This paper proposes a low-complexity concatenated (LCC) soft-in soft-out (SISO) detector for spreading OFDM systems. The LCC SISO detector uses the turbo principle to compute the extrinsic information of the optimal maximum a priori probability (MAP) SISO detector with extremely low complexity. To develop the LCC SISO detector, we first partition the spreading matrix into some concatenated sparse matrices separated by interleavers. Then, we use the turbo principle to concatenate some SISO detectors, which are separated by de-interleavers or interleavers. Each SISO detector computes the soft information for each sparse matrix. By exchanging the soft information between the SISO detectors, we find the extrinsic information of the MAP SISO detector with extremely low complexity. Simulation results show that using the LCC SISO detector produces a near-optimal performance for both uncoded and coded spreading OFDM systems. In addition, by using the LCC SISO detector, the spreading OFDM system significantly improves the BER of the conventional OFDM system.

In this paper, we show that a priori probabilities of information bits can be incorporated into metrics for syndrome decoding. Then it is confirmed that soft-in/soft-out decoding is also possible for syndrome decoding in the same way as for Viterbi decoding. The derived results again show that the two decoding algorithms are dual to each other.