Trapping-set criterion for high-probability correction by decoder diversity

Let $\mathcal{C}$ be an LDPC code, let $\mathcal{D}$ be a decoder diversity set, and let $\mathcal{E}^{[t]}(\Lambda^{(A,B)})$ be the union of the error sets associated with all trapping sets having parameters $a\leq A$ and $b\leq B$ through error patterns of weight at most $t$. Trapping-set criterion. If there exists a decoder diversity set $\mathcal{D}$ that corrects all patterns in the set $\mathcal{E}^{[t]} (\Lambda^{(A,B)})$ on the code $\mathcal{C}$ with $A=2t$ and sufficiently large $B$, then the decoder diversity set $\mathcal{D}$ will also correct all error patterns up to weight $t$ on the code $\mathcal{C}$ with high probability. This conjecture proposes a computationally tractable criterion for choosing the trapping-set parameters $A$ and $B$: correcting the associated error patterns for trapping sets up to size $2t$ and sufficiently large $B$ should yield high-probability correction of all errors of weight at most $t$.