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Error-trellis state complexity of LDPC convolutional codes based on circulant matrices

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3 Author(s)
Masato Tajima ; Graduate School of Sci. and Eng., University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan ; Koji Okino ; Takashi Miyagoshi

Let H(D) be the parity-check matrix of an LDPC convolutional code corresponding to the parity-check matrix H of a QC code obtained using the method of Tanner et al. We see that the entries in H(D) are all monomials and several rows (columns) have monomial factors. Let us cyclically shift the rows of H. Then the parity-check matrix H'(D) corresponding to the modified matrix H' defines another convolutional code. However, its free distance is lower-bounded by the minimum distance of the original QC code. Also, each row (column) of H'(D) has a factor different from the one in H(D). We show that the statespace complexity of the error-trellis associated with H'(D) can be significantly reduced by controlling the row shifts applied to H with the error-correction capability being preserved.

Published in:

Information Theory and its Applications (ISITA), 2010 International Symposium on

Date of Conference:

17-20 Oct. 2010