{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3GGUOAMJPDZB6VP5A77DR27563","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":"3429280d9c123b14d4ae58d78156afad035fbd85ac1094fea613701899d88550","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-24T13:55:11Z","title_canon_sha256":"07b758374090310da000e09007b3f29121bcdfedf2761bc473c794e9a58054cd"},"schema_version":"1.0","source":{"id":"1302.5906","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5906","created_at":"2026-05-18T00:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5906v8","created_at":"2026-05-18T00:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5906","created_at":"2026-05-18T00:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"3GGUOAMJPDZB","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3GGUOAMJPDZB6VP5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3GGUOAMJ","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:1774df66aab550d58ea404bdd3885d4f7e4f9604742aaf556d6a37d571707ded","target":"graph","created_at":"2026-05-18T00:12:16Z","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"},"paper":{"abstract_excerpt":"We propose a new coding scheme using only one lattice that achieves the $\\frac{1}{2}\\log(1+\\SNR)$ capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, when the signal-to-noise ratio $\\SNR>e-1$. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but otherwise does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which involves a quantization-good lattice as well as an AWGN-good lattice. Using the flatness factor, we show that the error probability of the propo","authors_text":"Cong Ling, Jean-Claude Belfiore","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-24T13:55:11Z","title":"Achieving AWGN Channel Capacity With Lattice Gaussian Coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5906","kind":"arxiv","version":8},"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:fbed1784477cca14085aa46a9bb771c12b1fb86224f41d10debc6e160c2d9790","target":"record","created_at":"2026-05-18T00:12:16Z","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":"3429280d9c123b14d4ae58d78156afad035fbd85ac1094fea613701899d88550","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-02-24T13:55:11Z","title_canon_sha256":"07b758374090310da000e09007b3f29121bcdfedf2761bc473c794e9a58054cd"},"schema_version":"1.0","source":{"id":"1302.5906","kind":"arxiv","version":8}},"canonical_sha256":"d98d47018978f21f55fd07fe38ebfdf6eb7ef5c1c2d44bf94b3e928b705478eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d98d47018978f21f55fd07fe38ebfdf6eb7ef5c1c2d44bf94b3e928b705478eb","first_computed_at":"2026-05-18T00:12:16.374842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:16.374842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x66Sr3UjUsa8Pm+j+alXVNi/0rkb0fScLp/nMbmRjmSztDCzimZbPUNljCF7qvZduxsKgHJha96dwDMDZ4IdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:16.375291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5906","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbed1784477cca14085aa46a9bb771c12b1fb86224f41d10debc6e160c2d9790","sha256:1774df66aab550d58ea404bdd3885d4f7e4f9604742aaf556d6a37d571707ded"],"state_sha256":"bb76644c10c521e7d6b8d727534366f2f0aeefd0e1e0f96f49b4e588b06339d0"}