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This paper presents a novel encoding algorithm for QC-LDPC codes constructed from Reed-Solomon codes. The encoding is performed in the transform domain via Galois Fourier transformation. Message bits are encoded in sections corresponding to sub-matrices of the parity-check matrix in the transform domain. Because of the structure of the parity-check matrices of these LDPC codes, the encoding can be...
This paper presents two novel low-complexity encoding algorithms for quasi-cyclic (QC) codes based on Galois Fourier transform. The key idea behind them is making use of the block diagonal structure of the transformed generator matrix. The first one, named encoding by Galois Fourier transform, is equivalent to the fast implementations of the traditional encoding by Galois Fourier transform. The second...
This paper presents a novel low-complexity encoding algorithm for binary quasi-cyclic (QC) codes based on matrix transformation. First, a message vector is encoded into a transformed codeword in the transform domain. Then, the transmitted codeword is obtained from the transformed codeword by the inverse Galois Fourier transform. Moreover, a simple and fast mapping is devised to post-process the transformed...
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