{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IEE6RD34PVT6ZXMSKIUI2GDZAM","short_pith_number":"pith:IEE6RD34","schema_version":"1.0","canonical_sha256":"4109e88f7c7d67ecdd9252288d18790304491ac7f71b2cd4f816139753bc96d9","source":{"kind":"arxiv","id":"1503.03359","version":1},"attestation_state":"computed","paper":{"title":"The Feedback Capacity of the $(1,\\infty)$-RLL Input-Constrained Erasure Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haim H. Permuter, Navin Kashyap, Oron Sabag","submitted_at":"2015-03-11T14:56:53Z","abstract_excerpt":"The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the $(1,\\infty)$-RLL constraint. We derive the capacity for this setting, which can be expressed as $C_{\\epsilon}=\\max_{0 \\leq p \\leq \\frac{1}{2}}\\frac{H_{b}(p)}{p+\\frac{1}{1-\\epsilon}}$, where $\\epsilon$ is the erasure probability and $ H_{b}(\\cdot)$ is the binary entropy function. Moreover, we prove that a-priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivale"},"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":"1503.03359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-11T14:56:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"aa8e9f9f4d67c603547c6beb135e6bad4d1b50e9711def5039a935a23dc259d5","abstract_canon_sha256":"9ee9c1004563db21b9be9e15e4135cecd7fda1e5bfcef2cf6f3bbdfdd98483c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:03.784276Z","signature_b64":"yPCKwSt4w989XpsZEBqGQXUyxdekUxwt/Ryww528XYte46RwZ2sjWkw9V0Vvw5pls7LgdUa7tIbQnyqN4EgoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4109e88f7c7d67ecdd9252288d18790304491ac7f71b2cd4f816139753bc96d9","last_reissued_at":"2026-05-18T02:25:03.783936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:03.783936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Feedback Capacity of the $(1,\\infty)$-RLL Input-Constrained Erasure Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haim H. Permuter, Navin Kashyap, Oron Sabag","submitted_at":"2015-03-11T14:56:53Z","abstract_excerpt":"The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the $(1,\\infty)$-RLL constraint. We derive the capacity for this setting, which can be expressed as $C_{\\epsilon}=\\max_{0 \\leq p \\leq \\frac{1}{2}}\\frac{H_{b}(p)}{p+\\frac{1}{1-\\epsilon}}$, where $\\epsilon$ is the erasure probability and $ H_{b}(\\cdot)$ is the binary entropy function. Moreover, we prove that a-priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03359","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":"1503.03359","created_at":"2026-05-18T02:25:03.783989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03359v1","created_at":"2026-05-18T02:25:03.783989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03359","created_at":"2026-05-18T02:25:03.783989+00:00"},{"alias_kind":"pith_short_12","alias_value":"IEE6RD34PVT6","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IEE6RD34PVT6ZXMS","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IEE6RD34","created_at":"2026-05-18T12:29:25.134429+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/IEE6RD34PVT6ZXMSKIUI2GDZAM","json":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM.json","graph_json":"https://pith.science/api/pith-number/IEE6RD34PVT6ZXMSKIUI2GDZAM/graph.json","events_json":"https://pith.science/api/pith-number/IEE6RD34PVT6ZXMSKIUI2GDZAM/events.json","paper":"https://pith.science/paper/IEE6RD34"},"agent_actions":{"view_html":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM","download_json":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM.json","view_paper":"https://pith.science/paper/IEE6RD34","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03359&json=true","fetch_graph":"https://pith.science/api/pith-number/IEE6RD34PVT6ZXMSKIUI2GDZAM/graph.json","fetch_events":"https://pith.science/api/pith-number/IEE6RD34PVT6ZXMSKIUI2GDZAM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM/action/storage_attestation","attest_author":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM/action/author_attestation","sign_citation":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM/action/citation_signature","submit_replication":"https://pith.science/pith/IEE6RD34PVT6ZXMSKIUI2GDZAM/action/replication_record"}},"created_at":"2026-05-18T02:25:03.783989+00:00","updated_at":"2026-05-18T02:25:03.783989+00:00"}