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This paper introduces a neural polar decoder (NPD) for deletion channels with a constant deletion rate. Existing polar decoders for deletion channels exhibit high computational complexity of O(N4), where N is the block length. This limits the application of polar codes for deletion channels to short-to-moderate block lengths. In this work, we demonstrate that employing NPDs for deletion channels can reduce the computational complexity. First, we extend the architecture of the NPD to support deletion channels. Specifically, the NPD architecture consists of four neural networks (NNs), each replicating fundamental successive cancellation (SC) decoder operations. To support deletion channels, we change the architecture of only one. The computational complexity of the NPD is O(ANlogN), where the parameter A represents a computational budget determined by the user and is independent of the channel. We evaluate the new extended NPD for deletion channels with deletion rates δ∈{0.01,0.1} and we verify the NPD with the ground truth given by the trellis decoder by Tal et al. We further show that due to the reduced complexity of the NPD, we are able to incorporate list decoding and further improve performance. We believe that the extended NPD presented here could have applications in future technologies like DNA storage. 

This paper introduces extensions to data-driven polar decoders, enabling list decoding and accommodating asymmetric input distributions. These are crucial steps to develop data-driven codes that 1) achieve capacity and 2) are competitive in moderate block lengths. We commence by integrating list de- coding into the data-driven polar codes, which significantly alleviates the inherent error propagation issues associated with successive cancellation decoding. Secondly, we expand the applicability of these codes to channels with stationary, non-uniform input distributions by incorporating the Honda-Yamamoto scheme. Both modifications are computationally efficient and do not require an explicit channel model. Numerical results validate the efficacy of our contributions, which offer a robust and versatile coding mechanism for various channel conditions. 

In this work, a novel data-driven methodology for designing polar codes is proposed. The methodology is suitable for the case where the channel is given as a ”black-box” and the designer has access to the channel for generating observations of its inputs and outputs, but does not have access to the explicit channel model. The methodology consists of two components: (1) a neural estimation of the sufficient statistic of the channel outputs using recent advances in Kullback Leibler (KL) estimation, and (2) a neural successive cancellation (NSC) decoder using three neural networks that replace the core elements of the successive cancellation (SC) decoder. The parameters of the neural networks are determined during a training phase where the mutual information of the effective channels is estimated. We demonstrate the performance of the algorithm on memoryless channels and on finite state channels. Then, we compare the results with the optimal decoding given by the SC and SC trellis decoders, respectively.