Trellis based Extended Min-Sum for decoding nonbinary LDPC codes

In this paper, we propose a new method to implement the Extended Min-Sum (EMS) algorithm based on trellis representation of inputting messages to the check node. The original EMS reduces the decoding complexity by choosing only n_m most reliable values and by introducing the idea of configuration sets conf(n_m, n_c), where n_c is the number of deviations from the most reliable output configuration. We propose to work directly on the deviation space by building a configuration trellis based on delta messages, which serves as a new reliability measure. The algorithm is called trellis-EMS (T-EMS). By using the new trellis representation, only n_c+1 minimum values from each row of the trellis need to be considered, which reduces the ordering complexity. The trellis representation in the deviation space also reduces the number of output configurations tested, without any performance degradation. Our method is especially suitable for moderate field size q and large check node degree nonbinary LDPC codes.