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Hua Zhou, D. Mitchell, N. Görtz, D. Costello:
"Distance spectrum estimation of LDPC convolutional codes";
Talk: IEEE International Symposium on Information Theory, Cambridge, MA, USA; 07-01-2012 - 07-06-2012; in: "Proceedings 2012 IEEE International Symposium on Information Theory (ISIT)", IEEE Xplore, (2012), ISBN: 978-1-4673-2580-6; 473 - 477.

Time-invariant low-density parity-check convolutional codes (LDPC-CCs) derived from corresponding quasi-cyclic (QC) LDPC block codes (LDPC-BCs) can be described by a polynomial syndrome former matrix (polynomial-domain transposed parity-check matrix). In this paper, an estimation of the distance spectrum of time-invariant LDPC-CCs is obtained by splitting the polynomial syndrome former matrix into submatrices representing "super codes" and then evaluating the linear dependence between codewords of the corresponding super codes. This estimation results in an upper bound on the minimum free distance of the original code and, additionally, a lower bound on the number of codewords Aw with Hamming weight w.

Time-invariant low-density parity-check convolutional codes (LDPC-CCs) derived from corresponding quasi-cyclic (QC) LDPC block codes (LDPC-BCs) can be described by a polynomial syndrome former matrix (polynomial-domain transposed parity-check matrix). In this paper, an estimation of the distance spectrum of time-invariant LDPC-CCs is obtained by splitting the polynomial syndrome former matrix into submatrices representing "super codes" and then evaluating the linear dependence between codewords of the corresponding super codes. This estimation results in an upper bound on the minimum free distance of the original code and, additionally, a lower bound on the number of codewords Aw with Hamming weight w.

LDPC convolutional codes, distance spectrum

http://dx.doi.org/10.1109/ISIT.2012.6284234