{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:PT4P7GJXWJK6BZBIUUCPCZDYNZ","short_pith_number":"pith:PT4P7GJX","canonical_record":{"source":{"id":"0807.3913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-07-24T15:34:59Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"aa473355d7ff63519fc0212a23e5ab8e0d8c3bff597164ce0ee458a4f1e2edb3","abstract_canon_sha256":"46a6237aea0178d881c03c3edee223aeb8e097a14364eb70c245fc64d329c793"},"schema_version":"1.0"},"canonical_sha256":"7cf8ff9937b255e0e428a504f164786e74874879a03b47843ed15ae878f345ff","source":{"kind":"arxiv","id":"0807.3913","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3913","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3913v1","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3913","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"pith_short_12","alias_value":"PT4P7GJXWJK6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"PT4P7GJXWJK6BZBI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"PT4P7GJX","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:PT4P7GJXWJK6BZBIUUCPCZDYNZ","target":"record","payload":{"canonical_record":{"source":{"id":"0807.3913","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-07-24T15:34:59Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"aa473355d7ff63519fc0212a23e5ab8e0d8c3bff597164ce0ee458a4f1e2edb3","abstract_canon_sha256":"46a6237aea0178d881c03c3edee223aeb8e097a14364eb70c245fc64d329c793"},"schema_version":"1.0"},"canonical_sha256":"7cf8ff9937b255e0e428a504f164786e74874879a03b47843ed15ae878f345ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:58.538740Z","signature_b64":"GB91H84mLUlK6e4FF7JfXuDyR7PLa0EqRERdT3PcnttYOXSznyv+RMxn+RA4EOzQKJ4HD69i0bIR9an0VCYMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cf8ff9937b255e0e428a504f164786e74874879a03b47843ed15ae878f345ff","last_reissued_at":"2026-05-18T00:57:58.538161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:58.538161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.3913","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":"2026-05-18T00:57:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4mNjg0vgh/jTh70r0xNcydxnUQEyl0uszIwgOZ/5OX5Ns5e6icmgbu8oKQVImlDjza3AmH5rUL6TA2Oxd/MCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:19:23.173087Z"},"content_sha256":"257c4b3d334b5a2139dd3f0b17f86eb7129c9fc7099594d1a5496e12ec0d3f73","schema_version":"1.0","event_id":"sha256:257c4b3d334b5a2139dd3f0b17f86eb7129c9fc7099594d1a5496e12ec0d3f73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:PT4P7GJXWJK6BZBIUUCPCZDYNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DMT of weighted Parallel Channels: Application to Broadcast Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore, Lina Mroueh, St\\'ephanie Rouquette-L\\'eveil","submitted_at":"2008-07-24T15:34:59Z","abstract_excerpt":"In a broadcast channel with random packet arrival and transmission queues, the stability of the system is achieved by maximizing a weighted sum rate capacity with suitable weights that depend on the queue size. The weighted sum rate capacity using Dirty Paper Coding (DPC) and Zero Forcing (ZF) is asymptotically equivalent to the weighted sum capacity over parallel single-channels. In this paper, we study the Diversity Multiplexing Tradeoff (DMT) of the fading broadcast channel under a fixed weighted sum rate capacity constraint. The DMT of both identical and different parallel weighted MISO ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3913","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":"2026-05-18T00:57:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PEyjgEm/xlyBOmupcnPEYx3X3gHN7/muf7LQGa6aNmjD4cL3AfAVHZij+8rxy2ouJ1OOkh++7rMSdDCqNgejDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:19:23.173449Z"},"content_sha256":"0b986271127849b4b8812c2bb2e1ef69df1d8fe83327478c0748887aa1db2322","schema_version":"1.0","event_id":"sha256:0b986271127849b4b8812c2bb2e1ef69df1d8fe83327478c0748887aa1db2322"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ/bundle.json","state_url":"https://pith.science/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ/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":"2026-06-04T12:19:23Z","links":{"resolver":"https://pith.science/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ","bundle":"https://pith.science/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ/bundle.json","state":"https://pith.science/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PT4P7GJXWJK6BZBIUUCPCZDYNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:PT4P7GJXWJK6BZBIUUCPCZDYNZ","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":"46a6237aea0178d881c03c3edee223aeb8e097a14364eb70c245fc64d329c793","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-07-24T15:34:59Z","title_canon_sha256":"aa473355d7ff63519fc0212a23e5ab8e0d8c3bff597164ce0ee458a4f1e2edb3"},"schema_version":"1.0","source":{"id":"0807.3913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.3913","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"arxiv_version","alias_value":"0807.3913v1","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.3913","created_at":"2026-05-18T00:57:58Z"},{"alias_kind":"pith_short_12","alias_value":"PT4P7GJXWJK6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"PT4P7GJXWJK6BZBI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"PT4P7GJX","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0b986271127849b4b8812c2bb2e1ef69df1d8fe83327478c0748887aa1db2322","target":"graph","created_at":"2026-05-18T00:57:58Z","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 a broadcast channel with random packet arrival and transmission queues, the stability of the system is achieved by maximizing a weighted sum rate capacity with suitable weights that depend on the queue size. The weighted sum rate capacity using Dirty Paper Coding (DPC) and Zero Forcing (ZF) is asymptotically equivalent to the weighted sum capacity over parallel single-channels. In this paper, we study the Diversity Multiplexing Tradeoff (DMT) of the fading broadcast channel under a fixed weighted sum rate capacity constraint. The DMT of both identical and different parallel weighted MISO ch","authors_text":"Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore, Lina Mroueh, St\\'ephanie Rouquette-L\\'eveil","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-07-24T15:34:59Z","title":"DMT of weighted Parallel Channels: Application to Broadcast Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3913","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":"sha256:257c4b3d334b5a2139dd3f0b17f86eb7129c9fc7099594d1a5496e12ec0d3f73","target":"record","created_at":"2026-05-18T00:57:58Z","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":"46a6237aea0178d881c03c3edee223aeb8e097a14364eb70c245fc64d329c793","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-07-24T15:34:59Z","title_canon_sha256":"aa473355d7ff63519fc0212a23e5ab8e0d8c3bff597164ce0ee458a4f1e2edb3"},"schema_version":"1.0","source":{"id":"0807.3913","kind":"arxiv","version":1}},"canonical_sha256":"7cf8ff9937b255e0e428a504f164786e74874879a03b47843ed15ae878f345ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cf8ff9937b255e0e428a504f164786e74874879a03b47843ed15ae878f345ff","first_computed_at":"2026-05-18T00:57:58.538161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:58.538161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GB91H84mLUlK6e4FF7JfXuDyR7PLa0EqRERdT3PcnttYOXSznyv+RMxn+RA4EOzQKJ4HD69i0bIR9an0VCYMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:58.538740Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.3913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:257c4b3d334b5a2139dd3f0b17f86eb7129c9fc7099594d1a5496e12ec0d3f73","sha256:0b986271127849b4b8812c2bb2e1ef69df1d8fe83327478c0748887aa1db2322"],"state_sha256":"162956f21c3ffaaeac967b8def6b9122a036d12288b297e6289f9a94eb485e18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/TIQ3oKmEfGHkOvQtr7qY4t/1jfTPmsSLGpElRiJp8KAd7dzB+hTALdFPrBaV52hHHSOMzTFrCQ8kIxFm7KBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:19:23.175386Z","bundle_sha256":"4527a82c90c56f7cfe942cf4d899dd6aab7316c413b48aecbab6cd346bab9a11"}}