论文信息 - The design of totally self-checking checkers for some classes of Hadamard codes

The design of totally self-checking checkers for some classes of Hadamard codes

Hadamard codes are derived from the rows of Hadamard matrices, and are widely used in signal processing, feature extractions, communications, and so forth. In this paper, the designs of totally self-checking checkers for these codes are considered. On account of their property that total number of codewords are small and their patterns are limited, same extra ideas are required to establish self-testing properties. There are 3 kinds of Hadamard matrices, Sylvester type, M sequence type and Paley type. The checker design obtained here is applicable to Paley type matrices of degree 8m+4, where m is a nonnegative integer, by making use of the property of difference sets. In the case of matrices of degree 8m+8, the checker design is still an open question. It is also shown that Sylvester type and M sequence type Hadamard codes checkers are obtained by systematic code checker design. Therefore, the total results obtained here cover the majority of Hadamard codes known so far.

[1] Irith Pomeranz,et al. On codeword testing of two-rail and parity TSC checkers , 1994, Proceedings of IEEE 24th International Symposium on Fault- Tolerant Computing.

[2] Richard Bauckham. Text-Books , 1904 .

[3] Dimitris Nikolos,et al. Fast and low cost TSC checkers for 1-out-of-n and (n- l)-out-of-n codes in MOS transistor implementation , 1991 .

[4] A. Roli. Artificial Neural Networks , 2012, Lecture Notes in Computer Science.

[5] J. Lindy. Books , 1985, The Lancet.

[7] Stanislaw J. Piestrak,et al. The minimal test set for sorting networks and the use of sorting networks in self-testing checkers for unordered codes , 1990, [1990] Digest of Papers. Fault-Tolerant Computing: 20th International Symposium.

[8] Kishan G. Mehrotra,et al. Elements of artificial neural networks , 1996 .

[9] J. A. Gordon,et al. Digital Majority Logic-Multiplexer Ustng Walsh Functions , 1971 .

[10] Maurice J. Bach. The Design of the UNIX Operating System , 1986 .

[11] I. M. Jacobs,et al. Principles of Communication Engineering , 1965 .

[12] S. M. Reddy. Note on Self-Checking Checkers , 1974, IEEE Transactions on Computers.

[13] E. J. Claire,et al. Practical Techniques for Transform Data Compression/Image Coding , 1971 .

[14] Henning F. Harmuth,et al. Applications of Walsh functions in communications , 1969, IEEE Spectrum.