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On the Minimum Distance of Generalized Spatially Coupled LDPC Codes

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Executive Summary

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, the authors 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.

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