  In this paper, we introduce a new channel model we term the q-ary multi-bit
channel (QMBC). This channel models a memory device, where q-ary symbols
(q=2^s) are stored in the form of current/voltage levels. The symbols are read
in a measurement process, which provides a symbol bit in each measurement step,
starting from the most significant bit. An error event occurs when not all the
symbol bits are known. To deal with such error events, we use GF(q) low-density
parity-check (LDPC) codes and analyze their decoding performance. We start with
iterative-decoding threshold analysis, and derive optimal edge-label
distributions for maximizing the decoding threshold. We later move to
finite-length iterative-decoding analysis and propose an edge-labeling
algorithm for improved decoding performance. We then provide finite-length
maximum-likelihood decoding analysis for both the standard non-binary random
ensemble and LDPC ensembles. Finally, we demonstrate by simulations that the
proposed edge-labeling algorithm improves finite-length decoding performance by
orders of magnitude.
