Polynomial complexity ML sequence and symbol-by-symbol detection in fading channels

The related problems of maximum likelihood sequence detection (MLSD) and symbol-by-symbol soft-decision metric (SbSSDM) generation in complex Gaussian flat-fading channels are considered in this paper. Traditional methods for the exact solution of these problems have exponential complexity with respect to the sequence length. In this paper, it is shown that both these problems can be solved in polynomial complexity with respect to the sequence length. Furthermore, motivated by the polynomial-complexity exact algorithm, an approximate fast algorithm is also derived. Simulation results for a low-density parity-check (LDPC) code transmitted on the aforementioned channel show that the performance of the approximate algorithm is very close to the exact sum-product algorithm.