{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6FI6S64OT6TPBT6R7AT4YIIJFN","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":"7f7bb0fcb0a879aa03e110440c8bd433860a0b137947463b3ab6a8afd8c7c2a9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T17:28:25Z","title_canon_sha256":"f6d4862d648bb24b700e126cc805a9abf5670aede0be1a1618ba5460bdf04be3"},"schema_version":"1.0","source":{"id":"1807.03767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03767","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03767v2","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03767","created_at":"2026-05-17T23:59:22Z"},{"alias_kind":"pith_short_12","alias_value":"6FI6S64OT6TP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6FI6S64OT6TPBT6R","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6FI6S64O","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:b1a7f246b4e91a28df57e72affe136a0c4b1dc39948f98c871f5566c33db7435","target":"graph","created_at":"2026-05-17T23:59:22Z","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":"Polar codes based on $2\\times2$ non-binary kernels are discussed in this work. The kernel over $\\text{GF}(q)$ is selected by maximizing the polarization effect and using Monte-Carlo simulation. Belief propagation (BP) and successive cancellation (SC) based decoding algorithms are extended to non-binary codes. Additionally, a successive cancellation list (SCL) decoding with a pruned tree is proposed. Simulation results show that the proposed decoder performs very close to a conventional SCL decoder with significantly lower complexity.","authors_text":"Fabian Steiner, Peihong Yuan","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T17:28:25Z","title":"Construction and Decoding Algorithms for for Polar Codes based on $2\\times2$ Non-Binary Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03767","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":"sha256:512348f1d9213856c1efb700403e6d300b2be22b5ec496f2d28d443dc2edbdb3","target":"record","created_at":"2026-05-17T23:59:22Z","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":"7f7bb0fcb0a879aa03e110440c8bd433860a0b137947463b3ab6a8afd8c7c2a9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-07-10T17:28:25Z","title_canon_sha256":"f6d4862d648bb24b700e126cc805a9abf5670aede0be1a1618ba5460bdf04be3"},"schema_version":"1.0","source":{"id":"1807.03767","kind":"arxiv","version":2}},"canonical_sha256":"f151e97b8e9fa6f0cfd1f827cc21092b66411ffa1ba0464b3ee6815bbc87964c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f151e97b8e9fa6f0cfd1f827cc21092b66411ffa1ba0464b3ee6815bbc87964c","first_computed_at":"2026-05-17T23:59:22.531895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:22.531895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"57S97uz67thIhUBe2/7ClgYQpYbLenJ2Mb3Vd0T7z9AAJk6WT6jXOMUKfFFruMupnExqvB/UO/EEnLePTGjhDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:22.532282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:512348f1d9213856c1efb700403e6d300b2be22b5ec496f2d28d443dc2edbdb3","sha256:b1a7f246b4e91a28df57e72affe136a0c4b1dc39948f98c871f5566c33db7435"],"state_sha256":"264c57bfd5a7b978e88119007795165063a290086ca0a44bb800c0b0f0804a80"}