Error-Correcting Codes With Large Field Size Under Non-Binary Segmented Burst Deletion/Insertion Channels and Unknown Codeword Boundaries
Chen Yi, Linqi Zou, Yong Li, Zhaoyang Qiu, Youqiang Hu, Francis C. M. Lau · IEEE Transactions on Communications · 2024
In this paper, we construct non-binary codes of lengthNwhich correct errors under a non-binary segment-Nmaxburst-Ddeletion and maxburst-Sinsertion (NB-SBDI(N, D, S)) channel without knowing the codeword boundaries. In this NB-SBDI(N, D, S) channel, at most a single non-binary burst (a block of consecutive bits/symbols) of deletions or insertions of length up toDorS, respectively, exists in a block ofNconsecutive non-binary symbols. One code named as BM-DB-MDS consists of a maximum distance separable (MDS) code, a block of periodic de Bruijn (DB) symbols, and a block of proposed periodic binary marker (BM) patterns with a period ofS+D+ 2. The other code called BM-MDS code consists of a BM code and an MDS code. We show that the rates of BM-DB-MDS and BM-MDS codes achieve λ/λ+1 (1 - 1/2t), λ ∈ N+and 1 - 1/t, respectively, whenN→ +∞, where λ represent the MDS code shortening factor, and 1/tis the rough proportion of the maximum length of burst deletions or insertions allowed in a code.