Pith Number

pith:R3YVECNI

pith:2026:R3YVECNIHV2XT6BW3BYTNCLMGG

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Vectorized Generalized Nearest Neighbor Decoding for In-block Memory Channel

Hao Wu, Shuqin Pang, Wenyi Zhang, Xinwei Li, Yuhao Liu

For in-block memory channels the optimal vectorized generalized nearest neighbor decoder admits an analytical characterization when Gaussian codebooks are employed.

arxiv:2605.15950 v1 · 2026-05-15 · cs.IT · math.IT

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Claims

C1strongest claim

Leveraging the generalized mutual information (GMI) as an operational lower bound on the mismatch capacity, an analytical characterization of the optimal Vec-GNND is obtained for general IBM channels with Gaussian codebooks. The formalism further provides closed-form optimality conditions and achievable GMIs for restricted variants of the receiver architecture.

C2weakest assumption

That Gaussian codebooks are employed and that the GMI lower bound remains sufficiently tight to characterize optimality for the vectorized receiver on general IBM channels (abstract, paragraph 2).

C3one line summary

Vec-GNND yields closed-form optimality conditions and achievable GMIs for IBM channels with Gaussian codebooks, plus a GMI-based joint covariance-metric design that reduces to covariance optimization.

References

49 extracted · 49 resolved · 0 Pith anchors

[1] A mathematical theory of communication, 1948

[2] I. M. Jacobs and J. Wozencraft,Principles of communication engineering.New York, NY , USA: Wiley, 1965 1965

[3] Massive MIMO systems with non-ideal hardware: Energy efficiency, estimation, and capacity limits, 2014

[4] Reliable communication under channel uncertainty, 2002

[5] Mismatched decoding: Error exponents, second-order rates and saddlepoint approximations, 2014

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:46.298684Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ef15209a83d7579f836d87136896c319ab573f4e0372889da7d25af2dd144a3

Aliases

arxiv: 2605.15950 · arxiv_version: 2605.15950v1 · doi: 10.48550/arxiv.2605.15950 · pith_short_12: R3YVECNIHV2X · pith_short_16: R3YVECNIHV2XT6BW · pith_short_8: R3YVECNI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/R3YVECNIHV2XT6BW3BYTNCLMGG \
  | 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: 8ef15209a83d7579f836d87136896c319ab573f4e0372889da7d25af2dd144a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15c7b8dce39ff727871642bf95e700bfd3f45e2d999c13c2bd7582ea5dabe180",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-15T13:41:19Z",
    "title_canon_sha256": "520f5a959f6f0a75bc918b30c963dc4235b844a14b9a71d967403606e3818b56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15950",
    "kind": "arxiv",
    "version": 1
  }
}