Error-Correcting Codes with Large Field Size under Non-Binary Segmented Burst Deletion/Insertion Channels and Unknown Codeword Boundaries

In this paper, we construct non-binary codes of length
N
which correct errors under a non-binary segment-
N
maxburst-
D
deletion and maxburst-
S
insertion (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 to
D
or
S
, respectively, exists in a block of
N
consecutive 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 of
S
+
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 - 1/2
t
), λ ∈ N
⁺
and 1 - 1/
t
, respectively, when
N
→ +∞, where λ represent the MDS code shortening factor, and 1/
t
is the rough proportion of the maximum length of burst deletions or insertions allowed in a code.