous films using standard photolithographic and dry etching techniques. After patterning of the top porous film, a second anodization can be performed, allowing an under-layer of highly uniform porosity and thickness to be achieved. High transmission greater than 40% is measured, and modeling results suggest that a change in diffraction efficiency of 1 dB for a 1% change in normalized refractive index can be achieved. Preliminary measurement of solvent vapor shows a large signal change from the grating sensor in agreement with models.

A phase-equivalence of a triangular grating and a "corresponding" blazed structure is proposed. This equivalence is used to simplify the analysis of the grating, which otherwise would require the repetitive application of the simplified modal method to each lamellar grating that constitutes the triangular grating. The concept is used to arrive at an equation for the phase introduced by the triangular grating. The proposed model is verified by finite element simulations. A method of fabricating a triangular grating in quartz is presented. The proposed theory, along with optical testing, can be used as a non-destructive means by which to estimate the height of the triangular grating during the dry etching process.

We describe a calibrator used to evaluate the response of an optical reflective sensor as a function of the reflector distance. It is easy to fabricate and assemble.