{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Q43F7SEY64MOO4YAAEJG7K42IV","short_pith_number":"pith:Q43F7SEY","schema_version":"1.0","canonical_sha256":"87365fc898f718e7730001126fab9a4571dd36fa038ee9e96ad2db04c4946019","source":{"kind":"arxiv","id":"1804.01922","version":1},"attestation_state":"computed","paper":{"title":"Approaching Waterfilling Capacity of Parallel Channels by Higher Order Modulation and Probabilistic Amplitude Shaping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fabian Steiner, Georg B\\\"ocherer, Patrick Schulte","submitted_at":"2018-04-05T15:53:34Z","abstract_excerpt":"Parallel, additive white Gaussian noise (AWGN) channels with an average sum power constraint are considered. It is shown how the waterfilling Shannon capacity can be approached by higher order modulation and probabilistic amplitude shaping (PAS). This is achieved by a new distribution matching approach called product distribution matching (PDM). The asymptotic performance of PDM is analyzed by achievable rates. A heuristic for optimizing the input distribution is proposed, which enables signaling at a target spectral efficiency with a fixed-rate forward error correction (FEC) code, while the o"},"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":"1804.01922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-05T15:53:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"94a87bc1d8224e5af377b977dc670453f50b0674f7f4e262e3742afa398b3c63","abstract_canon_sha256":"b43ea38e2b0adfe905d6d81803ea222e84df04d878e2f9c18d56c46e4d841ddb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:09.554497Z","signature_b64":"e/XCTFR9f0fAXRd5UVlKyNO1ntcAI3SoF8lDChAjzcBtP1qfMUNijRjftEkNSV3gC3Hvvf9b4ujO2Trkq5i7Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87365fc898f718e7730001126fab9a4571dd36fa038ee9e96ad2db04c4946019","last_reissued_at":"2026-05-18T00:19:09.553826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:09.553826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approaching Waterfilling Capacity of Parallel Channels by Higher Order Modulation and Probabilistic Amplitude Shaping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fabian Steiner, Georg B\\\"ocherer, Patrick Schulte","submitted_at":"2018-04-05T15:53:34Z","abstract_excerpt":"Parallel, additive white Gaussian noise (AWGN) channels with an average sum power constraint are considered. It is shown how the waterfilling Shannon capacity can be approached by higher order modulation and probabilistic amplitude shaping (PAS). This is achieved by a new distribution matching approach called product distribution matching (PDM). The asymptotic performance of PDM is analyzed by achievable rates. A heuristic for optimizing the input distribution is proposed, which enables signaling at a target spectral efficiency with a fixed-rate forward error correction (FEC) code, while the o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01922","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.01922","created_at":"2026-05-18T00:19:09.553930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01922v1","created_at":"2026-05-18T00:19:09.553930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01922","created_at":"2026-05-18T00:19:09.553930+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q43F7SEY64MO","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q43F7SEY64MOO4YA","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q43F7SEY","created_at":"2026-05-18T12:32:46.962924+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/Q43F7SEY64MOO4YAAEJG7K42IV","json":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV.json","graph_json":"https://pith.science/api/pith-number/Q43F7SEY64MOO4YAAEJG7K42IV/graph.json","events_json":"https://pith.science/api/pith-number/Q43F7SEY64MOO4YAAEJG7K42IV/events.json","paper":"https://pith.science/paper/Q43F7SEY"},"agent_actions":{"view_html":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV","download_json":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV.json","view_paper":"https://pith.science/paper/Q43F7SEY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01922&json=true","fetch_graph":"https://pith.science/api/pith-number/Q43F7SEY64MOO4YAAEJG7K42IV/graph.json","fetch_events":"https://pith.science/api/pith-number/Q43F7SEY64MOO4YAAEJG7K42IV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV/action/storage_attestation","attest_author":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV/action/author_attestation","sign_citation":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV/action/citation_signature","submit_replication":"https://pith.science/pith/Q43F7SEY64MOO4YAAEJG7K42IV/action/replication_record"}},"created_at":"2026-05-18T00:19:09.553930+00:00","updated_at":"2026-05-18T00:19:09.553930+00:00"}