Generalized Binary Representation for the Nonbinary LDPC Code With Decoder Design

In this paper, we consider the performance-optimized nonbinary low-density parity check code over general linear group, i.e.,
$\bar{\cal C}$
. A new methodology for constructing the binary representation [generalized binary representation (GBR)] of
$\bar{\cal C}$
is proposed, which can be optimized with regard to both degree distributions and girth. As to the decoding of the GBR, we develop a low-complexity hybrid parallel decoding process. It is shown that the decoding performance of the GBR under the proposed binary decoding process could closely approach the decoding performance of its mother code
$\bar{\cal C}$
under nonbinary belief propagation decoding. A simple code optimization algorithm for the GBR is also provided. Simulations show the comparative results and justify the advantages of the proposed constructions.