One Bit-Flipping/Insertion/Deletion Correcting Code for Substrings of Binary Circular String

Compression by Substring Enumeration (CSE), which is one of lossless data compression algorithms, and various versions of CSE have been proposed. In encoding of CSE, substrings of given fixed length and their frequencies within circular string for an input string are output as a codeword. The circular string is made by connecting the first symbol and the last symbol of an input string. In decoding of CSE, the circular string is reconstructed from its substrings and their frequencies. Furthermore, the minimum length of substrings for which the decoding does reconstruct the circular string has been proved, together with a reconstruction algorithm. However, the algorithm requires substrings to have no errors. Therefore, in this paper, we propose an error correcting algorithm which can detect one of substrings having one bit-flipping, one bit-insertion, or one bit-deletion error and correct the bit error. By applying the proposed algorithm, we can reconstruct a circular string from a set of substrings and their frequencies including only one substring which has at most one bit error.