Joint Detection/Decoding Algorithms for Nonbinary LDPC Codes over ISI Channels

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 harddecisions between the Viterbi detector and the generalized majority-logic decoder (GMLGD). As a byproduct, a variant of the original EMS algorithm is proposed, which is referred to as μ-EMS algorithm. In the μ-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 μ-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.