{"paper":{"title":"Capacity of Three-Dimensional Erasure Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Cheol Jeong, Won-Yong Shin","submitted_at":"2016-05-11T05:01:41Z","abstract_excerpt":"In this paper, we introduce a large-scale three-dimensional (3D) erasure network, where $n$ wireless nodes are randomly distributed in a cuboid of $n^{\\lambda}\\times n^{\\mu}\\times n^{\\nu}$ with $\\lambda+\\mu+\\nu=1$ for $\\lambda,\\mu,\\nu>0$, and completely characterize its capacity scaling laws. Two fundamental path-loss attenuation models (i.e., exponential and polynomial power-law models) are used to suitably model an erasure probability for packet transmission. Then, under the two erasure models, we introduce a routing protocol using percolation highway in 3D space, and then analyze its achiev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03282","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"}