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- W3208672775 abstract "Two of the most common models for channels with synchronisation errors are the Binary Deletion Channel with parameter $p$ ($text{BDC}_p$) -- a channel where every bit of the codeword is deleted i.i.d with probability $p$, and the Poisson Repeat Channel with parameter $lambda$ ($text{PRC}_lambda$) -- a channel where every bit of the codeword is repeated $text{Poisson}(lambda)$ times. Previous codes for these channels can be split into two main categories: inefficient constructions that prove the capacities of these channels are greater than $frac{1-p}{9}$, $frac{lambda}{9}$ respectively, and more recently, codes with efficient encoding and decoding algorithms that have lower rates $frac{1-p}{16}$, $frac{lambda}{17}$. In this work, we present a new method for concatenating synchronisation codes. This method can be used to transform lower bounds on the capacities of these channels into efficient constructions, at a negligible cost to the rate of the code. This yields a family of codes with quasi-linear encoding and decoding algorithms that achieve rates of $frac{1-p}{9}, frac{lambda}{9}$ respectively for these channels." @default.
- W3208672775 created "2021-11-08" @default.
- W3208672775 creator A5083459233 @default.
- W3208672775 date "2021-11-01" @default.
- W3208672775 modified "2023-09-27" @default.
- W3208672775 title "Explicit and Efficient Construction of (nearly) Optimal Rate Codes for Binary Deletion Channel and the Poisson Repeat Channel." @default.
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