Algebraic Decoding of a Class of Binary Cyclic Codes Via Lagrange Interpolation Formula

作者：Chang Yaotsu^*; Lee Chong Dao

来源：IEEE Transactions on Information Theory, 2010, 56(1): 130-139.

DOI：10.1109/TIT.2009.2034799

• Decoding algorithm
• general error-locator polynomial
• Lagrange interpolation formula (LIF)
• quadratic residue (QR) code
• syndrome

In this paper, three algebraic decoding algorithms are proposed for the binary quadratic residue (QR) codes generated by irreducible polynomials. The polynomial relations among the syndromes and the coefficients of the error-locator polynomials have been computed with Lagrange interpolation formula (LIF). Unlike some previous QR decoders, which may take several iterations to decode a corrupted word, the iteration number of the first two algorithms is at most one. The processes in the first algorithm are the calculation of consecutive syndromes, inverse-free Berlekamp-Massey algorithm (IFBMA), and the Chien search. One of Orsini-Sala's results on the structure of general error-locator polynomials is generalized and applied to derive the second (respectively, third) algorithm that consists of the determination of general error-locator polynomial (respectively, classical error-locator polynomials) and the Chien search. Finally, the (17, 9, 5), (23, 12, 7), and (41, 21, 9) QR decoders are illustrated and their complexity analyses are given.

• 出版日期2010-1