{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KJZLF46KKAWSB6EI7B433KLN6X","short_pith_number":"pith:KJZLF46K","canonical_record":{"source":{"id":"1302.1511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-06T20:50:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7e180f6a54581d120aa1d5b6d0f387949f61afaac378c644d3df6fcca8922361","abstract_canon_sha256":"3b847383c19d6bba4c5736c2b9650b711cac1ccb58a171efca5a497b3e424481"},"schema_version":"1.0"},"canonical_sha256":"5272b2f3ca502d20f888f879bda96df5c6a48a5936940cad7c2d041a353e40aa","source":{"kind":"arxiv","id":"1302.1511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1511","created_at":"2026-05-18T03:34:24Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1511v1","created_at":"2026-05-18T03:34:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1511","created_at":"2026-05-18T03:34:24Z"},{"alias_kind":"pith_short_12","alias_value":"KJZLF46KKAWS","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KJZLF46KKAWSB6EI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KJZLF46K","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KJZLF46KKAWSB6EI7B433KLN6X","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-06T20:50:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7e180f6a54581d120aa1d5b6d0f387949f61afaac378c644d3df6fcca8922361","abstract_canon_sha256":"3b847383c19d6bba4c5736c2b9650b711cac1ccb58a171efca5a497b3e424481"},"schema_version":"1.0"},"canonical_sha256":"5272b2f3ca502d20f888f879bda96df5c6a48a5936940cad7c2d041a353e40aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:24.061527Z","signature_b64":"tnZ7XPCQ/9fMZDPoHdm/w0kK35tyJXXkNnR4jJGtWNj65Ij3uGjpB2WhQ4BpC3UkOu0bh1ips+Oe+9q+aSqTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5272b2f3ca502d20f888f879bda96df5c6a48a5936940cad7c2d041a353e40aa","last_reissued_at":"2026-05-18T03:34:24.061093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:24.061093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1511","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKJzFIZcWDbdRScfdcnOWLzSnb4jLySuDAgsEyzMpC8oyiX/jbYbt0PHorH0ahkrSqaqxRUVW6HSXkp85EBXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:07:56.810752Z"},"content_sha256":"3d2c8fa51e2b36ac9e9e8b918157530ecda5fa5f9ffdcd1de0f58fe572d0899e","schema_version":"1.0","event_id":"sha256:3d2c8fa51e2b36ac9e9e8b918157530ecda5fa5f9ffdcd1de0f58fe572d0899e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KJZLF46KKAWSB6EI7B433KLN6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatially-Coupled Precoded Rateless Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kenta Kasai, Kohichi Sakaniwa, Kosuke Sakata","submitted_at":"2013-02-06T20:50:49Z","abstract_excerpt":"Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and decoders. Aref and Urbanke investigated the potential advantage of universal achieving-capacity property of proposed spatially-coupled (SC) low-density generator matrix (LDGM) codes. However the decoding error probability of SC-LDGM codes is bounded away from 0. In this paper, we investigate SC-LDGM codes concatenated with SC low-density parity-check codes. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1511","kind":"arxiv","version":1},"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":"2026-05-18T03:34:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t+Ky2un+NwSf6K/acxKpod9qRUR1H9QLVx6s4iUU/SRlw7U/YK3+Ol0FaEa/c16VFj5oIrk6TAcqevAu4H++AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T18:07:56.811158Z"},"content_sha256":"2dc928d45fe8266d67b0f8e832b347401640ac3969cffa60295bf163f4d8e420","schema_version":"1.0","event_id":"sha256:2dc928d45fe8266d67b0f8e832b347401640ac3969cffa60295bf163f4d8e420"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJZLF46KKAWSB6EI7B433KLN6X/bundle.json","state_url":"https://pith.science/pith/KJZLF46KKAWSB6EI7B433KLN6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJZLF46KKAWSB6EI7B433KLN6X/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":"2026-06-10T18:07:56Z","links":{"resolver":"https://pith.science/pith/KJZLF46KKAWSB6EI7B433KLN6X","bundle":"https://pith.science/pith/KJZLF46KKAWSB6EI7B433KLN6X/bundle.json","state":"https://pith.science/pith/KJZLF46KKAWSB6EI7B433KLN6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJZLF46KKAWSB6EI7B433KLN6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KJZLF46KKAWSB6EI7B433KLN6X","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":"3b847383c19d6bba4c5736c2b9650b711cac1ccb58a171efca5a497b3e424481","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-06T20:50:49Z","title_canon_sha256":"7e180f6a54581d120aa1d5b6d0f387949f61afaac378c644d3df6fcca8922361"},"schema_version":"1.0","source":{"id":"1302.1511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1511","created_at":"2026-05-18T03:34:24Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1511v1","created_at":"2026-05-18T03:34:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1511","created_at":"2026-05-18T03:34:24Z"},{"alias_kind":"pith_short_12","alias_value":"KJZLF46KKAWS","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KJZLF46KKAWSB6EI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KJZLF46K","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:2dc928d45fe8266d67b0f8e832b347401640ac3969cffa60295bf163f4d8e420","target":"graph","created_at":"2026-05-18T03:34:24Z","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":"Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and decoders. Aref and Urbanke investigated the potential advantage of universal achieving-capacity property of proposed spatially-coupled (SC) low-density generator matrix (LDGM) codes. However the decoding error probability of SC-LDGM codes is bounded away from 0. In this paper, we investigate SC-LDGM codes concatenated with SC low-density parity-check codes. T","authors_text":"Kenta Kasai, Kohichi Sakaniwa, Kosuke Sakata","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-06T20:50:49Z","title":"Spatially-Coupled Precoded Rateless Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1511","kind":"arxiv","version":1},"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":"sha256:3d2c8fa51e2b36ac9e9e8b918157530ecda5fa5f9ffdcd1de0f58fe572d0899e","target":"record","created_at":"2026-05-18T03:34:24Z","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":"3b847383c19d6bba4c5736c2b9650b711cac1ccb58a171efca5a497b3e424481","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-06T20:50:49Z","title_canon_sha256":"7e180f6a54581d120aa1d5b6d0f387949f61afaac378c644d3df6fcca8922361"},"schema_version":"1.0","source":{"id":"1302.1511","kind":"arxiv","version":1}},"canonical_sha256":"5272b2f3ca502d20f888f879bda96df5c6a48a5936940cad7c2d041a353e40aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5272b2f3ca502d20f888f879bda96df5c6a48a5936940cad7c2d041a353e40aa","first_computed_at":"2026-05-18T03:34:24.061093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:24.061093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tnZ7XPCQ/9fMZDPoHdm/w0kK35tyJXXkNnR4jJGtWNj65Ij3uGjpB2WhQ4BpC3UkOu0bh1ips+Oe+9q+aSqTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:24.061527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d2c8fa51e2b36ac9e9e8b918157530ecda5fa5f9ffdcd1de0f58fe572d0899e","sha256:2dc928d45fe8266d67b0f8e832b347401640ac3969cffa60295bf163f4d8e420"],"state_sha256":"405e5844bcaa4595a6c8d2237dd3c8f935853f437e53081b9e4d0d9d841dec2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2HMqdQE5Trb1SRt7zwR/5+qnBqUeGxuMcFY78fxDtkye8PmgVZRFu13k5UcwnvF8qqWWXLk+ZBMsL/fjT6UCBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T18:07:56.813418Z","bundle_sha256":"d2387f42a54d6f4306bbb472bb5b861437b91fe7ddffb24d201fa4d1f3b5f797"}}