Guessing random additive noise decoding with soft detection symbol reliability information - SGRAND

We recently introduced a noise-centric algorithm, Guessing Random Additive Noise Decoding (GRAND), that identifies a Maximum Likelihood (ML) decoding for arbitrary code-books. GRAND has the unusual property that its complexity decreases as code-book rate increases. Here we provide an extension to GRAND, soft-GRAND (SGRAND), that incorporates soft detection symbol reliability information and identifies a ML decoding in that context. In particular, we assume symbols received from the channel are declared to be error free or to have been potentially subject to additive noise. SGRAND inherits desirable properties of GRAND, including being capacity achieving when used with random code-books, and having a complexity that reduces as the code-rate increases.