q-ary GRAND — Draconitic Research

Abstract

We develop q-ary Guessing Random Additive Noise Decoding (GRAND) for linear codes over a q-ary alphabet. The decoder works on a sorted symbol-likelihood array and uses three local child generation rules to generate symbol deviation patterns. We then prove that these rules induce a monotone rooted spanning tree of the full row-index space, so best-first traversal gives maximum-likelihood (ML) decoding under unlimited search. Reed-Solomon simulations verify ML agreement and show the finite-budget performance-complexity tradeoff.

Cite

BibTeX RIS

BibTeX

@misc{dianat2026qary,
  title = {{q-ary GRAND}},
  author = {Reza Dianat and Majid Nasiri Khormuji and Hiroyuki Seki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10236},
  eprint = {2610.10236},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10236},
}

RIS

TY  - UNPB
TI  - q-ary GRAND
AU  - Reza Dianat
AU  - Majid Nasiri Khormuji
AU  - Hiroyuki Seki
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10236
UR  - https://arxiv.org/abs/2610.10236
AB  - We develop q-ary Guessing Random Additive Noise Decoding (GRAND) for linear codes over a q-ary alphabet. The decoder works on a sorted symbol-likelihood array and uses three local child generation rules to generate symbol deviation patterns. We then prove that these rules induce a monotone rooted spanning tree of the full row-index space, so best-first traversal gives maximum-likelihood (ML) decoding under unlimited search. Reed-Solomon simulations verify ML agreement and show the finite-budget performance-complexity tradeoff.
ER  -