Pith Number

pith:MA4RHKGV

pith:2026:MA4RHKGVUAFGEGTEPOZ5DZY5N4

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Capacity-Achieving BBT Polar Codes with Interleaver-Assisted BP Decoding

Xiao Ma, Xinyuanmeng Yao

Binary balanced tree transformation lets polar codes achieve capacity at any block length.

arxiv:2603.19938 v2 · 2026-03-20 · cs.IT · math.IT

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Claims

C1strongest claim

We prove that the proposed transformation induces channel polarization, thereby establishing that BBT polar codes achieve the capacity of binary-input memoryless symmetric (BMS) channels.

C2weakest assumption

The binary balanced tree transformation preserves the recursive polarization property of Arıkan's original construction when extended to arbitrary block lengths.

C3one line summary

BBT polar codes achieve capacity for any block length via a new tree transformation and support low-latency BP decoding through interleaving and sub-graph processing.

References

30 extracted · 30 resolved · 1 Pith anchors

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

[2] CRC-aided decoding of polar codes, 2012

[3] List decoding of polar codes, 2015

[4] 5G NR: Multiplexing and channel coding, 2018

[5] A practical approach to polar codes, 2011

Receipt and verification

First computed	2026-05-17T23:39:15.713647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

603913a8d5a00a621a647bb3d1e71d6f3e1055b4625c63286beb956ac1e94bb3

Aliases

arxiv: 2603.19938 · arxiv_version: 2603.19938v2 · doi: 10.48550/arxiv.2603.19938 · pith_short_12: MA4RHKGVUAFG · pith_short_16: MA4RHKGVUAFGEGTE · pith_short_8: MA4RHKGV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MA4RHKGVUAFGEGTEPOZ5DZY5N4 \
  | 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: 603913a8d5a00a621a647bb3d1e71d6f3e1055b4625c63286beb956ac1e94bb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b5c00a3523220c9aec2df97b6aabfa68525529b28a0faf3112d405e32b2f0d0",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-03-20T13:32:20Z",
    "title_canon_sha256": "d0af50127f9705ae37f5c1994ece0dc1d77ad2e5db4cb407809d197e1a4279e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.19938",
    "kind": "arxiv",
    "version": 2
  }
}