Simplified LLR-based Viterbi decoder for convolutional codes in symmetric alpha-stable noise

Abstract

The design of a simplified Viterbi decoder for signals in symmetric alpha-stable noise is considered. The conventional Viterbi decoder, which has a branch metric optimized for Gaussian noise, performs poorly in symmetric alpha-stable noise. Since the optimal maximum likelihood (ML) branch metric is impractically complex, simplified approaches are needed. A simple 1-norm nonlinearity has been used instead of the Euclidean distance in the Gaussian branch metric to improve the performance of the Viterbi decoder. It shows performance improvement for higher values of alpha; however, the performance degrades when alpha approaches 1. In this paper, we propose a simplified branch metric which depends on a piecewise linear approximation of the log likelihood ratio (LLR). The Viterbi decoder with the proposed branch metric gives near-optimal performance for different values of alpha at low complexity. The simulation results show that the performance improvement of the Viterbi decoder with the proposed branch metric is approximately 1.5–4 dB compared to the Viterbi decoder with the 1-norm nonlinearity for different values of alpha.