Jørn Justesen

Performance of Product Codes and Related Structures with Iterated Decoding

Several modifications of product codes have been suggested as standards for optical networks. We show that the performance exhibits a threshold that can be estimated from a result about random graphs. For moderate input bit error probabilities, the output error rates for codes of finite length can be found by easy simulations. The analysis indicates that the performance curve can be extrapolated until the error floor is reached. The analysis allows us to calculate the error floors and avoid time-consuming simulations.

Error correcting coding for OTN

Forward error correction codes for 100 Gb/s optical transmission are currently receiving much attention from transport network operators and technology providers. We discuss the performance of hard decision decoding using product type codes that cover a single OTN frame or a small number of such frames. In particular we argue that a three-error correcting BCH is the best choice for the component code in such systems.

Analysis of Iterated Hard Decision Decoding of Product Codes with Reed-Solomon Component Codes

Products of Reed-Solomon codes are important in applications because they offer a combination of large blocks, low decoding complexity, and good performance. A recent result on random graphs can be used to show that with high probability a large number of errors can be corrected by iterating minimum distance decoding. We present an analysis related to density evolution which gives the exact asymptotic value of the decoding threshold and also provides a closed form approximation to the distribution of errors in each step of the decoding of finite length codes.

Graph Codes with Reed-Solomon Component Codes

We treat a specific case of codes based on bipartite expander graphs coming from finite geometries. The code symbols are associated with the branches and the symbols connected to a given node are restricted to be codewords in a Reed-Solomon code. We give results on the parameters of the codes and methods for their encoding

Spatial and temporal changes in the morphology of preosteoblastic cells seeded on microstructured tantalum surfaces

It has been widely reported that surface morphology on the micrometer scale affects cell function as well as cell shape. In this study, we have systematically compared the influence of 13 topographically micropatterned tantalum surfaces on the temporal development of morphology, including spreading, and length of preosteoblastic cells (MC3T3-E1). Cells were examined after 0.5, 1, 4, and 24 h on different Ta microstructures with vertical dimensions (heights) of 0.25 and 1.6 mum. Cell morphologies depended upon the underlying surface topography, and the length and spreading of cells varied as a function of time with regard to the two-dimensional pattern and vertical dimension of the structure. Microstructures of parallel grooves/ridges caused elongated cell growth after 1 and 4 h in comparison to a flat, nonstructured, reference surface. For microstructures consisting of pillars, cell spreading was found to depend on the distance between the pillars with one specific pillar structure exhibiting a decreased spreading combined with a radical change in morphology of the cells. Interestingly, this morphology on the particular pillar structure was associated with a markedly different distribution of the actin cytoskeleton. Our results provide a basis for further work toward topographical guiding of cell function.

On the sizes of expander graphs and minimum distances of graph codes

Abstract We give lower bounds for the minimum distances of graph codes based on expander graphs. The bounds depend only on the second eigenvalue of the graph and the parameters of the component codes. We also give an upper bound on the size of a degree regular graph with given second eigenvalue.

Calculation of power spectra for block coded signals

We present some improvements in the procedure for calculating power spectra of signals based on finite state descriptions and constant block size. In addition to simplified calculations, our results provide some insight into the form of the closed expressions and to the relation between the spectra and other properties of the codes.

The minimum distance of graph codes

We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other geometries. We give results on the minimum distances of the codes.

Block Pickard Models for Two-Dimensional Constraints

In Pickard random fields (PRF), the probabilities of finite configurations and the entropy of the field can be calculated explicitly, but only very simple structures can be incorporated into such a field. Given two Markov chains describing a boundary, an algorithm is presented which determines whether a PRF consistent with the distribution on the boundary and a 2-D constraint exists. Iterative scaling is used as part of the algorithm, which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists. A PRF is defined for the domino tiling constraint represented by a quaternary alphabet. PRF models are also presented for higher order constraints, including the no isolated bits (n.i.b.) constraint, and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols.

On the dimension of graph codes with Reed-Solomon component codes

We study a class of graph based codes with Reed-Solomon component codes as affine variety codes. We give a formulation of the exact dimension of graph codes in general. We give an algebraic description of these codes which makes the exact computation of the dimension of the graph codes easier.