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.

In this paper, we introduce a deep learning-based decoder designed for concatenated coding schemes over a deletion/substitution channel. Specifically, we focus on serially concatenated codes, where the outer code is either a convolutional or a low-density parity-check (LDPC) code, and the inner code is a marker code. We utilize Bidirectional Gated Recurrent Units (BI-GRUs) as log-likelihood ratio (LLR) estimators and outer code decoders for estimating the message bits. Our results indicate that decoders powered by BI-GRUs perform comparably in terms of error rates with the MAP detection of the marker code. We also find that a single network can work well for a wide range of channel parameters. In addition, it is possible to use a single BI-GRU based network to estimate the message bits via one-shot decoding when the outer code is a convolutional code.11Code is available at https://github.com/Bilkent-CTAR-Lab/DNN-for-Deletion-Channel