Noise-Centric Decoding

Abstract

Maximum Likelihood (ML) decoding of forward error correction codes is known to be optimally accurate, but is not used in practice due to the lack of a feasible implementation. As the common approach in coding theory is a code-centric one, designing a ML decoder is a challenging code-specific task. We establish a noise-centric approach for decoding of error correction codes that enables us to introduce a universal ML soft detection decoder called Soft Guessing Random Additive Noise Decoder (SGRAND), which is a development of a previously described hard detection ML decoder called Guessing Random Additive Noise Decoder (GRAND), that fully avails of soft detection information. SGRAND is suitable for use with any arbitrary moderate redundancy block code. A further development of the algorithm is provided that can decode coded signals transmitted on Multiple Access Channels (MACs), where transmitters not only suffer from noise, but also interfere one another. We propose a scheme that deals with the two problems of MAC separately: interference and the noise. We prove that a scheme based on SGRAND results in optimally accurate decodings. Finally, we study how correlated noise between orthogonal channels can be used to improve rates and reduce Block Error Rate (BLER) performance via a scheme called Noise Recycling.