{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T5JZHBKCT5NN4LQRXXVGEKMFT6","short_pith_number":"pith:T5JZHBKC","canonical_record":{"source":{"id":"1508.01640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-07T08:47:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"27f843e27916ed39f4e98b33a905d3bcec0d72e766d49b7d7bdb9cff85a8f684","abstract_canon_sha256":"e5e013293349bcf0e900e59abd6254b6ec12b054109c0091e0aebb06237c4b4f"},"schema_version":"1.0"},"canonical_sha256":"9f539385429f5ade2e11bdea6229859f906aa8513ee0bf09c1ea23faf93e7493","source":{"kind":"arxiv","id":"1508.01640","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01640","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01640v2","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01640","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"T5JZHBKCT5NN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T5JZHBKCT5NN4LQR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T5JZHBKC","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T5JZHBKCT5NN4LQRXXVGEKMFT6","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-07T08:47:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"27f843e27916ed39f4e98b33a905d3bcec0d72e766d49b7d7bdb9cff85a8f684","abstract_canon_sha256":"e5e013293349bcf0e900e59abd6254b6ec12b054109c0091e0aebb06237c4b4f"},"schema_version":"1.0"},"canonical_sha256":"9f539385429f5ade2e11bdea6229859f906aa8513ee0bf09c1ea23faf93e7493","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:20.783755Z","signature_b64":"dSOneMfcuOB0h+R+M1AAthnMg8417zjVmj5/VCEZmUSKtr9Orh0zmFubKpAZ6pxAnKQ+XdPAM6q+zZvnb8DaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f539385429f5ade2e11bdea6229859f906aa8513ee0bf09c1ea23faf93e7493","last_reissued_at":"2026-05-18T00:54:20.783336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:20.783336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01640","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":"2026-05-18T00:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3+TLZIoMuWDE6u3q/p2xwv5t132lBIsKFZUdrkVhIMgHZf0R07Oity3m3XqbhO5gBfEJSCtV4zrVyfGre7wCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:48:33.762432Z"},"content_sha256":"cd8d4b8fa8ac67c5dee97be53310578a97731a7cee6e3028d829f81b1938f67e","schema_version":"1.0","event_id":"sha256:cd8d4b8fa8ac67c5dee97be53310578a97731a7cee6e3028d829f81b1938f67e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T5JZHBKCT5NN4LQRXXVGEKMFT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Programming Decoding of Binary Linear Codes for Symbol-Pair Read Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Shigeichi Hirasawa, Shunsuke Horii, Toshiyasu Matsushima","submitted_at":"2015-08-07T08:47:26Z","abstract_excerpt":"In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read resolution. The proposed decoding algorithm is based on a linear programming (LP). It is proved that the proposed LP decoder has the maximum-likelihood (ML) certificate property, i.e., the output of the decoder is guaranteed to be the ML codeword when it is integral. We also introduce the fractional pair distance $d_{fp}$ of a code which is a lower bound on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01640","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":"2026-05-18T00:54:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rnDAGQDidgImrQNbilUE6T5I9GSkn1B5TT1UEArV0LmF3DCCme8NF8PUBD+50SqCpy0qkZZka+kgO328RGEKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:48:33.762783Z"},"content_sha256":"ba9ab0ab186c83f1cd9f87ae420d311006682c038b97d4139a51a813d208c191","schema_version":"1.0","event_id":"sha256:ba9ab0ab186c83f1cd9f87ae420d311006682c038b97d4139a51a813d208c191"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6/bundle.json","state_url":"https://pith.science/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6/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":"2026-06-24T08:48:33Z","links":{"resolver":"https://pith.science/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6","bundle":"https://pith.science/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6/bundle.json","state":"https://pith.science/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5JZHBKCT5NN4LQRXXVGEKMFT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T5JZHBKCT5NN4LQRXXVGEKMFT6","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":"e5e013293349bcf0e900e59abd6254b6ec12b054109c0091e0aebb06237c4b4f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-07T08:47:26Z","title_canon_sha256":"27f843e27916ed39f4e98b33a905d3bcec0d72e766d49b7d7bdb9cff85a8f684"},"schema_version":"1.0","source":{"id":"1508.01640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01640","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01640v2","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01640","created_at":"2026-05-18T00:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"T5JZHBKCT5NN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T5JZHBKCT5NN4LQR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T5JZHBKC","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:ba9ab0ab186c83f1cd9f87ae420d311006682c038b97d4139a51a813d208c191","target":"graph","created_at":"2026-05-18T00:54:20Z","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, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read resolution. The proposed decoding algorithm is based on a linear programming (LP). It is proved that the proposed LP decoder has the maximum-likelihood (ML) certificate property, i.e., the output of the decoder is guaranteed to be the ML codeword when it is integral. We also introduce the fractional pair distance $d_{fp}$ of a code which is a lower bound on ","authors_text":"Shigeichi Hirasawa, Shunsuke Horii, Toshiyasu Matsushima","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-07T08:47:26Z","title":"Linear Programming Decoding of Binary Linear Codes for Symbol-Pair Read Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01640","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:cd8d4b8fa8ac67c5dee97be53310578a97731a7cee6e3028d829f81b1938f67e","target":"record","created_at":"2026-05-18T00:54:20Z","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":"e5e013293349bcf0e900e59abd6254b6ec12b054109c0091e0aebb06237c4b4f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-07T08:47:26Z","title_canon_sha256":"27f843e27916ed39f4e98b33a905d3bcec0d72e766d49b7d7bdb9cff85a8f684"},"schema_version":"1.0","source":{"id":"1508.01640","kind":"arxiv","version":2}},"canonical_sha256":"9f539385429f5ade2e11bdea6229859f906aa8513ee0bf09c1ea23faf93e7493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f539385429f5ade2e11bdea6229859f906aa8513ee0bf09c1ea23faf93e7493","first_computed_at":"2026-05-18T00:54:20.783336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:20.783336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSOneMfcuOB0h+R+M1AAthnMg8417zjVmj5/VCEZmUSKtr9Orh0zmFubKpAZ6pxAnKQ+XdPAM6q+zZvnb8DaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:20.783755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd8d4b8fa8ac67c5dee97be53310578a97731a7cee6e3028d829f81b1938f67e","sha256:ba9ab0ab186c83f1cd9f87ae420d311006682c038b97d4139a51a813d208c191"],"state_sha256":"68d6bc2335ff18cd594cdb7a2c5a319dec359aea0b2f62e928dbba0d19865780"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FWdvPWrzgBR8j/gvb7syKrqY4h/l7gGrKXvx8pdyn+JwVLeZl7304eHtHBCG/dHV2jmb8l/TerU+BJxblNG+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:48:33.764722Z","bundle_sha256":"083e4db500d2d87349cea506a2b0fd97ea8c880d57c37c8280163fc73817ee25"}}