We introduce a probabilistic burst insertion/deletion channel (BIDC) model and investigate practical concatenated coding schemes for BIDCs with multiple burst errors. First, the existence of channel capacity for BIDCs is established, and the capacity upper and lower bounds for BIDCs are analyzed and computed. For the capacity upper bound, genie-aided information is provided to the receiver, and then the informationtheoretic upper bound can be computed via the Blahut-Arimoto algorithm. For the capacity lower bound, the achievable information rates of BIDCs with independent and identically distributed inputs are computed by using trellis structures of the corresponding channels. Second, marker codes, constructed by concatenating marker bits with low-density parity-check (LDPC) codes, are investigated for BIDCs. The forward and backward (FB) detection algorithm of marker codes, initially designed for random insertion/deletion errors, may not be optimal for BIDCs. Therefore, a new FB detection algorithm of marker codes is designed according to the characteristics of BIDCs. Furthermore, an inter-frame interleaving scheme is proposed to enhance the decoding performance of marker codes over BIDCs. Simulation results show that the error rate performance of our newly designed FB algorithm for BIDCs is superior to that of the original FB algorithm when the burst characteristics of the channel are explicitly considered. Furthermore, the performance of the proposed algorithm is also better than that of the recently designed deep learning-based decoding method for marker codes over insertion/deletion channels.

Marker code is an effective coding scheme to protect data from insertions and deletions. It has potential applications in future storage systems, such as DNA storage and racetrack memory. When decoding marker codes, perfect channel state information (CSI), i.e., insertion and deletion probabilities, are required to detect insertion and deletion errors. Sometimes, the perfect CSI is not easy to obtain or the accurate channel model is unknown. Therefore, it is deserved to develop detecting algorithms for marker code without the knowledge of perfect CSI. In this paper, we propose two CSI-agnostic detecting algorithms for marker code based on deep learning. The first one is a model-driven deep learning method, which deep unfolds the original iterative detecting algorithm of marker code. In this method, CSI become weights in neural networks and these weights can be learned from training data. The second one is a data-driven method which is an end-to-end system based on the deep bidirectional gated recurrent unit network. Simulation results show that error performances of the proposed methods are significantly better than that of the original detection algorithm with CSI uncertainty. Furthermore, the proposed data-driven method exhibits better error performances than other methods for unknown channel models.