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This work gives an explicit construction of a family of error correctingcodes for the binary deletion channel and for the Poisson repeat channel. Inthe binary deletion channel with parameter $p$ (BDC$_p$) every bit is deletedindependently with probability $p$. A lower bound of $(1-p)/9$ is known on thecapacity of the BDC$_p$ \cite{mitzenmacher2006simple}, yet no explicitconstruction is known to achieve this rate. We give an explicit family of codesof rate $(1-p)/16$, for every $p$. This improves upon the work of Guruswami andLi \cite{guruswami2017efficiently} that gave a construction of rate$(1-p)/120$. The codes in our family have polynomial time encoding and decodingalgorithms.  Another channel considered in this work is the Poisson repeat channel withparameter $\lambda$ (PRC$_{\lambda}$) in which every bit is replaced with adiscrete Poisson number of copies of that bit, where the number of copies hasmean $\lambda$. We show that our construction works for this channel as well.As far as we know, this is the first explicit construction of an errorcorrecting code for PRC$_{\lambda}$.

Explicit and Efficient Constructions of Coding Schemes for the Binary Deletion Channel and the Poisson Repeat Channel