Pith Number

pith:O5TKVVUD

pith:2025:O5TKVVUDRWSWC2OGPIK6VYA5KJ

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ORBGRAND Is Exactly Capacity-achieving via Rank Companding

Wenyi Zhang, Zhuang Li

By companding ranks in ORBGRAND with the inverse CDF of channel reliability, CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs.

arxiv:2512.00347 v5 · 2025-11-29 · cs.IT · math.IT

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Claims

C1strongest claim

via suitably companding the ranks in ORBGRAND according to the inverse cumulative distribution function (CDF) of channel reliability, the resulting CDF-ORBGRAND algorithm exactly achieves the mutual information, i.e., the symmetric capacity.

C2weakest assumption

The result holds for general binary-input memoryless channels under symmetric input distribution; if the input distribution deviates from symmetry or the channel has memory, the exact capacity achievement may not hold.

C3one line summary

CDF-ORBGRAND exactly achieves the symmetric capacity for binary-input memoryless channels under symmetric inputs and the BICM capacity in bit-interleaved coded modulation.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Performance Analysis and Optimal Design of ORB-Type GRAND Algorithms

Receipt and verification

First computed	2026-06-23T03:13:52.030403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7766aad6838da56169c67a15eae01d52679027b966af4d4450549fafb4e0af69

Aliases

arxiv: 2512.00347 · arxiv_version: 2512.00347v5 · doi: 10.48550/arxiv.2512.00347 · pith_short_12: O5TKVVUDRWSW · pith_short_16: O5TKVVUDRWSWC2OG · pith_short_8: O5TKVVUD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/O5TKVVUDRWSWC2OGPIK6VYA5KJ \
  | 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: 7766aad6838da56169c67a15eae01d52679027b966af4d4450549fafb4e0af69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccf55b46eff350bd1a0ccd6d6d46bbf4cfd9226a66c21d5d714dfa0993ec2b88",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2025-11-29T06:36:33Z",
    "title_canon_sha256": "9a8e7ca6ece39d68b71377c91962e7afb806fb65a9915bbc1499f8885bfd1260"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.00347",
    "kind": "arxiv",
    "version": 5
  }
}