{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:NKBPBYTZ3VKQWYVTRGCLEEO7XL","short_pith_number":"pith:NKBPBYTZ","canonical_record":{"source":{"id":"2006.06240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2020-06-11T07:57:15Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"91cc42d0cf43ee46b8c3ba4ec018fc7039801d2616d468fb66f9f35d120c21ee","abstract_canon_sha256":"1819194c15f9c6b0f3e750af6d71f0a77d75cd8333b7200b0ba4bacc7ce1e0ca"},"schema_version":"1.0"},"canonical_sha256":"6a82f0e279dd550b62b38984b211dfbac5464ec3e25adeeaa0b34f830d334199","source":{"kind":"arxiv","id":"2006.06240","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.06240","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"2006.06240v1","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.06240","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"NKBPBYTZ3VKQ","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"NKBPBYTZ3VKQWYVT","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"NKBPBYTZ","created_at":"2026-07-05T01:10:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:NKBPBYTZ3VKQWYVTRGCLEEO7XL","target":"record","payload":{"canonical_record":{"source":{"id":"2006.06240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2020-06-11T07:57:15Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"91cc42d0cf43ee46b8c3ba4ec018fc7039801d2616d468fb66f9f35d120c21ee","abstract_canon_sha256":"1819194c15f9c6b0f3e750af6d71f0a77d75cd8333b7200b0ba4bacc7ce1e0ca"},"schema_version":"1.0"},"canonical_sha256":"6a82f0e279dd550b62b38984b211dfbac5464ec3e25adeeaa0b34f830d334199","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:16.368685Z","signature_b64":"nCfjBVmyTF7k9DDyqfGiPY/yZktVQTuCi+zZ0jQrYp/faHLVUBe7FL0QKqV0wdHO3vJ2P2B0E4JQoC8vivmRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a82f0e279dd550b62b38984b211dfbac5464ec3e25adeeaa0b34f830d334199","last_reissued_at":"2026-07-05T01:10:16.368148Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:16.368148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.06240","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":"2026-07-05T01:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MldA9F0IohPcBR72QujCeW/3dd7h+AqEFniNeMkjfRGGjCmwHH1TEZkfXFsgqj1OoYJH2fec04sOAc/JABUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:42:33.951377Z"},"content_sha256":"3f686cca822e9fac66d33266c8cba6d6a837d25f8667d89fd0fbe62efaace7c8","schema_version":"1.0","event_id":"sha256:3f686cca822e9fac66d33266c8cba6d6a837d25f8667d89fd0fbe62efaace7c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:NKBPBYTZ3VKQWYVTRGCLEEO7XL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A PDD Decoder for Binary Linear Codes With Neural Check Polytope Projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"eess.SP","authors_text":"Ming Lei, Ming-Min Zhao, Min-Jian Zhao, Yi Wei","submitted_at":"2020-06-11T07:57:15Z","abstract_excerpt":"Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity and poor performance at the low signal-to-noise ratio (SNR) region. In this letter, we adopt the penalty dual decomposition (PDD) framework and propose a PDD algorithm to address the fundamental polytope based maximum likelihood (ML) decoding problem. Furthermore, we propose to integrate machine learning techniques into the most time-consuming part of the PDD "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.06240","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.06240/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+A0Y8Tuc04/pASmGbQhhSGL/tZcEr14A1s2ao+242xvsvQHUUJcfs7IPTiu+xvGW7M6BsmFXprdoHWB+lPxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:42:33.951751Z"},"content_sha256":"c88a173e4a06d4a5d6dc8d86e0c3deca737c3c5077a0f1b23ec21a9df0ca9c24","schema_version":"1.0","event_id":"sha256:c88a173e4a06d4a5d6dc8d86e0c3deca737c3c5077a0f1b23ec21a9df0ca9c24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL/bundle.json","state_url":"https://pith.science/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL/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":"2026-07-07T14:42:33Z","links":{"resolver":"https://pith.science/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL","bundle":"https://pith.science/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL/bundle.json","state":"https://pith.science/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKBPBYTZ3VKQWYVTRGCLEEO7XL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NKBPBYTZ3VKQWYVTRGCLEEO7XL","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":"1819194c15f9c6b0f3e750af6d71f0a77d75cd8333b7200b0ba4bacc7ce1e0ca","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2020-06-11T07:57:15Z","title_canon_sha256":"91cc42d0cf43ee46b8c3ba4ec018fc7039801d2616d468fb66f9f35d120c21ee"},"schema_version":"1.0","source":{"id":"2006.06240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.06240","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"2006.06240v1","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.06240","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"NKBPBYTZ3VKQ","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"NKBPBYTZ3VKQWYVT","created_at":"2026-07-05T01:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"NKBPBYTZ","created_at":"2026-07-05T01:10:16Z"}],"graph_snapshots":[{"event_id":"sha256:c88a173e4a06d4a5d6dc8d86e0c3deca737c3c5077a0f1b23ec21a9df0ca9c24","target":"graph","created_at":"2026-07-05T01:10:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.06240/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity and poor performance at the low signal-to-noise ratio (SNR) region. In this letter, we adopt the penalty dual decomposition (PDD) framework and propose a PDD algorithm to address the fundamental polytope based maximum likelihood (ML) decoding problem. Furthermore, we propose to integrate machine learning techniques into the most time-consuming part of the PDD ","authors_text":"Ming Lei, Ming-Min Zhao, Min-Jian Zhao, Yi Wei","cross_cats":["cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2020-06-11T07:57:15Z","title":"A PDD Decoder for Binary Linear Codes With Neural Check Polytope Projection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.06240","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":"sha256:3f686cca822e9fac66d33266c8cba6d6a837d25f8667d89fd0fbe62efaace7c8","target":"record","created_at":"2026-07-05T01:10:16Z","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":"1819194c15f9c6b0f3e750af6d71f0a77d75cd8333b7200b0ba4bacc7ce1e0ca","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2020-06-11T07:57:15Z","title_canon_sha256":"91cc42d0cf43ee46b8c3ba4ec018fc7039801d2616d468fb66f9f35d120c21ee"},"schema_version":"1.0","source":{"id":"2006.06240","kind":"arxiv","version":1}},"canonical_sha256":"6a82f0e279dd550b62b38984b211dfbac5464ec3e25adeeaa0b34f830d334199","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a82f0e279dd550b62b38984b211dfbac5464ec3e25adeeaa0b34f830d334199","first_computed_at":"2026-07-05T01:10:16.368148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:10:16.368148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nCfjBVmyTF7k9DDyqfGiPY/yZktVQTuCi+zZ0jQrYp/faHLVUBe7FL0QKqV0wdHO3vJ2P2B0E4JQoC8vivmRAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:10:16.368685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.06240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f686cca822e9fac66d33266c8cba6d6a837d25f8667d89fd0fbe62efaace7c8","sha256:c88a173e4a06d4a5d6dc8d86e0c3deca737c3c5077a0f1b23ec21a9df0ca9c24"],"state_sha256":"33993b0c285ca24b24684ddc7bb900c9ef352eba2a9a3fd99e1bac30c39f26db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMsCx/ysVtPiKUC6fQEFHvlUvmo2K65ZlUXo1r5P9zrA7qT8JsY5hhOQf2CC3v4IMk80F6RzSI1JmHorYZ5fAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:42:33.953646Z","bundle_sha256":"6db75fccd2b6b752eee3b5488114967697072dbb11ef68164c2d3a9945e7b73c"}}