Symbol-Level Deep Learning-Based Decoders for Concatenated Codes Over Insertion/Deletion Channels

Synchronization errors, such as insertions and deletions, pose significant challenges in communication and storage systems, including DNA data storage. Among different alternatives, serially concatenated coding schemes, where a powerful outer code is concatenated with an inner marker code, have proven effective in mitigating such errors. A common method of decoding the inner marker code is to employ the forward-backward algorithm implementing bitwise or symbolwise maximum a posteriori (MAP) detection. Recently, bit-level deep-learning based solutions have also been proposed for decoding marker codes. In this paper, we consider symbol-level deep-learning based decoders, which exploit correlations among adjacent bits to improve the decoding performance, and develop new channel detection algorithms. Unlike existing symbol-level MAP decoding approaches that can combine only two or three consecutive bits, the proposed deep-learning methods extend well beyond this limit, and achieve improved error correction performance. We also develop deep-learning based decoders for insertion/deletion channels further exacerbated by intersymbol interference, motivated by bit-patterned media recording channels and nanopore sequencing. Extensive numerical results show that the proposed symbol-level deep-learning architectures are highly effective for communication over insertion/deletion channels.