On the Minimum Distance of Generalized Spatially Coupled LDPC Codes

TL;DR

This paper demonstrates that generalized spatially-coupled LDPC codes not only have superior iterative decoding thresholds but are also asymptotically good with large minimum distance growth rates, enhancing their error correction capabilities.

Contribution

It establishes that GSC-LDPC codes are asymptotically good and possess large minimum distance growth rates, extending their known decoding threshold advantages.

Findings

GSC-LDPC codes have better iterative decoding thresholds than block codes.

Ensembles of GSC-LDPC codes are asymptotically good.

GSC-LDPC codes exhibit large minimum distance growth rates.

Abstract

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.