{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/low-field-size-rate-optimal-streaming-codes","title":"Low Field-size, Rate-Optimal Streaming Codes for Channels With Burst and Random Erasures","arxiv_id":"1903.06210","date":"2019-03-14","proceeding":null,"authors":["M. Nikhil Krishnan","Deeptanshu Shukla","P. Vijay Kumar"],"abstract":"In this paper, we design erasure-correcting codes for channels with burst and random erasures, when a strict decoding delay constraint is in place. We consider the sliding-window-based packet erasure model proposed by Badr et al., where any time-window of width $w$ contains either up to $a$ random erasures or an erasure burst of length at most $b$. One needs to recover any erased packet, where erasures are as per the channel model, with a strict decoding delay deadline of $\\tau$ time slots. Presently existing rate-optimal constructions in the literature require, in general, a field-size which grows exponential in $\\tau$, for a constant $\\frac{a}{\\tau}$. In this work, we present a new rate-optimal code construction covering all channel and delay parameters, which requires an $O(\\tau^2)$ field-size. As a special case, when $(b-a)=1$, we have a field-size linear in $\\tau$. We also present three other constructions having linear field-size, under certain constraints on channel and decoding delay parameters. As a corollary, we obtain low field-size, rate-optimal convolutional codes for any given column distance and column span. Simulations indicate that the newly proposed streaming code constructions offer lower packet-loss probabilities compared to existing schemes, for selected instances of Gilbert-Elliott and Fritchman channels.","url_abs":"http://arxiv.org/abs/1903.06210v1","url_pdf":"http://arxiv.org/pdf/1903.06210v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"low-field-size-rate-optimal-streaming-codes","repo_url":"https://github.com/deeptanshu04/StreamingCodes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}