Robert T. Chien

On the Connection Assignment Problem of Diagnosable Systems

This paper treats the problem of automatic fault diagnosis for systems with multiple faults. The system is decomposed into n units u 1 , u 2 , . . . , u n , where a unit is a well-identifiable portion of the system which cannot be further decomposed for the purpose of diagnosis. By means of a given arrangement of testing links (connection assignment) each unit of the system tests a subset of units, and a proper diagnosis can be arrived at for any diagnosable fault pattern. Methods for optimal assignments are given for instantaneous and sequential diagnosis procedures.

Planning Collision-Free Paths for Robotic Arm Among Obstacles

A theory for planning collision-free paths of a moving object among obstacles is described. Using the concepts of state space and rotation mapping, the relationship between the positions and the corresponding collision-free orientations of a moving object among obstacles is represented as some set of a state space. This set is called the rotation mapping graph (RMG) of that object. The problem of finding collision-free paths for an object translating and rotating among obstacles is thus transformed to that of considering the connectivity of the RMG. Since the connectivity of the graph can be solved by topological methods, the problem of planning collision-free paths is easily solved in theory. Using this theory, a topological method for planning collision-free paths of a rod-object translating and rotating among obstacles is presented. If a nonrigid robotic arm is viewed as a composite rod with some degrees of freedom, the planning of collision-free paths of a robotic arm can be solved in a similar way to a rod.

Algebraic generalization of BCH-Goppa-Helgert codes

Based on the Mattsom-Solomon polynomial, a class of algebraic linear error-correcting codes is proposed, which includes the Bose-Chaudhuri-Hocquenghen (BCH) codes, Goppa codes, and Srivastava codes as subclasses. Several constructive bounds on the minimum distance of these codes are derived and are shown to be achievable using either Berlekamps iterative decoding algorithm or Goppas method based on divided difference. Moreover, it is shown that this class of codes asymptotically approaches the Varshamov-Gilbert bound as n \rightarrow \infty . Although some binary Goppa codes were previously known to have n \leq 2^m, r \leq m \cdot t , and d \geq 2t+ 1 , it is shown that a much larger class of codes also possesses such parameters. Finally, shortened codes are considered. With a limited computer search, a number of good codes were found. It is also observed that the proposed codes have no fundamental difference from those recently given by Helgert.

Two New Edge Detectors

This paper introduces two new edge detection algorithms. One uses multiple difference-based edge detectors. This scheme selects peak center by absolute maximum or center of mass techniques. The other algorithm is motivated by the observation that second-order enhancement improves human contour extraction, but generally confuses difference-based edge detectors. This algorithm translates intensity images into three state images (plus one, zero, and minus one), then uses multiple three-state edge masks to find edge positions. The second scheme has a multiple hardware implementation and interesting biological analogs. Finally, the two operators introduced are compared to some popular edge detection techniques from the literature.

Some results on the minimum distance structure of cyclic codes

This paper presents a number of interesting results relating to the determination of actual minimum distance of cyclic codes. Codes with multiple sets of consecutive roots are constructed. A bound on the minimum weight of odd-weight codewords is determined. Relations on the distribution of roots of the generator polynomial are investigated. Location polynomials of reversible codes are examined. These results are used to obtain better estimates of the minimum distance of many new cyclic codes.

Motion detection and analysis of matching graphs of intermediate-level primitives

Introduces a new primitive, the half-chunk, for encoding boundary, region, and surface information in graph form. General graph matching is discussed and a specific graph matching system based on half-chunk graphs is presented. Following matching, bindings are interpreted as object component motion or depth. The half-chunk graph allows scale and coordinate system independent object models to be represented. Half-chunk graphs may encode 2-D or 3-D structure equally well.

Multiple-burst-error correction by threshold decoding*

A class of cyclic product codes capable of correcting multiple-burst errors is studied. A code of dimension p is constructed by forming the cyclic product of p one-dimensional single-parity-check codes of relatively prime block lengths. A consideration of the parity-check matrix shows that there are p orthogonal parity checks on each digit, and a burst of length b can corrupt at most one of the parity checks. The maximum allowable value of b can be easily calculated. The codes are completely orthogonal and [p/2] bursts of length b or less can be corrected by one-step threshold decoding. These codes have a very interesting geometric structure which is also discussed. Using the geometric structure, we show that the codes can also correct 2p−2 bursts of relatively short lengths. However, in this case the errors cannot be corrected by threshold decoding.

Coding for error control

Tutorially presented are theoretical and practical concepts that underlie error-control coding for data computing, storage, and transmission systems. Emphasis is on cyclic codes, the most deeply studied and widely used of the many available codes. Operations of typical binary shift registers illustrate the encoding and decoding processes. Strategic considerations for applying coding to computer-communication systems are discussed. Actual applications further exemplify the basis for code selection.

Single- and multiple-burst-correcting properties of a class of cyclic product codes

The direct product of p single parity-check codes of block lengths n_1,n_2, \cdots ,n_p is a cyclic code of block length n_1 \times n_2 \times \cdots \times n_p with (n_1 - 1) \times (n_2 - 1) \times \cdots \times (n_p - 1) information symbols per block, if the integers n_1,n_2 \cdots ,n_p are relatively prime in pairs. A lower bound for the single-burst-correction (SBC) capability of these codes is obtained. Then, a detailed analysis is made for p = 3 , and it is shown that the codes can correct one long burst or two short bursts of errors. A lower bound for the double-burst-correction (DBC) capability is derived, and a simple decoding algorithm is obtained. The generalization to correcting an arbitrary number of bursts is discussed.

Some Results in the Theory of Arithmetic Codes

This paper presents a number-theoretic investigation of the structure of cyclic binary arithmetic AN codes. The interval [0, B − 1] of represented integers is related to the code length n through 2 n −1 = AB . The analysis is based on the partition of the integers 1 ⩽ N ⩽ B − 1 into orbits, which are analogous to cosets of the multiplicative subgroup of the powers of 2 modulo B . The relation between the minimum distance and the orbit, and properties of composite numbers are used in developing a simple search strategy for codes. The presented analysis is used as a guide for the construction of many codes of moderate distance and high rate which lie between the two known extremes of the single-error correcting Brown codes and of the maximum-sequence-like codes of Barrows and Mandelbaum. The analysis also leads to a class of nontrivial augmented codes obtained from known codes. A list of codes of length ⩽ 36 generated by computer search of orbits is finally presented.