Design of Codes for One Insertion and at Most Two Consecutive Deletion Errors

This paper proposes a novel binary code to correct one insertion and at most two consecutive deletion errors simultaneously occurring in a codeword. Our proposed code is intended first to isolate the possible error cases among all the error scenarios, and then correct the errors. Furthermore, we provide detailed descriptions of the code construction and also suggest a decoding strategy for the proposed code. According to the proposed code, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\log _{2} n +O(1)$ </tex-math></inline-formula> redundancy bits are required to correct one insertion and at most two consecutive deletion errors occurring in a codeword. In addition, a decoding procedure of the proposed code is comprehensively presented for all error scenarios including a single insertion error, an insertion and a deletion error, and an insertion and two consecutive deletion errors.