Sum-product algorithm for decoding of low-density parity-check (LDPC) codes cannot directly be applied to channels with memory e.g. frequency selective fading channels, because the algorithm is proposed for memoryless channels such as AWGN channel. In order to apply LDPC codes to channels with memory, it is necessary to calculate likelihood information of the channels adequately. In frequency selective fading channels, MAP (Maximum a posteriori probability) equalizer can calculate the likelihood information. However, MAP equalizer requires large complexity to calculate soft decision value. In this paper, to apply LDPC codes to frequency selective fading channels, we propose a receiver using an equalizer like MLSE (Maximum likelihood sequence estimation) which has less complexity than MAP equalizer. In the proposed receiver, the likelihood information of the channel is estimated by the use of the decoded sequence and received signals, and is updated at each decoding iteration to improve the decoding performance. The simulation results show that the proposed receiver achieves nearly the same performance as a receiver using MAP equalizer although the computational complexity of the proposed receiver is greatly reduced.
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