The write-margin of the iterative decoding systems for the binary and non-binary low-density parity-check (LDPC) codes are studied in the magnetic recording system using a bit-patterned medium (BPM) R/W channel with write-errors caused by the write-head field gradient, the media switching field distribution (SFD), the magnetization fields from adjacent islands, and the island position deviation. The performances of iterative decoding systems using the binary and non-binary LDPC codes are evaluated by computer simulation at an areal recording density of 2 Tb/inch2. The results show that the non-binary LDPC coding and iterative decoding system improves the write-margin compared with the binary LDPC system. Furthermore it is clarified that in order to obtain the sufficient write-margin, it is important to suppress the influence of the demagnetization fields from adjacent islands.

One of the primacy concerns in developing computer embedded safety-critical systems is how to develop quality software. Software must fulfill its functional requirements and must not contribute to the violation of safety properties of the entire system. To this end, capturing error free and satisfactory functional requirements is crucial before proceeding to the subsequent development phases. We describe an approach to specifying and verifying software for safety-critical systems with the practical formal method SOFL (Structured-Object-based-Formal Language). Requirements specification focuses on the functionality of the software, but with the consideration of safety constraints and its interaction with the surrounding operational environment. The verification of specifications can be carried out using three techniques: data flow reachability checking, specification, testing, and rigorous proofs, respectively. We apply this approach to a realistic railway crossing controller for a case study and analyzes its result.

An efficient 3D object management system using the hierarchical spatial data structure, called the MD-tree, is developed for an interactive walkthrough for the wide area facility management system. In the system, 3D objects in a city area are automatically generated from 2D-maps based on the appropriate rules. The entire 3D space is split into several layers depending on the height. The objects intersecting with a layer are managed by a 2D MD-tree corresponding to that layer. The objects close to a viewpoint are searched by the MD-tree corresponding to the lower layers. To provide the background of the scene (the distance view), far objects are searched by the MD-tree corresponding to the higher layer, because the lower objects far from the viewpoint may not be visible. The potentially visible objects can be obtained in a few milliseconds by the MD-trees. According as the number of the obtained objects and the distance from the viewpoint to the object, the rendering complexity of each object is controlled to accomplish the constant time rendering. With these techniques, an interactive walkthrough with the constant time response can be realized for the wide city area with more than 200,000 objects.>

A new multidimensional data structure, multidimensional tree (MD-tree), is proposed. The MD-tree is developed by extending the concept of the B-tree to the multidimensional data, so that the MD-tree is a height balanced tree similar to the B-tree. The theoretical worst-case storage utilization is guaranteed to hold more than 66.7% (2/3) of full capacity. The structure of the MD-tree and the algorithms to perform the insertion, deletion, and spatial searching are described. By the series of simulation tests, the performances of the MD-tree and conventional methods are compared. The results indicate that storage utilization is more than 80% in practice, and that retrieval performance and dynamic characteristics are superior to conventional methods.>

An efficient spatial data management method for non-zero size spatial objects, called R(Region)MD-tree, is proposed. In this method, a graphic object in an N-dimensional space is represented as a point in a 2*N dimensional space by the centroid and the extension in each axial direction. The point data are managed by the MD-tree after applying the coordinate transformation. The point location problem or range searching in the original N-dimensional space are carried out by the hyper-rectangular range searching to the point data in the 2*N dimensional space. In this representation and data management, data objects are sorted and classified according to not only the location but also the size of the data. By the simulation experiments, the performances and efficiencies of the RMD-tree are compared with the conventional MD-tree and the R-tree. As the data objects become larger, the RMD-tree is superior in the searching speed by 2 approximately 4 times to the conventional ones, and the performances are almost comparable even if the objects are points or small graphic data.>

A multilayer (ML) data structure, which is a hierarchical data structure for N-dimensional data classified into layers, is proposed. In the ML structure, a node structure is extended so that data can be stored not only in the leaves (terminal nodes) but also in internal nodes by adding a layer-management mechanism. The creation, management, and searching methods of the ML structure are described, taking two-dimensional point data classified into layers as an object. The management of line data or expansion to n(n>2)-dimensional data can be easily realized. Good retrieval performances are obtained in the case of a spatial search for a specific layer's data and that for plural layers' data.>

A multidimensional data structure, the MD-tree (multidimensional tree), is proposed. The MD-tree is developed by extending the concept of the B-tree to multidimensional data, so that the MD-tree is a height-balanced tree similar to the B-tree and, even its worst-case storage utilization is more than 66.7%. A description is given of the structure of an MD-tree and the results of a series of simulation tests which indicate that the storage utilization is more than 80% in practice and that the retrieval performance and the dynamic characteristics are superior to those of conventional methods.>