LLR estimation using machine learning

Abstract

Many decoders of error-correcting codes use the Log-Likelihood Ratio (LLR) as an input, which involves the probability density function (pdf) of the noise. In impulsive noise, the pdf of the noise is not accessible in closed form and is only available through very complex numerical computation. Therefore, the LLR calculation for Binary Phase Shift Keying (BPSK) is too complex. It becomes even more complex for high-order modulations. Moreover, the LLR computational complexity grows as the modulation order increases. The main contribution of our work lies in the LLR approximation for high-order modulations and its estimation using supervised machine learning, without requiring prior knowledge of the noise distribution model. To this end, we propose two approaches to approximate the LLR values using supervised machine learning, for high-order modulated symbols. The first approach can also be used for BPSK modulated symbols. The second approach aims to approximate the LLR for high-order modulated symbols in a more simplified manner compared to the first approach. For both approaches, we estimate the parameters of the approximate LLR under known noise channel conditions using the linear regression algorithm. To estimate these parameters without prior knowledge of the noise distribution model, we use a binary logistic regression algorithm. Our simulations focus on the second proposed approach to estimate the LLR with unknown noise distributions. The results are presented for the 4-ASK (Amplitude Shift Keying) modulation scheme, where the receiver is assumed to suffer from noise ranging from Gaussian to highly impulsive models. The proposed LLR estimation is shown to achieve a comparable performance to the one attained using the exact LLR function.

Keywords

• LLR
• High order modulations
• BPSK
• Estimation
• Approximation
• Machine learning