{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UCEN5LYSDW254YE2HDCBD5VMDZ","short_pith_number":"pith:UCEN5LYS","canonical_record":{"source":{"id":"1701.03264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-12T08:17:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d9651da82387b13274745e5919f7bd4503878f83ec955283429ddde524a0c14a","abstract_canon_sha256":"72404df84a4a74b4d7019633d73b6783f983d7dfb4b651da6bae94137d069656"},"schema_version":"1.0"},"canonical_sha256":"a088deaf121db5de609a38c411f6ac1e426c70e0eb9ff0c6ff60d8fabfff6f47","source":{"kind":"arxiv","id":"1701.03264","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03264","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03264v2","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03264","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"UCEN5LYSDW25","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UCEN5LYSDW254YE2","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UCEN5LYS","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UCEN5LYSDW254YE2HDCBD5VMDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.03264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-12T08:17:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d9651da82387b13274745e5919f7bd4503878f83ec955283429ddde524a0c14a","abstract_canon_sha256":"72404df84a4a74b4d7019633d73b6783f983d7dfb4b651da6bae94137d069656"},"schema_version":"1.0"},"canonical_sha256":"a088deaf121db5de609a38c411f6ac1e426c70e0eb9ff0c6ff60d8fabfff6f47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:43.840872Z","signature_b64":"AkoewCln8t/j0ZbYpyXpES/fTt1NrCwdx/Cj0m/7bI59+FoXnqW8JpXi3wXyBS3yC7wryzcqYaMdTGkxSJm6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a088deaf121db5de609a38c411f6ac1e426c70e0eb9ff0c6ff60d8fabfff6f47","last_reissued_at":"2026-05-18T00:52:43.840299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:43.840299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.03264","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l00POivQqnt/RjbIiMI93R0+PPBsHHr1YYZ8XEGbeX6u3fPwXzZa6jKrHAr8S8Kx7QcteAfQqm42RODnZGDKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:59:12.745710Z"},"content_sha256":"c9a9340f6a4dd484c7a1f9e667cf89a8ebb8f3d1f3c3603ed6fb96f2a27b7158","schema_version":"1.0","event_id":"sha256:c9a9340f6a4dd484c7a1f9e667cf89a8ebb8f3d1f3c3603ed6fb96f2a27b7158"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UCEN5LYSDW254YE2HDCBD5VMDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Successive Cancellation Decoding of Polar Codes with Arbitrary Linear Binary Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chunjiang Duanmu, Feiyan Zhang, Ming Chen, Shiyi Zhang, Zhiliang Huang","submitted_at":"2017-01-12T08:17:30Z","abstract_excerpt":"A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed. We devise a $l$-expressions method which can obtain simplified recursive formulas of SC decoder in likelihood ratio form for arbitrary linear binary kernels to reduce the complexity of corresponding SC decoder. By considering the bit-channel transition probabilities $W_{G}^{(\\cdot)}(\\cdot|0)$ and $W_{G}^{(\\cdot)}(\\cdot|1)$ separately, a $W$-expressions method is proposed to further reduce the complexity of HDLBK based SC decoder. For a $m\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03264","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QuZe5Pqt4p86j2YQ5qtgp5rsE7qVzyHteJ/ISQNBeWty6b5t68B7iZssKnMuMR7GxiPVBOGbpAvOLgCfCbk4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:59:12.746377Z"},"content_sha256":"16bc467112708d3e27fb38744a0b89caf7ca3b9803ebc6886e5400c5c95902c6","schema_version":"1.0","event_id":"sha256:16bc467112708d3e27fb38744a0b89caf7ca3b9803ebc6886e5400c5c95902c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCEN5LYSDW254YE2HDCBD5VMDZ/bundle.json","state_url":"https://pith.science/pith/UCEN5LYSDW254YE2HDCBD5VMDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCEN5LYSDW254YE2HDCBD5VMDZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T16:59:12Z","links":{"resolver":"https://pith.science/pith/UCEN5LYSDW254YE2HDCBD5VMDZ","bundle":"https://pith.science/pith/UCEN5LYSDW254YE2HDCBD5VMDZ/bundle.json","state":"https://pith.science/pith/UCEN5LYSDW254YE2HDCBD5VMDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCEN5LYSDW254YE2HDCBD5VMDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UCEN5LYSDW254YE2HDCBD5VMDZ","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":"72404df84a4a74b4d7019633d73b6783f983d7dfb4b651da6bae94137d069656","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-12T08:17:30Z","title_canon_sha256":"d9651da82387b13274745e5919f7bd4503878f83ec955283429ddde524a0c14a"},"schema_version":"1.0","source":{"id":"1701.03264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03264","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03264v2","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03264","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"UCEN5LYSDW25","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UCEN5LYSDW254YE2","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UCEN5LYS","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:16bc467112708d3e27fb38744a0b89caf7ca3b9803ebc6886e5400c5c95902c6","target":"graph","created_at":"2026-05-18T00:52:43Z","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":"A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed. We devise a $l$-expressions method which can obtain simplified recursive formulas of SC decoder in likelihood ratio form for arbitrary linear binary kernels to reduce the complexity of corresponding SC decoder. By considering the bit-channel transition probabilities $W_{G}^{(\\cdot)}(\\cdot|0)$ and $W_{G}^{(\\cdot)}(\\cdot|1)$ separately, a $W$-expressions method is proposed to further reduce the complexity of HDLBK based SC decoder. For a $m\\","authors_text":"Chunjiang Duanmu, Feiyan Zhang, Ming Chen, Shiyi Zhang, Zhiliang Huang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-12T08:17:30Z","title":"On the Successive Cancellation Decoding of Polar Codes with Arbitrary Linear Binary Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03264","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:c9a9340f6a4dd484c7a1f9e667cf89a8ebb8f3d1f3c3603ed6fb96f2a27b7158","target":"record","created_at":"2026-05-18T00:52:43Z","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":"72404df84a4a74b4d7019633d73b6783f983d7dfb4b651da6bae94137d069656","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-01-12T08:17:30Z","title_canon_sha256":"d9651da82387b13274745e5919f7bd4503878f83ec955283429ddde524a0c14a"},"schema_version":"1.0","source":{"id":"1701.03264","kind":"arxiv","version":2}},"canonical_sha256":"a088deaf121db5de609a38c411f6ac1e426c70e0eb9ff0c6ff60d8fabfff6f47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a088deaf121db5de609a38c411f6ac1e426c70e0eb9ff0c6ff60d8fabfff6f47","first_computed_at":"2026-05-18T00:52:43.840299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:43.840299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AkoewCln8t/j0ZbYpyXpES/fTt1NrCwdx/Cj0m/7bI59+FoXnqW8JpXi3wXyBS3yC7wryzcqYaMdTGkxSJm6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:43.840872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9a9340f6a4dd484c7a1f9e667cf89a8ebb8f3d1f3c3603ed6fb96f2a27b7158","sha256:16bc467112708d3e27fb38744a0b89caf7ca3b9803ebc6886e5400c5c95902c6"],"state_sha256":"78caa68bbcb48b0544953cc4913d2006598c17e406430b60c2b84511615a514c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kFUEfCgSoV/lOGeyrdBlSIaiJUbsQNJvs/KS7HL8TXifbb/BHTrTqpeIQu3xGAVA1FxiYOCiKwpXXFblrLkkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:59:12.750996Z","bundle_sha256":"d7427abf2adfc108bc45d1e8280092aeb521d8d83302ab9aafab657624e16cc9"}}