{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GKNLNP75PBU3S7S7TI3IM4FST2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9a5b2158f2aa1766c754f553c0ca4e29b45654fc0c30493257d3a3ed727be1d7","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-03T16:10:31Z","title_canon_sha256":"dd7026e82db1247745b461711c8da97a5e68d7bcc8538976404f8dfe1bc29051"},"schema_version":"1.0","source":{"id":"1002.0777","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0777","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0777v2","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0777","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"GKNLNP75PBU3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GKNLNP75PBU3S7S7","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GKNLNP75","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:bafd31d4ec9aae770e2dd25973d19bc05657ba36e3b710843779cdc08726ed46","target":"graph","created_at":"2026-05-18T04:42:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, polar codes for the $m$-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Ar{\\i}kan's polarization technique applied individually to each user transforms independent uses of a $m$-user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: (i) the `uniform sum rate' of the original MAC is preserved, (ii) the extremal MACs have uniform rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded ","authors_text":"Emmanuel Abbe, Emre Telatar","cross_cats":["cs.DM","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-03T16:10:31Z","title":"Polar Codes for the m-User MAC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0777","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3c3e16412d8f2516c34b0774235f41eabeff988ae1bffed71323b0ae4f440fac","target":"record","created_at":"2026-05-18T04:42:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9a5b2158f2aa1766c754f553c0ca4e29b45654fc0c30493257d3a3ed727be1d7","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-02-03T16:10:31Z","title_canon_sha256":"dd7026e82db1247745b461711c8da97a5e68d7bcc8538976404f8dfe1bc29051"},"schema_version":"1.0","source":{"id":"1002.0777","kind":"arxiv","version":2}},"canonical_sha256":"329ab6bffd7869b97e5f9a368670b29e9131d1f792ab0836f17dcedf082eb15c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"329ab6bffd7869b97e5f9a368670b29e9131d1f792ab0836f17dcedf082eb15c","first_computed_at":"2026-05-18T04:42:33.710235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:33.710235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JnwIOtiUGdLlesWlddmV0Oaod1msyj5ISOedNx9fwrl/RZkqco1kDtv+MGynqkKu2OHTCNU4svPZXR63I2iIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:33.710890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0777","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c3e16412d8f2516c34b0774235f41eabeff988ae1bffed71323b0ae4f440fac","sha256:bafd31d4ec9aae770e2dd25973d19bc05657ba36e3b710843779cdc08726ed46"],"state_sha256":"da04d17012d8c38b21bdd04eb2e2039c460d451096fd6fa724c72f5e684b7fdd"}