Two-stage decoding algorithm for unmodulated parallel combinatory high-compaction multicarrier modulation signals

A new decoding algorithm that consists of two decoding stages to reduce the computational complexity of maximum likelihood decoding for parallel combinatory high-compaction multicarrier modulation is proposed. The first decoding stage is responsible for a preliminary decision that serves to roughly find candidate messages using the QRD-M algorithm, and the second decoding stage is responsible for the final decision that reduces the error contained in the candidate and determines the message using the minimum value of the Hamming distances between the candidate and the replicas of the message. The complexity is considerably reduced by the proposed two-stage decoding algorithm at a cost of approximately 1.5 dB or less in Eb/N0 with respect to the bit-error rate of 10−3 under the given parameter settings.