An efficient method to improve machine learning decoders using automorphisms group

Abstract

The decoding of error-correcting codes (ECCs) is a critical aspect of communication systems, yet traditional decoding techniques can often be computationally demanding or ineffective for certain codes, necessitating innovative approaches. In this study, we introduce a hybrid approach that combines machine learning and automorphism techniques to optimize the decoding process. Specifically, we train multilayer perceptron (MLP) models to learn the mapping between error syndromes and their corresponding errors. While these models exhibit robust learning capabilities, their performance sometimes does not reach 100%. To mitigate this limitation, we exploit the automorphism group of the code—a set of structure-preserving transformations—to convert the errors that the MLP struggles to decode into ones it can process more effectively. We use a minimum number of p permutations, pre-calculating and storing all possible automorphisms to ensure computational efficiency. Our experimental results reveal that this hybrid approach substantially enhances the decoding performance of the MLP model, presenting a promising avenue for decoding ECCs. Importantly, this approach is not limited to MLP models and can be applied to any machine learning model with a learning score less than 100%, broadening its applicability and impact. By integrating machine learning with traditional algebraic coding theory, we propose a new paradigm that holds the potential to revolutionize the design of decoding systems, making them more efficient and effective.