{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4FYN3RSM7CX5PUM7LY24CZQQ4K","short_pith_number":"pith:4FYN3RSM","canonical_record":{"source":{"id":"1605.00979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-03T16:47:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"63ef4889565f08f96bd46855e09652638f8bdc4136d184743e2f9d295d780f01","abstract_canon_sha256":"8b62fa9adb6514830be58415ba8ebc4e994fd721dbf799a0e7396157cb272cfd"},"schema_version":"1.0"},"canonical_sha256":"e170ddc64cf8afd7d19f5e35c16610e28a2fd67c918cf7165dabf72ab3564f97","source":{"kind":"arxiv","id":"1605.00979","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00979","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00979v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00979","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"4FYN3RSM7CX5","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FYN3RSM7CX5PUM7","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FYN3RSM","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4FYN3RSM7CX5PUM7LY24CZQQ4K","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-03T16:47:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"63ef4889565f08f96bd46855e09652638f8bdc4136d184743e2f9d295d780f01","abstract_canon_sha256":"8b62fa9adb6514830be58415ba8ebc4e994fd721dbf799a0e7396157cb272cfd"},"schema_version":"1.0"},"canonical_sha256":"e170ddc64cf8afd7d19f5e35c16610e28a2fd67c918cf7165dabf72ab3564f97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:47.536824Z","signature_b64":"jSeXgmPQJIOGDsu8tdgVmGqR//tkVs9dEJEUbddFncJUpTzyol57yPR68nVkkUkQ8EKLqB/ykWvAIxApea25Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e170ddc64cf8afd7d19f5e35c16610e28a2fd67c918cf7165dabf72ab3564f97","last_reissued_at":"2026-05-18T01:15:47.536189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:47.536189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00979","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdYe1yYEvzHLT8FpUvquRo04yyH1zKDvTTMGDLXwYrgGAORbY8awwcsotUygqbYOmHnRgfXxE+DMx9rgm4iKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:48:56.698488Z"},"content_sha256":"9b28ee09457fc19eee479c2e038e9e9c16661e0d595363af82044b39227ac4e6","schema_version":"1.0","event_id":"sha256:9b28ee09457fc19eee479c2e038e9e9c16661e0d595363af82044b39227ac4e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4FYN3RSM7CX5PUM7LY24CZQQ4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian Two-Way Channels With Discrete Inputs and Quantized Outputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ershad Banijamali","submitted_at":"2016-05-03T16:47:42Z","abstract_excerpt":"In this paper, Gaussian two-way channel with uniform output quantization is studied. For Gaussian inputs, the optimum uniform finite-level quantizer is determined numerically for different values of Signal-to-Noise Ratio (SNR). The two-way channel with constellation-based transmitters is then investigated. A formulation for the so-called Shannon achievable region of this channel is developed and numerical computations of this region are presented for particular constellations. It is shown that if one transmitter utilizes a rotated version of the constellation used at the other transmitter, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00979","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":"2026-05-18T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0KJvJCgFNsOTf0hD0qbUpdcDAdE7ihVwpHDod7Ab8umHDL/Z+ANRaAYmOSMO2pDfDlbxdaTqIWBjUUbxpZ0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:48:56.698829Z"},"content_sha256":"9eff8d73234565d401e0e0754d9984b95010e2aff3810b4ba28f279b06744054","schema_version":"1.0","event_id":"sha256:9eff8d73234565d401e0e0754d9984b95010e2aff3810b4ba28f279b06744054"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K/bundle.json","state_url":"https://pith.science/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K/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":"2026-07-01T11:48:56Z","links":{"resolver":"https://pith.science/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K","bundle":"https://pith.science/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K/bundle.json","state":"https://pith.science/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FYN3RSM7CX5PUM7LY24CZQQ4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4FYN3RSM7CX5PUM7LY24CZQQ4K","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":"8b62fa9adb6514830be58415ba8ebc4e994fd721dbf799a0e7396157cb272cfd","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-03T16:47:42Z","title_canon_sha256":"63ef4889565f08f96bd46855e09652638f8bdc4136d184743e2f9d295d780f01"},"schema_version":"1.0","source":{"id":"1605.00979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00979","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00979v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00979","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"4FYN3RSM7CX5","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FYN3RSM7CX5PUM7","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FYN3RSM","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:9eff8d73234565d401e0e0754d9984b95010e2aff3810b4ba28f279b06744054","target":"graph","created_at":"2026-05-18T01:15:47Z","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":"In this paper, Gaussian two-way channel with uniform output quantization is studied. For Gaussian inputs, the optimum uniform finite-level quantizer is determined numerically for different values of Signal-to-Noise Ratio (SNR). The two-way channel with constellation-based transmitters is then investigated. A formulation for the so-called Shannon achievable region of this channel is developed and numerical computations of this region are presented for particular constellations. It is shown that if one transmitter utilizes a rotated version of the constellation used at the other transmitter, the","authors_text":"Ershad Banijamali","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-03T16:47:42Z","title":"Gaussian Two-Way Channels With Discrete Inputs and Quantized Outputs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00979","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":"sha256:9b28ee09457fc19eee479c2e038e9e9c16661e0d595363af82044b39227ac4e6","target":"record","created_at":"2026-05-18T01:15:47Z","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":"8b62fa9adb6514830be58415ba8ebc4e994fd721dbf799a0e7396157cb272cfd","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-03T16:47:42Z","title_canon_sha256":"63ef4889565f08f96bd46855e09652638f8bdc4136d184743e2f9d295d780f01"},"schema_version":"1.0","source":{"id":"1605.00979","kind":"arxiv","version":1}},"canonical_sha256":"e170ddc64cf8afd7d19f5e35c16610e28a2fd67c918cf7165dabf72ab3564f97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e170ddc64cf8afd7d19f5e35c16610e28a2fd67c918cf7165dabf72ab3564f97","first_computed_at":"2026-05-18T01:15:47.536189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.536189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jSeXgmPQJIOGDsu8tdgVmGqR//tkVs9dEJEUbddFncJUpTzyol57yPR68nVkkUkQ8EKLqB/ykWvAIxApea25Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.536824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b28ee09457fc19eee479c2e038e9e9c16661e0d595363af82044b39227ac4e6","sha256:9eff8d73234565d401e0e0754d9984b95010e2aff3810b4ba28f279b06744054"],"state_sha256":"f7cf5e5c7745eb2dbc7fb15470eeee018a0d1d4d599c7a8cef9cf62cdae15f35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9HO2FFI+qOALwZ/Y1UVcufmAE9XauLDa6zlkZM126ezV3xPwWeomEADQSnWW37bln6uUZKBjZb87yUIbgh5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T11:48:56.700725Z","bundle_sha256":"b7e5c08cd4804816e481fbcfa7eb891c07d930f2222b37cdc501120d0955aac5"}}