Simple Finite-Length Achievability and Converse Bounds for the Deletion Channel and the Insertion Channel

[2504.20961] Simple Finite-Length Achievability and Converse Bounds for the Deletion Channel and the Insertion Channel Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Information Theory arXiv:2504.20961 (cs) [Submitted on 29 Apr 2025 ( v1 ), last revised 11 Apr 2026 (this version, v4)] Title: Simple Finite-Length Achievability and Converse Bounds for the Deletion Channel and the Insertion Channel Authors: Ruslan Morozov , Tolga Mete Duman View a PDF of the paper titled Simple Finite-Length Achievability and Converse Bounds for the Deletion Channel and the Insertion Channel, by Ruslan Morozov and 1 other authors View PDF HTML (experimental) Abstract: We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse bound, which, though available for any channel, is inefficient and not easily computable without a good reference distribution over the output alphabet. We obtain a reference output distribution for a general finite-input finite-output channel and provide a simple formula for the converse bound on the capacity employing this distribution. We then evaluate the bound for the deletion channel with a finite block length, and show that the resulting upper bound on the code size is tighter than that for a binary erasure channel, which is the only alternative converse bound for the finite-length setting. We also provide similar results for the insertion channel. Furthermore, we present a simple algorithm for computing an achievability bound for a general discrete-input discrete-output channel. Although the algorithm has exponential complexity, it is useful for comparison purposes. Comments: 12 pages, 5 tables, 4 figures, extended version of ISIT-2025 paper Subjects: Information Theory (cs.IT) MSC classes: 94B70 Cite as: arXiv:2504.20961 [cs.IT] (or arXiv:2504.20961v4 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2504.20961 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ruslan Morozov [ view email ] [v1] Tue, 29 Apr 2025 17:32:27 UTC (104 KB) [v2] Fri, 2 May 2025 16:55:13 UTC (104 KB) [v3] Sun, 11 May 2025 14:54:27 UTC (104 KB) [v4] Sat, 11 Apr 2026 10:32:50 UTC (956 KB) Full-text links: Access Paper: View a PDF of the paper titled Simple Finite-Length Achievability and Converse Bounds for the Deletion Channel and the Insertion Channel, by Ruslan Morozov and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.IT < prev | next > new | recent | 2025-04 Change to browse by: cs math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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