{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "arikan-polar-capacity-codes-2009",
    "title": "Arıkan: polar codes approach a channel’s symmetric capacity",
    "summary": "Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.\n\nA noisy communication link cannot reliably carry arbitrary amounts of information. Shannon had identified its capacity; the remaining challenge was to exhibit code families with provable performance and manageable encoding and decoding. Arıkan recursively combined independent copies of a binary-input channel, then split the result into channels seen by a successive decoder. Most resulting channels become either nearly perfect or nearly useless. Sending information through the good channels and freezing the other inputs gives polar codes. The 2009 paper proves asymptotic symmetric-capacity achievability and O(N log N) encoding and decoding; its initial error bound is polynomial in block length. Symmetric capacity uses equally likely input symbols and need not equal unrestricted capacity for an asymmetric channel. The original paper also says exact general code construction lacks an efficient algorithm and that its basic successive decoder may require impractically long blocks. It proposes approximations and stronger decoders for further study. Reed–Muller coding, Plotkin constructions and Shannon’s framework remain separately credited. The stronger error-rate result credited to Arıkan and Telatar is a separate contribution, not exclusively assigned to this sole-author paper.",
    "boundary": "The capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.",
    "area": "Coding theory and reliable communication",
    "topic": "Information theory",
    "year": 2009,
    "lane": "HUMAN",
    "result": "ALGORITHM",
    "package_id": "arikan-polar-capacity-codes-2009",
    "target": {
      "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
      "version": 1,
      "content_hash": "sha256:b6be2ef65c907ba09e42f96b315523f0d489bad5e31e646ac84e7f7b4c7e3036"
    },
    "humans": [
      "Erdal Arıkan"
    ],
    "authors_complete": true,
    "human_role_note": "Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.",
    "agents": [],
    "related": [
      "shannon",
      "reed-solomon-polynomial-codes-1960",
      "hamming-error-correction"
    ],
    "subresults": [],
    "scientific_assessment": {
      "source_review": "SOURCE_CURATED",
      "scientific_review": "NOT_REVIEWED_BY_WRS",
      "formal_replay": "NOT_RUN",
      "provider_attestation": "NONE"
    },
    "sources": [
      {
        "id": "wrs24-arikan2009-polar-journal",
        "title": "Arıkan,ChannelPolarization,IEEETransactionsInformationTheory55(7),3051-3073(2009),originaljournal",
        "url": "https://www.mit.edu/~medard/bakeraward/05075875.pdf"
      },
      {
        "id": "wrs24-arikan2009-polar-arxiv-metadata",
        "title": "AuthorarXiv0807.3917v5 metadata,abstract andversionhistory",
        "url": "https://arxiv.org/abs/0807.3917v5"
      }
    ],
    "points": "180000",
    "published_grade": {
      "id": "arikan-polar-capacity-codes-2009",
      "entry_id": "arikan-polar-capacity-codes-2009",
      "band": "A",
      "modifier": null,
      "target": {
        "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
        "version": 1,
        "content_hash": "sha256:b6be2ef65c907ba09e42f96b315523f0d489bad5e31e646ac84e7f7b4c7e3036"
      },
      "what_changed": "Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.",
      "scope": "Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model. The capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.",
      "status": "PROVISIONAL_EDITORIAL",
      "scientific_correctness_certified": false
    },
    "assessment_disposition": {
      "status": "ASSESSED",
      "label": "Provisionally assessed",
      "reason": "A current grade and separate reference score identify this exact contribution.",
      "target": {
        "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
        "version": 1,
        "content_hash": "sha256:b6be2ef65c907ba09e42f96b315523f0d489bad5e31e646ac84e7f7b4c7e3036"
      },
      "edition": "ratings-e039106f30dec177"
    }
  },
  "version": {
    "kind": "PUBLIC_RECORD_VIEW",
    "previous": null,
    "published_at": "2026-10-03T00:00:00Z",
    "publisher": {
      "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33",
      "role": "WRS_EDITORIAL_PUBLICATION"
    },
    "record": {
      "contributors": [
        {
          "attribution_basis": "SOURCE_CITED",
          "credit": "historical_scientific",
          "entity_kind": "historical_person",
          "name": "Erdal Arıkan",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "formulator"
          ],
          "source": {
            "citation": "Arıkan,ChannelPolarization,IEEETransactionsInformationTheory55(7),3051-3073(2009),originaljournal",
            "url": "https://www.mit.edu/~medard/bakeraward/05075875.pdf"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "Arıkan,ChannelPolarization,IEEETransactionsInformationTheory55(7),3051-3073(2009),originaljournal",
            "url": "https://www.mit.edu/~medard/bakeraward/05075875.pdf"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-1",
          "kind": "source_reference",
          "source": {
            "citation": "AuthorarXiv0807.3917v5 metadata,abstract andversionhistory",
            "url": "https://arxiv.org/abs/0807.3917v5"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "The capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.",
        "domain": "Coding theory and reliable communication"
      },
      "sources": [
        {
          "citation": "Arıkan,ChannelPolarization,IEEETransactionsInformationTheory55(7),3051-3073(2009),originaljournal",
          "url": "https://www.mit.edu/~medard/bakeraward/05075875.pdf"
        },
        {
          "citation": "AuthorarXiv0807.3917v5 metadata,abstract andversionhistory",
          "url": "https://arxiv.org/abs/0807.3917v5"
        }
      ],
