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In this work, a novel data-driven methodology for designing polar codes forchannels with and without memory is proposed. The methodology is suitable forthe case where the channel is given as a "black-box" and the designer hasaccess to the channel for generating observations of its inputs and outputs,but does not have access to the explicit channel model. The proposed methodleverages the structure of the successive cancellation (SC) decoder to devise aneural SC (NSC) decoder. The NSC decoder uses neural networks (NNs) to replacethe core elements of the original SC decoder, the check-node, the bit-node andthe soft decision. Along with the NSC, we devise additional NN that embeds thechannel outputs into the input space of the SC decoder. The proposed method issupported by theoretical guarantees that include the consistency of the NSC.Also, the NSC has computational complexity that does not grow with the channelmemory size. This sets its main advantage over successive cancellation trellis(SCT) decoder for finite state channels (FSCs) that has complexity of$O(|\mathcal{S}|^3 N\log N)$, where $|\mathcal{S}|$ denotes the number ofchannel states. We demonstrate the performance of the proposed algorithms onmemoryless channels and on channels with memory. The empirical results arecompared with the optimal polar decoder, given by the SC and SCT decoders. Wefurther show that our algorithms are applicable for the case where there SC andSCT decoders are not applicable.

Data-Driven Neural Polar Codes for Unknown Channels With and Without Memory