Efficient Decoding Algorithm for Cyclically Permutable Code

When a sender side and a receiver side are not synchronized, it is difficult to correctly decode a received codeword. In this study, we investigate a Cyclically Permutable Code (CPC) to immunize the synchronization loss as well as an additive noise over a communication channel. A cyclic code retains the characteristic that cyclically shifted codewords belong to the same code. The codewords in cyclic code can form small cyclic groups such that all codeword in each group is a cyclically shifted version of a certain codeword. The CPC encoder selects each one codeword in each group. Even if a received codeword is cyclically shifted from an original codeword, the receiver can identify the group to which the original codeword belongs. Although there are some methods to generate CPC, the decoding method has not been discussed. Considering the algebraic property of CPC, an efficient decoding method is proposed in this study. The validity of the proposed method is evaluated by simulation.