Low-complexity near-optimal map decoder for convolutional codes in symmetric alpha-stable noise

The design of the MAP decoder for signals in impulsive noise modeled using the symmetric α-stable (SαS) distribution is considered. The conventional MAP decoder, which optimizes the a posteriori probability for Gaussian noise, performs poorly in SαS noise. On the other hand, the optimal MAP decoder possesses impractical complexity due to the lack of a closed form expression of the probability density function. To simplify the implementation of the MAP decoder, the Huber nonlinearity was previously proposed, which results in a performance improvement over the conventional Gaussian MAP decoder. However, the performance is still far from optimal. In this paper, a simple unified approach to design low complexity suboptimal MAP decoder is proposed. The proposed approach uses the log likelihood ratio (LLR) as a metric to evaluate how close the suboptimal MAP decoder from the optimal. Based on this approach, a piecewise linear approximation of the LLR is used to design a sub-optimal MAP decoder which gives near optimal performance with low implementation complexity. The performance improvement of the MAP decoder is approximately 2-6 dB for different values of α compared to the MAP decoder with the Huber nonlinearity, with low complexity.