      "statement": "# Arıkan: polar codes approach a channel’s symmetric capacity\n\nArıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.\n\nA noisy communication link cannot reliably carry arbitrary amounts of information. Shannon had identified its capacity; the remaining challenge was to exhibit code families with provable performance and manageable encoding and decoding. Arıkan recursively combined independent copies of a binary-input channel, then split the result into channels seen by a successive decoder. Most resulting channels become either nearly perfect or nearly useless. Sending information through the good channels and freezing the other inputs gives polar codes. The 2009 paper proves asymptotic symmetric-capacity achievability and O(N log N) encoding and decoding; its initial error bound is polynomial in block length. Symmetric capacity uses equally likely input symbols and need not equal unrestricted capacity for an asymmetric channel. The original paper also says exact general code construction lacks an efficient algorithm and that its basic successive decoder may require impractically long blocks. It proposes approximations and stronger decoders for further study. Reed–Muller coding, Plotkin constructions and Shannon’s framework remain separately credited. The stronger error-rate result credited to Arıkan and Telatar is a separate contribution, not exclusively assigned to this sole-author paper.\n\n## Scientific scope\n\nThe capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.\n\n## People and systems\n\nErdal Arıkan\n\n\n\n## Original sources\n\n- [Arıkan,ChannelPolarization,IEEETransactionsInformationTheory55(7),3051-3073(2009),originaljournal](https://www.mit.edu/~medard/bakeraward/05075875.pdf)\n- [AuthorarXiv0807.3917v5 metadata,abstract andversionhistory](https://arxiv.org/abs/0807.3917v5)\n",
      "summary": "Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.\n\nA noisy communication link cannot reliably carry arbitrary amounts of information. Shannon had identified its capacity; the remaining challenge was to exhibit code families with provable performance and manageable encoding and decoding. Arıkan recursively combined independent copies of a binary-input channel, then split the result into channels seen by a successive decoder. Most resulting channels become either nearly perfect or nearly useless. Sending information through the good channels and freezing the other inputs gives polar codes. The 2009 paper proves asymptotic symmetric-capacity achievability and O(N log N) encoding and decoding; its initial error bound is polynomial in block length. Symmetric capacity uses equally likely input symbols and need not equal unrestricted capacity for an asymmetric channel. The original paper also says exact general code construction lacks an efficient algorithm and that its basic successive decoder may require impractically long blocks. It proposes approximations and stronger decoders for further study. Reed–Muller coding, Plotkin constructions and Shannon’s framework remain separately credited. The stronger error-rate result credited to Arıkan and Telatar is a separate contribution, not exclusively assigned to this sole-author paper.",
      "title": "Arıkan: polar codes approach a channel’s symmetric capacity"
    },
    "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
      "version": 1,
      "content_hash": "sha256:b6be2ef65c907ba09e42f96b315523f0d489bad5e31e646ac84e7f7b4c7e3036"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:7fa563d69877154a29576b9e9fca8a93f5a3884599caf592437fe7bf236fe47d"
  },
  "target": {
    "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
    "version": 1,
    "content_hash": "sha256:b6be2ef65c907ba09e42f96b315523f0d489bad5e31e646ac84e7f7b4c7e3036"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "arikan-polar-capacity-codes-2009",
    "entry_id": "arikan-polar-capacity-codes-2009",
    "revision": 1,
    "title": "Arıkan: polar codes approach a channel’s symmetric capacity",
    "context": "Coding theory and reliable communication",
    "track": "Coding theory and reliable communication",
    "band": "A",
    "modifier": null,
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-10-04",
    "evidence_cutoff": "2026-10-04",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model.",
    "scope": "Arıkan introduced channel polarization and polar codes that achieve the symmetric capacity of binary-input discrete memoryless channels, with encoding and successive cancellation decoding costs of O(N log N) under the stated operation model. The capacity result concerns independent uses of a binary-input discrete memoryless channel, block lengths N=2^n and fixed rate below symmetric mutual information. This equals unrestricted capacity for symmetric channels. The original successive-cancellation error rate and operation count are asymptotic; general code construction, finite-block optimality and physical implementation costs remain separate. Frozen-bit averaging in general channels differs from the symmetric-channel bound. Later sharper rates, list decoding and 5G implementations are not credited to this paper alone.",
    "evidence_summary": "Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.",
    "references": [
      {
        "title": "Arıkan, Channel Polarization, IEEETransactions Information Theory 55(7),3051-3073(2009), originaljournal",
        "url": "https://www.mit.edu/~medard/bakeraward/05075875.pdf",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      },
      {
        "title": "Authorar Xiv 0807.3917 v 5 metadata, abstract andversionhistory",
        "url": "https://arxiv.org/abs/0807.3917v5",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      }
    ],
    "roles": [
      {
        "who": "Erdal Arıkan",
        "did": "Original source-listed scientific author of this scoped work; byline does not determine effort fractions.",
        "credit": "SCIENCE"
      }
    ],
    "target": {
      "record_id": "urn:uuid:f72325fd-7ced-4854-ae0e-cbe09b9c3910",
      "version": 1,
      "content_hash": "sha256:b6be2ef65c907ba09e42f96b315523f0d489bad5e31e646ac84e7f7b4c7e3036"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "180000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}