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    On the Minimum Distance of Array-Based Spatially-Coupled Low-Density Parity-Check Codes

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    An array low-density parity-check (LDPC) code is a quasi-cyclic LDPC code specified by two integers qq and mm, where qq is an odd prime and m≀qm \leq q. The exact minimum distance, for small qq and mm, has been calculated, and tight upper bounds on it for m≀7m \leq 7 have been derived. In this work, we study the minimum distance of the spatially-coupled version of these codes. In particular, several tight upper bounds on the optimal minimum distance for coupling length at least two and m=3,4,5m=3,4,5, that are independent of qq and that are valid for all values of qβ‰₯q0q \geq q_0 where q0q_0 depends on mm, are presented. Furthermore, we show by exhaustive search that by carefully selecting the edge spreading or unwrapping procedure, the minimum distance (when qq is not very large) can be significantly increased, especially for m=5m=5.Comment: 5 pages. To be presented at the 2015 IEEE International Symposium on Information Theory, June 14-19, 2015, Hong Kon

    On the Minimum Distance of Generalized Spatially Coupled LDPC Codes

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    Families of generalized spatially-coupled low-density parity-check (GSC-LDPC) code ensembles can be formed by terminating protograph-based generalized LDPC convolutional (GLDPCC) codes. It has previously been shown that ensembles of GSC-LDPC codes constructed from a protograph have better iterative decoding thresholds than their block code counterparts, and that, for large termination lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding threshold of the underlying generalized LDPC block code ensemble. Here we show that, in addition to their excellent iterative decoding thresholds, ensembles of GSC-LDPC codes are asymptotically good and have large minimum distance growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory 201
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