Unsupervised Log-Likelihood Ratio Estimation for Short Packets in Impulsive Noise

Impulsive noise, where large amplitudes arise with a relatively high probability, arises in many communication systems including interference in Low Power Wide Area Networks. A challenge in coping with impulsive noise, particularly alpha-stable models, is that tractable expressions for the log-likelihood ratio (LLR) are not available, which has a large impact on soft-input decoding schemes, e.g., low-density parity-check (LDPC) packets. On the other hand, constraints on packet length also mean that pilot signals are not available resulting in non-trivial approximation and parameter estimation problems for the LLR. In this paper, a new unsupervised parameter estimation algorithm is proposed for LLR approximation. In terms of the frame error rate (FER), this algorithm is shown to significantly outperform existing unsupervised estimation methods for short LDPC packets (on the order of 500 symbols), with nearly the same performance as when the parameters are perfectly known. The performance is also compared with an upper bound on the information-theoretic limit for the FER, which suggests that in impulsive noise further improvements require the use of an alternative code structure other than LDPC.