A construction of single error correcting and multiple unidirectional error detecting codes

Abstract

This paper proposes a construction method for a code (SEC‐MUED code) which corrects single errors and detects multiple unidirectional errors. It is a kind of concatenated code which can be obtained by concatenating the check bits of a Hamming single error correcting code, Berger code, parity code and Berger code with natural number weight assigned to logic value 0 with the information bits. Another method of construction of an SEC‐MUED code has already been proposed by Bose et al. This paper first discusses the construction of the proposed code, proof of the code and construction of the encoder and the decoder. Then a quantitative comparison is made of the proposed code and the code by Berger et al. from the viewpoint of the number of check bits, the number of gates in the signal path of the encoder and decoder, and the complexity of hardware from the implementation viewpoint. As a result, it is shown that the proposed code results in fewer check bits than the code by Bose et al., fewer gates in the encoder and the decoder and less hardware complexity. For example, for information bit length of 64, the number of gates is 69% and 58% of the Bose code in encoding and decoding, respectively, and the hardware complexity is 51% of the Bose code. The proposed code is thus shown to be a more efficient SEC‐MUED code.