Abstract

In this paper, we present an efficient systematic encoding algorithm for quasi-cyclic (QC) low-density parity-check (LDPC) codes which are related to cyclic maximum-distance separable (MDS) codes. The algorithm has linear time complexity, and it can be easily implemented by using polynomial multiplication and division circuits. We show that the division polynomials can be completely characterized by its zeros and that the sum of the numbers of the zeros is equal to the parity-length of the codes.

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