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.

Low-density parity-check (LDPC) codes with protograph-based raptor-like (PBRL) structure have been chosen as the data channel coding scheme for the fifth-generation (5G) enhanced mobile broad band (eMBB) services. However, these 5G LDPC codes are not optimized for the scenarios of Ultra Reliable and Low Latency Communications (URLLC) and massive Machine Type Communications (mMTC) in which small transport block sizes are usually used. In this paper, a new method is proposed to construct PBRL LDPC codes for URLLC and mMTC. This method incorporates degree-distribution optimization, base matrix derived from parity-check matrix of quadratic residue codes, masking technique and modified progressive-edge-growth (PEG) algorithm. Simulation results show that the proposed PBRL LDPC codes outperform 5G LDPC short codes in terms of error-correcting performance.