Studies on construction of error-correcting codes and soft-input soft-output decoding

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The soft-input and soft-output decoding is important technology as decoding of parallel(turbo)and serial concatenated codes. The soft-in soft out decoding and the concatenated codes are key technology of reliability of the advanced communication technology. In this Study, it is aiming to propose the new decoding algorithm and new code construction. The alogorithm is based on the soft-in soft-out decoding and the code is suitable for new soft-in soft-out decoding. For the study, we construct the simulator of turbo decoding for the turbo code with memory channel, which is adaptable various data format of turbo codes and magnetic and mobile channel with/without turbo equalization.The soft-output information(i.e.reliability information)is the posterior probability of each information bit, and is calculated by maximum a posteriori(MAP)decoding, theoretically. The algorithms of MAP decoding(BCJR algorithm and so on)require complicated computation. That is not only number of operation but also memory space of working data. Therefore, sub-optimal, simplified soft-in soft-out decoding algorithms(i.e.SOVA and so on)have been studies. theretical studies of such a decoding have been studied from the viewpoints of learning theory, symbol dynamics, derivative geometry and so on.In this study, we find new viewpoint to achieve highly reliability of feedback decoding with soft-output. That is ordering of feed back scheme, and is related the variable threshold decoding of soft-input decoding of majority logic decodable codes.