Two of the most common models for channels with synchronisation errors are the Binary Deletion Channel with parameter p (BDC_p) - a channel where every bit of the codeword is deleted i.i.d with probability p, and the Poisson Repeat Channel with parameter λ (PRC_λ) - a channel where every bit of the codeword is repeated Poisson(λ) times. Previous constructions based on synchronisation strings yielded codes with rates far lower than the capacities of these channels [Con and Shpilka, 2019; Guruswami and Li, 2018], and the only efficient construction to achieve capacity on the BDC at the time of writing this paper is based on the far more advanced methods of polar codes [Tal et al., 2021]. In this work, we present a new method for concatenating synchronisation codes and use it to construct simple and efficient encoding and decoding algorithms for both channels with nearly optimal rates.
@InProceedings{rubinstein:LIPIcs.ICALP.2022.105, author = {Rubinstein, Ittai}, title = {{Explicit and Efficient Construction of Nearly Optimal Rate Codes for the Binary Deletion Channel and the Poisson Repeat Channel}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {105:1--105:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.105}, URN = {urn:nbn:de:0030-drops-164466}, doi = {10.4230/LIPIcs.ICALP.2022.105}, annote = {Keywords: Error Correcting Codes, Algorithmic Coding Theory, Binary Deletion Channel} }
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