Characterizing the Gilbert-Elliott Parameter Space under LDPC Decoding

There has been much recent interest in analyzing the performance of LDPC codes in channels with memory. Density evolution (DE) may be used to analyze estimation-decoding algorithms employing the Sum-Product Algorithm for LDPC codes in Gilbert-Elliott (GE) channels. In this paper, we provide theoretical results which mitigate the complexity of characterizing the 4-dimensional GE parameter space using DE. For each point in the parameter space which is shown by DE to converge to Pe → 0, we show that a region of convergence is induced, within which all points also converge to Pe → 0. Conversely, for points found not to converge, we show that a region of non-convergence is induced. Using these results, the GE parameter space is partitioned into a region of convergence, a region of nonconvergence, and an uncertain region, which guides the selection of new points to test using DE.