KO Codes

ABSTRACT: Landmark codes underpin reliable physical layer communication, e.g.,  Reed-Muller, BCH, Convolution, Turbo, LDPC  and Polar codes: each is a linear code and represents a mathematical breakthrough. The impact on humanity is huge: each of these codes has been used in global wireless communication standards (satellite, WiFi, cellular). Reliability of communication over the classical additive white Gaussian noise (AWGN) channel enables benchmarking and ranking of the different codes. In this paper, we construct KO codes, a computationally efficient family of deep-learning driven (encoder, decoder) pairs that outperform the state-of-the-art reliability performance on the standardized AWGN channel. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding, in the challenging short-to-medium block length regime on the AWGN channel.  We show that the gains of KO codes are primarily due to the nonlinear mapping of information bits directly to transmit symbols (bypassing modulation) and yet possess  an efficient, high performance   decoder.  The key technical innovation that renders this possible is the design of a novel family of neural architectures inspired by the computation tree of the Kronecker Operation (KO) central to Reed-Muller and Polar codes. These architectures pave the way for the discovery of a much richer class of hitherto unexplored nonlinear algebraic structures. The code is available at   https://github.com/deepcomm/KOcodes.

This is joint work with A. Makkuva, X. Liu, V. Jamali, S. Mahdavifar and S. Oh.

BIO: Pramod Viswanath is the Gilmore Family Endowed Professor at the University of Illinois at Urbana-Champaign. His interests include a first principles research in coding and communication protocols through the lens of deep learning advances.

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