{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HHDEBLMXNGVNLETF4REXSIWTAD","short_pith_number":"pith:HHDEBLMX","schema_version":"1.0","canonical_sha256":"39c640ad9769aad59265e4497922d300fb6b3058605fc50b2a7f4d581800a419","source":{"kind":"arxiv","id":"1009.5764","version":2},"attestation_state":"computed","paper":{"title":"The E8 Lattice and Error Correction in Multi-Level Flash Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Brian M. Kurkoski","submitted_at":"2010-09-29T03:52:35Z","abstract_excerpt":"A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF($2^8$) is well suited. This is a type of coded modulation, where the Euclidean distance of the lattice, which is an eight-dimensional signal constellation, is combined with the Hamming distance of the code. This system is compared with the conventional technique for flash memories, BCH codes using Gray-coded PAM. The described construction has a performance advantage of 1.6 to 1.8 dB at a probability of word error of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.5764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-09-29T03:52:35Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"014e6eac0118193930db5c3129a216561d25c6f2c05c4953cfb60953543cefbf","abstract_canon_sha256":"d172b0ab4d34a3ee77773487f2c7d99f57efbbd265c12049cbfb58c65734ee2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:36.987147Z","signature_b64":"ga6LJYns70gWQQFHemhwFw40DLAi7BnfXww4AAIkwv2l1f2SJRqYdhjkfJ/sJ3q0fZEJV7sX9gJGrFLVCtZQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39c640ad9769aad59265e4497922d300fb6b3058605fc50b2a7f4d581800a419","last_reissued_at":"2026-05-18T04:28:36.986663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:36.986663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The E8 Lattice and Error Correction in Multi-Level Flash Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Brian M. Kurkoski","submitted_at":"2010-09-29T03:52:35Z","abstract_excerpt":"A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF($2^8$) is well suited. This is a type of coded modulation, where the Euclidean distance of the lattice, which is an eight-dimensional signal constellation, is combined with the Hamming distance of the code. This system is compared with the conventional technique for flash memories, BCH codes using Gray-coded PAM. The described construction has a performance advantage of 1.6 to 1.8 dB at a probability of word error of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5764","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.5764","created_at":"2026-05-18T04:28:36.986732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.5764v2","created_at":"2026-05-18T04:28:36.986732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5764","created_at":"2026-05-18T04:28:36.986732+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHDEBLMXNGVN","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHDEBLMXNGVNLETF","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHDEBLMX","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD","json":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD.json","graph_json":"https://pith.science/api/pith-number/HHDEBLMXNGVNLETF4REXSIWTAD/graph.json","events_json":"https://pith.science/api/pith-number/HHDEBLMXNGVNLETF4REXSIWTAD/events.json","paper":"https://pith.science/paper/HHDEBLMX"},"agent_actions":{"view_html":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD","download_json":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD.json","view_paper":"https://pith.science/paper/HHDEBLMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.5764&json=true","fetch_graph":"https://pith.science/api/pith-number/HHDEBLMXNGVNLETF4REXSIWTAD/graph.json","fetch_events":"https://pith.science/api/pith-number/HHDEBLMXNGVNLETF4REXSIWTAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD/action/storage_attestation","attest_author":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD/action/author_attestation","sign_citation":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD/action/citation_signature","submit_replication":"https://pith.science/pith/HHDEBLMXNGVNLETF4REXSIWTAD/action/replication_record"}},"created_at":"2026-05-18T04:28:36.986732+00:00","updated_at":"2026-05-18T04:28:36.986732+00:00"}