Data-Driven Neural Polar Decoders for Unknown Channels with and Without Memory

In this work, a novel data-driven methodology for designing neural polar decoders for channels with and without memory 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 proposed method leverages the structure of the successive cancellation (SC) decoder to devise a neural SC (NSC) decoder. The NSC decoder uses neural networks (NNs) to replace the core elements of the original SC decoder, the check-node, the bit-node and the soft-decision. Along with the NSC, we devise additional NN that embeds the channel outputs into the input space of the SC decoder. The proposed method is supported by theoretical guarantees that include the consistency of the NSC. Additionally, the computational complexity of the NSC decoder does not increase with the channel's memory size and is given by O(mdN\log N) , where N is the block length, and d and m represent the dimensions of the input and the hidden units of the implemented NNs, respectively. This sets its main advantage over successive cancellation trellis (SCT) decoder for finite state channels (FSCs) that has complexity of O(|S}|3N log N), where |S|denotes the number of channel states. We demonstrate the performance of the proposed algorithms on memoryless channels and on channels with memory. The empirical results are compared with the analytic polar decoder, given by the SC and SCT decoders. We further show that our algorithms are applicable for the case where there SC and SCT decoders are not applicable.