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Landmark codes underpin reliable physical layer communication, e.g.,Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes: each is a linearcode and represents a mathematical breakthrough. The impact on humanity ishuge: each of these codes has been used in global wireless communicationstandards (satellite, WiFi, cellular). Reliability of communication over theclassical additive white Gaussian noise (AWGN) channel enables benchmarking andranking of the different codes. In this paper, we construct KO codes, acomputationaly efficient family of deep-learning driven (encoder, decoder)pairs that outperform the state-of-the-art reliability performance on thestandardized AWGN channel. KO codes beat state-of-the-art Reed-Muller and Polarcodes, under the low-complexity successive cancellation decoding, in thechallenging short-to-medium block length regime on the AWGN channel. We showthat the gains of KO codes are primarily due to the nonlinear mapping ofinformation bits directly to transmit real symbols (bypassing modulation) andyet possess an efficient, high performance decoder. The key technicalinnovation that renders this possible is design of a novel family of neuralarchitectures inspired by the computation tree of the {\bf K}ronecker {\bfO}peration (KO) central to Reed-Muller and Polar codes. These architecturespave way for the discovery of a much richer class of hitherto unexplorednonlinear algebraic structures. The code is available at\href{https://github.com/deepcomm/KOcodes}{https://github.com/deepcomm/KOcodes}

KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning