Estimation of the decoding threshold of LDPC codes over the q-ary partial erasure channel

In this paper, we discuss bounds and approximations for the decoding threshold of LDPC codes over the q-ary partial erasure channel (QPEC), introduced in [1]. The QPEC has a q-ary input, and its output is either one symbol or a set of 2 ≤ M ≤ q possible symbols. We show how an upper bound on the decoding threshold can be derived using a single-letter recurrence relation, when M > q/2. In addition, we discuss complexity issues in the calculation of the threshold, and provide two approximation models that lead to reasonable results with a fraction of the complexity required for the exact calculation.