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

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 , 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 (2018) 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 λ (PRC λ) in which every bit is replaced with a discrete Poisson number of copies of that bit, where the number of copies has mean λ . 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 λ.