The design of codes for communicating reliably over a statistically well defined channel is an important endeavor involving deep mathematical research and wide-ranging practical applications. In this work, we present the first family of codes obtained via deep learning, which significantly beats state-of-the-art codes designed over several decades of research. The communication channel under consideration is the Gaussian noise channel with feedback, whose study was initiated by Shannon; feedback is known theoretically to improve reliability of communication, but no practical codes that do so have ever been successfully constructed.We break this logjam by integrating information theoretic insights harmoniously with recurrent-neural-network based encoders and decoders to create novel codes that outperform known codes by 3 orders of magnitude in reliability. We also demonstrate several desirable properties of the codes: (a) generalization to larger block lengths, (b) composability with known codes, (c) adaptation to practical constraints. This result also has broader ramifications for coding theory: even when the channel has a clear mathematical model, deep learning methodologies, when combined with channel-specific information-theoretic insights, can potentially beat state-of-the-art codes constructed over decades of mathematical research.

Coding theory is a central discipline underpinning wireline and wireless modems that are the workhorses of the information age. Progress in coding theory is largely driven by individual human ingenuity with sporadic breakthroughs over the past century. In this paper we study whether it is possible to automate the discovery of decoding algorithms via deep learning. We study a family of sequential codes parametrized by recurrent neural network (RNN) architectures. We show that creatively designed and trained RNN architectures can decode well known sequential codes such as the convolutional and turbo codes with close to optimal performance on the additive white Gaussian noise (AWGN) channel, which itself is achieved by breakthrough algorithms of our times (Viterbi and BCJR decoders, representing dynamic programing and forward-backward algorithms). We show strong generalizations, i.e., we train at a specific signal to noise ratio and block length but test at a wide range of these quantities, as well as robustness and adaptivity to deviations from the AWGN setting.

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BackgroundLitchi is an evergreen woody tree widely cultivated in subtropical and tropical regions. Defective flowering is a major challenge for litchi production in time of climate change and global warming. Previous studies have shown that high temperature conditions encourage the growth of rudimentary leaves in panicles and suppress litchi flowering, while reactive oxygen species (ROS) generated by methyl viologen dichloride hydrate (MV) promote flowering and abortion of rudimentary leaves. To understand the molecular function of the ROS-induced abortion of rudimentary leaves in litchi, we sequenced and de novo assembled the litchi transcriptome.ResultsOur assembly encompassed 82,036 unigenes with a mean size of 710 bp, and over 58% (47,596) of unigenes showed significant similarities to known sequences in GenBank non-redundant (nr) protein database. 5,865 unigenes were found to be differentially expressed between ROS-treated and un-treated rudimentary leaves, and genes encoding signaling components of plant hormones such as ABA and ethylene were significantly enriched.ConclusionOur transcriptome data represents the comprehensive collection of expressed sequence tags (ESTs) of litchi leaves, which is a vital resource for future studies on the genomics of litchi and other closely related species. The identified differentially expressed genes also provided potential candidates for functional analysis of genes involved in litchi flowering underlying the control of rudimentary leaves in the panicles.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2164-15-805) contains supplementary material, which is available to authorized users.