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• W2974238532 abstract "This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (BDC$_p$) every bit is deleted independently with probability $p$. A lower bound of $(1-p)/9$ is known on the capacity of the BDC$_p$ cite{mitzenmacher2006simple}, yet no explicit construction is known to achieve this rate. We give an explicit family of codes of rate $(1-p)/16$, for every $p$. This improves upon the work of Guruswami and Li cite{guruswami2017efficiently} that gave a construction of rate $(1-p)/120$. The codes in our family have polynomial time encoding and decoding algorithms. Another channel considered in this work is the Poisson repeat channel with parameter $lambda$ (PRC$_{lambda}$) in which every bit is replaced with a discrete Poisson number of copies of that bit, where the number of copies has mean $lambda$. We show that our construction works for this channel as well. As far as we know, this is the first explicit construction of an error correcting code for PRC$_{lambda}$." @default.
• W2974238532 created "2019-09-26" @default.
• W2974238532 creator A5004182247 @default.
• W2974238532 creator A5025677091 @default.
• W2974238532 date "2019-09-23" @default.
• W2974238532 modified "2023-09-27" @default.
• W2974238532 title "Explicit and Efficient Constructions of Coding Schemes for the Binary Deletion Channel and the Poisson Repeat Channel" @default.
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• W2974238532 hasPublicationYear "2019" @default.
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