Maximum-likelihood decoding for cyclic codes using the spectrum masking
Koki Shibata, Shin-ya Murata, Kiyoshi Tanaka, Tatsuo Sugimura, Shinjiro Osita · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 2000
This paper proposes an efficient maximum-likelihood decoding algorithm (hard decision) for cyclic codes such as BCH code. As the first step, the frequency spectrum of the polynomial over the finite field is analyzed by the Fourier transform over the finite field. The normalizing polynomial that masks the particular spectrum is introduced based on the viewpoint of the spectrum. Then, the normalizing parity check polynomial is used to extract the information concerned with errors on the received word. Based on the extracted information concerned with errors, and the fact that the occurrence probability is higher for the error with a smaller weight, maximum-likelihood decoding is shown to be executed efficiently in hard-decision decoding using the code word obtained from the successively generated error candidates. Furthermore, an efficient generation method for the error candidates is also proposed. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(1): 78–89, 2000