Iterative Decoding of LDPC Codes over the q-ary Partial Erasure Channel

In this paper, we develop a new channel model, which we name the q-ary partial erasure channel (QPEC). The QPEC has a q-ary input, and its output is either one symbol or a set of M symbols, where M may be smaller than q. This channel serves as a generalization to the binary erasure channel (BEC), and mimics situations when a symbol output from the channel is known only partially; that is, the output symbol contains some ambiguity, but is not fully erased. This type of channel is motivated by non-volatile memory multi-level read channels. In such channels the readout is obtained by a sequence of current/voltage measurements, which may terminate with partial knowledge of the stored level. Our investigation is concentrated on the performance of low-density parity-check (LDPC) codes when used over this channel, thanks to their low decoding complexity using belief propagation. We provide the density-evolution equations that describe the decoding process, and suggest several bounds and approximations. In addition, we provide tools for the practical design of LDPC codes for use over the QPEC.