Pith Number

pith:BXQ2B3SS

pith:2026:BXQ2B3SSBWQISDJ5HTA2PVZCUV

not attested not anchored not stored refs resolved

Sequential Automorphism Ensemble Decoding with Early Stopping

Bassant Selim, Charles Pillet, Fran\c{c}ois Leduc-Primeau, Pascal Giard

A sequential activation scheme with early stopping thresholds cuts the complexity of automorphism ensemble decoding by 6 to 22 times while keeping block error rates almost unchanged.

arxiv:2605.00255 v1 · 2026-04-30 · cs.IT · math.IT

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Claims

C1strongest claim

For various code parameters and a BLER below 10^{-3}, simulation results show that average decoding complexity is reduced by a factor of at least 6×, and up to 22×, compared to the original AED complexity, with a negligible degradation in BLER.

C2weakest assumption

That the observed correlation between the SC path metric and the final decoding outcome is strong enough and stable enough across code parameters that pre-optimized thresholds chosen on one set of simulations will continue to satisfy the BLER constraint on unseen data without requiring per-instance re-tuning.

C3one line summary

Sequential activation with early termination thresholds for automorphism ensemble SC decoders reduces average complexity by 6x to 22x at BLER below 10^{-3} with negligible error-rate loss.

References

21 extracted · 2 resolved · 0 Pith anchors

[1] A class of multiple-error-correcting codes and the decoding scheme, 1954

[2] Application of boolean algebra to switching circuit design and to error detection, 1954

[3] Channel polarization: a method for constructing capacity- achieving codes for symmetric binary-input memoryless channels, 2009

[4] On the efficiency of polar-like decoding for symmetric codes, 2022

[5] Automorphism ensemble decoding of Reed-Muller codes, 2021

Receipt and verification

First computed	2026-05-21T17:03:39.764556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0de1a0ee520da0890d3d3cc1a7d722a542d1e5ae1fc08519e6fde24f62d5b453

Aliases

arxiv: 2605.00255 · arxiv_version: 2605.00255v1 · doi: 10.48550/arxiv.2605.00255 · pith_short_12: BXQ2B3SSBWQI · pith_short_16: BXQ2B3SSBWQISDJ5 · pith_short_8: BXQ2B3SS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BXQ2B3SSBWQISDJ5HTA2PVZCUV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0de1a0ee520da0890d3d3cc1a7d722a542d1e5ae1fc08519e6fde24f62d5b453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81205dc1807c61591ed273edb420d159c00ba981b640ff6b09beec329e2c16af",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-04-30T21:37:54Z",
    "title_canon_sha256": "05d78922c15b68d66ff19138d9c3c2145693508d6c6706462aab3162931fcbd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00255",
    "kind": "arxiv",
    "version": 1
  }
}