In the most advanced and ubiquitous technologies of flash storage, cells are used with q discrete levels, where q is an integer power of 2 (e.g. q=8). The resulting channel has both q-ary and binary effects, because reading is carried out by a sequence of binary measurements comparing a cell level to a reference value. To capture this duality, we propose a new channel model we call the q-ary multi-bit channel (QMBC). The QMBC belongs to the family of partial-erasure channels, whereby the channel output is either the correct symbol or some sub-set of GF(q) containing it. In the QMBC the partial-erasure subsets assume a special structure following from the multi-bit channel structure. In the talk we show some interesting theoretical results aiding the design of LDPC codes for multi-bit channels, both in the threshold and finite-length regimes.