Abstract
AbstractThis paper proposes a method of constructing nonlinear cyclic codes that form an additive group for which the decoding complexity or error correcting performance is improved relative to RS codes, which are typical linear cyclic codes. First, a code with information digit count k = 1 is constructed by using multiple RS code basis vectors obtained from Galois field Fourier transforms. Then, for k 1, codes are constructed from this code by using idempotent elements. Also, a code with code length n = 7 was constructed as an example, and both its minimal trellis diagram complexity and bit error rate on the AWGN channel due to a computer simulation were shown to be excellent. In addition, an iterative decoder was applied to the codes with k = 4 and 5, which had peak trellis diagram complexity, and it was shown that the decoding complexity could be reduced. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 86(7): 64–73, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.1170
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