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

In the binary deletion channel with parameter p (BDCp) every bit is deleted independently with probability p. [1] proved a lower bound of (1−p)/9 on the capacity of the BDCp, yet currently no explicit construction achieves this rate. In this work we give an explicit family of codes of rate (1 −p)/16, for every p. This improves upon the work of Guruswami and Li [2] that gave a construction of rate (1−p)/120. The codes in our family have polynomial time encoding and decoding algorithms.