LDPC codes for partial-erasure channels in multi-level memories

In this paper, we develop a new channel model, which we name the q-ary partial erasure channel (QPEC). QPEC has a q-ary input, and its output is either one symbol or a set of M possible values. This channel mimics situations when current/voltage levels in measurement channels are only partially known, due to high read rates or imperfect current/voltage sensing. Our investigation is concentrated on the performance of low-density parity-check (LDPC) codes when used over this channel, due to their low decoding complexity with iterative-decoding algorithms. We give the density evolution equations of this channel, and develop its decoding-threshold analysis. Part of the analysis shows that finding the exact decoding threshold efficiently lies upon a solution to an open problem in additive combinatorics. For this part, we give bounds and approximations.