Peter Oswald

Capacity-achieving sequences for the erasure channel

This paper starts a systematic study of capacity-achieving (c.a.) sequences of low-density parity-check codes for the erasure channel. We introduce a class A of analytic functions and develop a procedure to obtain degree distributions for the codes. We show various properties of this class which help us to construct new distributions from old ones. We then study certain types of capacity-achieving sequences and introduce new measures for their optimality. For instance, it turns out that the right-regular sequence is c.a. in a much stronger sense than, e.g., the Tornado sequence. This also explains why numerical optimization techniques tend to favor graphs with only one degree of check nodes.

Composite primal/dual √3-subdivision schemes

We present new families of primal and dual subdivision schemes for triangle meshes and √3-refinement. The proposed schemes use two simple local rules which cycle between primal and dual meshes a number of times. The resulting surfaces become very smooth at regular vertices if the number of cycles is ≥ 2. The C1-property is violated only at low-valence irregular vertices, and can be restored by slight modifications of the local rules used.As a generalization, we introduce a wide class of composite subdivision schemes suitable for arbitrary topologies and refinement rules. A composite scheme is defined by a simple upsampling from the coarse to a refined topology, embedded into a cascade of geometric averaging operators acting on coarse and/or refined topologies. We propose a small set of such averaging rules (and some of their parametric extensions) which allow for the switching between control nets associated with the same or different topologic elements (vertices, edges, faces), and show a number of examples, based on triangles, that the resulting class of composite subdivision schemes contains new and old, primal and dual schemes for √3-refinement as well as for quadrisection. As a common observation from the examples considered, we found that irregular vertex treatment is necessary only at vertices of low valence, and can easily be implemented by using generic modifications of some elementary averaging rules.

Greedy algorithms and bestm-term approximation with respect to biorthogonal systems

The article extends upon previous work by Temlyakov, Konyagin, and Wojtaszczyk on comparing the error of certain greedy algorithms with that of best m-term approximation with respect to a general biorthogonal system in a Banach space X. We consider both necessary and sufficient conditions which cover most of the special cases previously considered. Some new results concerning the Haar system in L1, L∞, and BMO are also included.

Analysis of scalable PMD compensators using FIR filters and wavelength-dependent optical power measurements

We investigate the potential of optical n-stage FIR filter architectures for PMD compensation (PMDC) based on frequency-dependent optical power monitoring. The measurement information is used to partially estimate the channels Jones matrix U(/spl omega/), and the filter parameters are adjusted based on solving a nonlinear least-squares problem which mimics the approximate inversion of U(/spl omega/) by the filter. Numerical studies of the optimization method and outage probability simulations show the robustness and scalability of the proposed concept.

Compact integrated tunable dispersion compensators

Tunable dispersion compensators for 10 and 40 Gb/s signals using planar waveguide ring-resonator allpass filters are reviewed. Recent work using tunable ring-resonators as building blocks for PMD emulation, compensation and monitoring are also discussed.

The application of integrated ring resonators to dynamic dispersion compensation

Recent results using planar waveguide ring-resonator allpass filters to compensate chromatic dispersion on 10 and 40 Gb/s signals are reviewed. Tunable ring-resonator filter architectures for PMD emulation, compensation and monitoring are also discussed.

Reset-free integrated polarization controller using phase shifters

An endless, reset-free polarization controller implemented with planar lightwave circuits using phase shifters for tuning is proposed and demonstrated. By avoiding the need for tunable polarization mode converters, simple fabrication processes and a large range of material systems can be used, since neither the electrooptic effect nor a rotatable birefringence axis are necessary for device operation. The proof of concept is demonstrated by implementing the equivalent of a rotating waveplate using Ge-doped silica-on-silicon waveguides and thermooptic phase shifters. The polarization controller is shown to have excellent tolerance to fabrication variations. Fast thermooptic control (on the order of 10 kHz) is achieved using high-index-contrast (4%) waveguides.