Construction of capacity achieving deletion correcting codes has been a
baffling challenge for decades. A recent breakthrough by Brakensiek etal.,
alongside novel applications in DNA storage, have reignited the interest in
this longstanding open problem. In spite of recent advances, the amount of
redundancy in existing codes is still orders of magnitude away from being
optimal. In this paper, a novel approach for constructing binary two-deletion
correcting codes is proposed. By this approach, parity symbols are computed
from indicator vectors (i.e., vectors that indicate the positions of certain
patterns) of the encoded message, rather than from the message itself. Most
interestingly, the parity symbols and the proof of correctness are a direct
generalization of their counterparts in the Varshamov-Tenengolts construction.
Our techniques require 7log(n)+o(log(n) redundant bits to encode an~n-bit
message, which is near-optimal
