  Guessing random additive noise decoding (GRAND) is a universal
maximum-likelihood decoder that recovers code-words by guessing rank-ordered
putative noise sequences and inverting their effect until one or more valid
code-words are obtained. This work explores how GRAND can leverage
additive-noise statistics and channel-state information in fading channels.
Instead of computing per-bit reliability information in detectors and passing
this information to the decoder, we propose leveraging the colored noise
statistics following channel equalization as pseudo-soft information for
sorting noise sequences. We investigate the efficacy of pseudo-soft information
extracted from linear zero-forcing and minimum mean square error equalization
when fed to a hardware-friendly soft-GRAND (ORBGRAND). We demonstrate that the
proposed pseudo-soft GRAND schemes approximate the performance of
state-of-the-art decoders of CA-Polar and BCH codes that avail of complete soft
information. Compared to hard-GRAND, pseudo-soft ORBGRAND introduces up to 10dB
SNR gains for a target 10^-3 block-error rate.
