{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UQKGRS7ZQV7G4HYGBH5JFBFMHG","short_pith_number":"pith:UQKGRS7Z","canonical_record":{"source":{"id":"1608.03874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-12T18:57:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"29f67ebd092602c89f49837a1d658b6d5537ad09906baedf060c46b172311246","abstract_canon_sha256":"b52fff36dd132e8091d9add0a37a401f927e6519d4aea8fdf9c7e23623765718"},"schema_version":"1.0"},"canonical_sha256":"a41468cbf9857e6e1f0609fa9284ac39860452b2b5b37139e9cad19f75bc3d18","source":{"kind":"arxiv","id":"1608.03874","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03874","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03874v1","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03874","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"UQKGRS7ZQV7G","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UQKGRS7ZQV7G4HYG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UQKGRS7Z","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UQKGRS7ZQV7G4HYGBH5JFBFMHG","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-12T18:57:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"29f67ebd092602c89f49837a1d658b6d5537ad09906baedf060c46b172311246","abstract_canon_sha256":"b52fff36dd132e8091d9add0a37a401f927e6519d4aea8fdf9c7e23623765718"},"schema_version":"1.0"},"canonical_sha256":"a41468cbf9857e6e1f0609fa9284ac39860452b2b5b37139e9cad19f75bc3d18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:11.139606Z","signature_b64":"naFPWJ7rrFRxBhOY1VoLHfgkg4aQz5fA76LLkgvlKNOb3jsKFCDje5/fPSvhqLhtxydDLc+0Rw+KuiTi5TIGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a41468cbf9857e6e1f0609fa9284ac39860452b2b5b37139e9cad19f75bc3d18","last_reissued_at":"2026-05-18T01:09:11.138930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:11.138930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03874","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":"2026-05-18T01:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EfZtF1hqkcrlyk1VYlol/DNoE056dDl+SpmzI1+eOcxKMCLg2fkJyCuGv4UM8ewcfGlrk7mAM+P20lzD3eu4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:21:17.235208Z"},"content_sha256":"0d4393047ef4f91a09747beee941c06d332b385f76b59ff92d84612aa5d0f54f","schema_version":"1.0","event_id":"sha256:0d4393047ef4f91a09747beee941c06d332b385f76b59ff92d84612aa5d0f54f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UQKGRS7ZQV7G4HYGBH5JFBFMHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"LDPC Lattice Codes for Full-Duplex Relay Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dariush Kiani, Hassan Khodaiemehr, Mohammad-Reza Sadeghi","submitted_at":"2016-08-12T18:57:06Z","abstract_excerpt":"Low density parity check (LDPC) lattices are obtained from Construction D' and a family of nested binary LDPC codes. We consider an special case of these lattices with one binary LDPC code as underlying code. This special case of LDPC lattices can be obtained by lifting binary LDPC codes using Construction A lattices. The LDPC lattices were the first family of lattices which have efficient decoding in high dimensions. We employ the encoding and decoding of the LDPC lattices in a cooperative transmission framework. We establish two efficient shaping methods based on hypercube shaping and Vorono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03874","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":"2026-05-18T01:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuR32BXpFbrnww4Kkex3owSMdWyt+jiF03dU4EoizFPugDn7PkDySulm2/Izj2rrkoCa/sY3B9y9451vyX5xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:21:17.235568Z"},"content_sha256":"be0b82018737ff7dded2d0bfea7039d695d17f009f63f6402be7d7906e20628f","schema_version":"1.0","event_id":"sha256:be0b82018737ff7dded2d0bfea7039d695d17f009f63f6402be7d7906e20628f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG/bundle.json","state_url":"https://pith.science/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG/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":"2026-07-02T10:21:17Z","links":{"resolver":"https://pith.science/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG","bundle":"https://pith.science/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG/bundle.json","state":"https://pith.science/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQKGRS7ZQV7G4HYGBH5JFBFMHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UQKGRS7ZQV7G4HYGBH5JFBFMHG","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":"b52fff36dd132e8091d9add0a37a401f927e6519d4aea8fdf9c7e23623765718","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-12T18:57:06Z","title_canon_sha256":"29f67ebd092602c89f49837a1d658b6d5537ad09906baedf060c46b172311246"},"schema_version":"1.0","source":{"id":"1608.03874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03874","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03874v1","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03874","created_at":"2026-05-18T01:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"UQKGRS7ZQV7G","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UQKGRS7ZQV7G4HYG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UQKGRS7Z","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:be0b82018737ff7dded2d0bfea7039d695d17f009f63f6402be7d7906e20628f","target":"graph","created_at":"2026-05-18T01:09:11Z","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":"Low density parity check (LDPC) lattices are obtained from Construction D' and a family of nested binary LDPC codes. We consider an special case of these lattices with one binary LDPC code as underlying code. This special case of LDPC lattices can be obtained by lifting binary LDPC codes using Construction A lattices. The LDPC lattices were the first family of lattices which have efficient decoding in high dimensions. We employ the encoding and decoding of the LDPC lattices in a cooperative transmission framework. We establish two efficient shaping methods based on hypercube shaping and Vorono","authors_text":"Dariush Kiani, Hassan Khodaiemehr, Mohammad-Reza Sadeghi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-12T18:57:06Z","title":"LDPC Lattice Codes for Full-Duplex Relay Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03874","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":"sha256:0d4393047ef4f91a09747beee941c06d332b385f76b59ff92d84612aa5d0f54f","target":"record","created_at":"2026-05-18T01:09:11Z","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":"b52fff36dd132e8091d9add0a37a401f927e6519d4aea8fdf9c7e23623765718","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-12T18:57:06Z","title_canon_sha256":"29f67ebd092602c89f49837a1d658b6d5537ad09906baedf060c46b172311246"},"schema_version":"1.0","source":{"id":"1608.03874","kind":"arxiv","version":1}},"canonical_sha256":"a41468cbf9857e6e1f0609fa9284ac39860452b2b5b37139e9cad19f75bc3d18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a41468cbf9857e6e1f0609fa9284ac39860452b2b5b37139e9cad19f75bc3d18","first_computed_at":"2026-05-18T01:09:11.138930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:11.138930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"naFPWJ7rrFRxBhOY1VoLHfgkg4aQz5fA76LLkgvlKNOb3jsKFCDje5/fPSvhqLhtxydDLc+0Rw+KuiTi5TIGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:11.139606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d4393047ef4f91a09747beee941c06d332b385f76b59ff92d84612aa5d0f54f","sha256:be0b82018737ff7dded2d0bfea7039d695d17f009f63f6402be7d7906e20628f"],"state_sha256":"038f4f672b0325d484c31ea95d56a73818767cc45f38ca6cf16247f4c0012df3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LvA1Ltct4h8abLmsNahXryDGxHfmIiCv8w6/KEundLWcQxOynYzDsOs/fbeSMqd5zEP9m6rOlfadyaUIrJTkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:21:17.237553Z","bundle_sha256":"50b6c7ca1c041aad3db091945ec261af520498a71e550d5294f74014f5289280"}}