  This paper is concerned with the application of nonbinary low-density
parity-check (NB-LDPC) codes to binary input inter-symbol interference (ISI)
channels. Two low-complexity joint detection/decoding algorithms are proposed.
One is referred to as max-log-MAP/X-EMS algorithm, which is implemented by
exchanging soft messages between the max-log-MAP detector and the extended
min-sum (EMS) decoder. The max-log-MAP/X-EMS algorithm is applicable to general
NB-LDPC codes. The other one, referred to as Viterbi/GMLGD algorithm, is
designed in particular for majority-logic decodable NB-LDPC codes. The
Viterbi/GMLGD algorithm works in an iterative manner by exchanging
hard-decisions between the Viterbi detector and the generalized majority-logic
decoder(GMLGD). As a by-product, a variant of the original EMS algorithm is
proposed, which is referred to as \mu-EMS algorithm. In the \mu-EMS algorithm,
the messages are truncated according to an adaptive threshold, resulting in a
more efficient algorithm. Simulations results show that the max-log-MAP/X-EMS
algorithm performs as well as the traditional iterative detection/decoding
algorithm based on the BCJR algorithm and the QSPA, but with lower complexity.
The complexity can be further reduced for majority-logic decodable NB-LDPC
codes by executing the Viterbi/GMLGD algorithm with a performance degradation
within one dB. Simulation results also confirm that the \mu-EMS algorithm
requires lower computational loads than the EMS algorithm with a fixed
threshold. These algorithms provide good candidates for trade-offs between
performance and complexity.
