We proposed a soft-decision decoding algorithm for cyclic codes based on energy minimization principle. This letter presents the algorithm which improves decoding performance and decoding complexity of the previous method by giving more initial positions and introducing a new criterion for terminating the decoding procedure. Computer simulation results show that both the decoded block error rate and the decoding complexity decrease by this method more than by the previous method.

We propose a novel soft-decision decoding algorithm for cyclic codes based on energy minimization principle. The well-known soft-decision decoding algorithms for block codes perform algebraic (hard-decision) decoding several times in order to generate candidate codewords using the reliability of received symbols. In contrast, the proposed method defines energy as the Euclidean distance between the received signal and a codeword and alters the values of information symbols so as to decrease the energy in order to seek the codeword of minimum energy, which is the most likely codeword. We let initial positions be the information parts of signals obtained by cyclically shifting a received signal and look for the point, which represents a codeword, of minimum energy by moving each point from several initial positions. This paper presents and investigates reducing complexity of the soft-decision decoding algorithm. We rank initial positions in order of reliability and reduce the number of initial positions in decoding. Computer simulation results show that this method reduces decoding complexity.