| Summary: | 碩士 === 義守大學 === 資訊工程學系碩士班 === 96 === Among the well-known error correcting codes, the quadratic residue (QR) codes can correct more random errors than other cyclic codes, but they are difficult to decode for the insufficient consecutive syndromes. A method using the Lagrange interpolation formula to obtain the missing syndromes in binary QR codes is proposed by Chang.The obtained formula is the represention of the primary unknown syndrome in terms of the primary known syndrome and has nice properties, namely L(x). In this thesis, we proposed several efficient hardware designs to implement this obtained polynomial. Thus, the primary unknown syndrome can be calculated by those proposed hardware designs. Then we can compute the all needed consecutive syndromes to decode the binary QR codes by accompany the module of free discrepancy Berlekamp-Massey algorithm and Chien search. Finally, a QR decoder hardware with length 41 will be implemented and is based on the proposed decoding design. We hope that QR decoder can realized in the future digital product.
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