|Syndrome Compression for Optimal Redundancy Codes
|Jin Sima, California Institute of Technology, United States; Ryan Gabrys, University of California San Diego, United States; Jehoshua Bruck, California Institute of Technology, United States
|M.8: Insertion Deletion Substitution Codes II
|Coding for Storage and Memories
|Click here to download the manuscript
|Click here to watch in the Virtual Symposium
|We introduce a general technique that we call syndrome compression, for designing low-redundancy error correcting codes. The technique allows us to boost the redundancy efficiency of hash/labeling-based codes by further compressing the labeling. We apply syndrome compression to different types of adversarial deletion channels and present code constructions that correct up to a constant number of errors. Our code constructions achieve the redundancy of twice the Gilbert-Varshamov bound, which improve upon the state of art for these channels. The encoding/decoding complexity of our constructions is of order equal to the size of the corresponding deletion balls, namely, it is polynomial in the code length.