1 research outputs found
Edge Coloring and Stopping Sets Analysis in Product Codes with MDS components
We consider non-binary product codes with MDS components and their iterative
row-column algebraic decoding on the erasure channel. Both independent and
block erasures are considered in this paper. A compact graph representation is
introduced on which we define double-diversity edge colorings via the rootcheck
concept. An upper bound of the number of decoding iterations is given as a
function of the graph size and the color palette size . Stopping sets are
defined in the context of MDS components and a relationship is established with
the graph representation. A full characterization of these stopping sets is
given up to a size , where and are the minimum
Hamming distances of the column and row MDS components respectively. Then, we
propose a differential evolution edge coloring algorithm that produces
colorings with a large population of minimal rootcheck order symbols. The
complexity of this algorithm per iteration is , for a given
differential evolution parameter , where itself is small
with respect to the huge cardinality of the coloring ensemble. The performance
of MDS-based product codes with and without double-diversity coloring is
analyzed in presence of both block and independent erasures. In the latter
case, ML and iterative decoding are proven to coincide at small channel erasure
probability. Furthermore, numerical results show excellent performance in
presence of unequal erasure probability due to double-diversity colorings.Comment: 82 pages, 14 figures, and 4 tables, Submitted to the IEEE
Transactions on Information Theory, Dec. 2015, paper IT-15-110