Soft-Input, Soft-Output Joint Detection and GRAND

Guessing random additive noise decoding (GRAND) is a maximum likelihood (ML) decoding method that identifies the noise effects corrupting code-words of arbitrary code-books. In a joint detection and decoding framework, this work demonstrates how GRAND can leverage crude soft information in received symbols and channel state information to generate, through guesswork, soft bit reliability outputs in log-likelihood ratios (LLRs). The LLRs are generated via successive computations of Euclidean-distance metrics corresponding to candidate noise-recovered words. Noting that the entropy of noise is much smaller than that of information bits, a small number of noise effect guesses generally suffices to hit a code-word, which allows generating LLRs for critical bits; LLR saturation is applied to the remaining bits. In an iterative (turbo) mode, the generated LLRs at a given soft-input, soft-output GRAND iteration serve as enhanced a priori information that adapts noise-sequence guess ordering in a subsequent iteration. Simulations demonstrate that a few turbo-GRAND iterations match the performance of ML-detection-based soft-GRAND in both AWGN and Rayleigh fading channels at a complexity cost that, on average, grows linearly (instead of exponentially) with the number of symbols.