{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T02:09:21Z","timestamp":1780538961522,"version":"3.54.1"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T00:00:00Z","timestamp":1626652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-0939370  CCF-1908308"],"award-info":[{"award-number":["CCF-0939370  CCF-1908308"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","award":["4191101"],"award-info":[{"award-number":["4191101"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61971264"],"award-info":[{"award-number":["61971264"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["2018YFB1801102"],"award-info":[{"award-number":["2018YFB1801102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Short-packet transmission has attracted considerable attention due to its potential to achieve ultralow latency in automated driving, telesurgery, the Industrial Internet of Things (IIoT), and other applications emerging in the coming era of the Six-Generation (6G) wireless networks. In 6G systems, a paradigm-shifting infrastructure is anticipated to provide seamless coverage by integrating low-Earth orbit (LEO) satellite networks, which enable long-distance wireless relaying. However, how to efficiently transmit short packets over a sizeable spatial scale remains open. In this paper, we are interested in low-latency short-packet transmissions between two distant nodes, in which neither propagation delay, nor propagation loss can be ignored. Decode-and-forward (DF) relays can be deployed to regenerate packets reliably during their delivery over a long distance, thereby reducing the signal-to-noise ratio (SNR) loss. However, they also cause decoding delay in each hop, the sum of which may become large and cannot be ignored given the stringent latency constraints. This paper presents an optimal relay deployment to minimize the error probability while meeting both the latency and transmission power constraints. Based on an asymptotic analysis, a theoretical performance bound for distant short-packet transmission is also characterized by the optimal distance\u2013latency\u2013reliability tradeoff, which is expected to provide insights into designing integrated LEO satellite communications in 6G.<\/jats:p>","DOI":"10.3390\/e23070916","type":"journal-article","created":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T10:07:37Z","timestamp":1626689257000},"page":"916","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Low-Latency Short-Packet Transmission over a Large Spatial Scale"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9386-9359","authenticated-orcid":false,"given":"Lei","family":"Huang","sequence":"first","affiliation":[{"name":"Beijing National Research Center for Information Science and Technology (BNRist), Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Beijing National Research Center for Information Science and Technology (BNRist), Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9066-1448","authenticated-orcid":false,"given":"Wei","family":"Chen","sequence":"additional","affiliation":[{"name":"Beijing National Research Center for Information Science and Technology (BNRist), Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2062-131X","authenticated-orcid":false,"given":"H. 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