Near Optimal Viterbi Decoders for Convolutional Codes in Symmetric Alpha-Stable Noise

Abstract

The design of Viterbi decoders for signals in noise modeled using the symmetric α-stable distribution is considered. The traditional Viterbi decoder, which has a branch metric optimized for Gaussian noise, performs poorly in symmetric α-stable noise. Since the optimal maximum likelihood branch metric is impractically complex, many suboptimal metrics have been proposed, such as the hard decision, p-norm and absolute (1-norm) metric. A Viterbi decoder that uses the absolute branch metric has better performance and lower complexity, however, its performance degrades when α decreases. In this paper, the effects of the suboptimal metrics on the performance of the Viterbi decoder are analyzed, and a clear justification for the performance of the decoder that uses the Gaussian and absolute metrics is provided. Moreover, this analysis is used to design a low complexity suboptimal branch metric that improves the performance of the Viterbi decoder by about 0.75 to 2 dB compared to the absolute branch metric for different values of α, at almost no additional complexity.