Abstract
AbstractThe error‐control code is used widely at present in digital communication and storage systems. When the error‐control code is applied to the actual system, however, several problems arise that cannot be solved by the traditional code theory.One such problem is synchronization. In the usual application of the error‐control code, it is not tacitly assumed that the synchronization is already established. Such an assumption is not always valid in the actual situation. If the synchronization is not established, it is difficult for the error‐control code to exhibit its full error correction ability.From such a viewpoint, this paper does not use the assumption that the synchronization is established. Both the initial synchronization and error control are considered, i.e., the establishment of synchronization from the unsynchronized state and the execution of the correct decoding are discussed.This paper proposes the initial synchronization decoding model. Two code structures are considered, and the decoding method as well as the asymptotic properties of the error exponent are discussed. As a result, a practical theory for the synchronization and error control is shown, considering simultaneously the initial synchronization and error control. Its features are the high efficiency and the decoding which is not very complex.
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