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We consider non-binary product codes with MDS components and their iterativerow-column algebraic decoding on the erasure channel. Both independent andblock erasures are considered in this paper. A compact graph representation isintroduced on which we define double-diversity edge colorings via the rootcheckconcept. An upper bound of the number of decoding iterations is given as afunction of the graph size and the color palette size $M$. Stopping sets aredefined in the context of MDS components and a relationship is established withthe graph representation. A full characterization of these stopping sets isgiven up to a size $(d_1+1)(d_2+1)$, where $d_1$ and $d_2$ are the minimumHamming distances of the column and row MDS components respectively. Then, wepropose a differential evolution edge coloring algorithm that producescolorings with a large population of minimal rootcheck order symbols. Thecomplexity of this algorithm per iteration is $o(M^{\aleph})$, for a givendifferential evolution parameter $\aleph$, where $M^{\aleph}$ itself is smallwith respect to the huge cardinality of the coloring ensemble. The performanceof MDS-based product codes with and without double-diversity coloring isanalyzed in presence of both block and independent erasures. In the lattercase, ML and iterative decoding are proven to coincide at small channel erasureprobability. Furthermore, numerical results show excellent performance inpresence of unequal erasure probability due to double-diversity colorings.

Edge Coloring and Stopping Sets Analysis in Product Codes with MDS components