The two-user interference channel is a model for multi one-to-one communications, where two transmitters wish to communicate with their corresponding receivers via a shared wireless medium. Two most common and simple coding schemes are time division
(TD) and treating interference as noise (TIN). Interestingly, it is shown that there exists an asymptotic scheme, called Han-Kobayashi scheme, that performs better than TD and TIN. However, Han-Kobayashi scheme has impractically high complexity and is designed for asymptotic settings, which leads to a gap between information theory and practice. In this paper, we focus on designing practical codes for interference channels. As it is challenging to analytically design practical codes with feasible complexity, we apply deep learning to learn codes for interference channels. We demonstrate that DeepIC, a convolutional neural network-based code with an iterative decoder, outperforms TD and TIN by a significant margin for two-user additive white Gaussian noise channels with moderate amount of interference.
Distributed source coding is the task of encoding an input in the absence of correlated side information that is only available to the decoder. Remarkably, Slepian and Wolf showed in 1973 that an encoder that has no access to the correlated side info
rmation can asymptotically achieve the same compression rate as when the side information is available at both the encoder and the decoder. While there is significant prior work on this topic in information theory, practical distributed source coding has been limited to synthetic datasets and specific correlation structures. Here we present a general framework for lossy distributed source coding that is agnostic to the correlation structure and can scale to high dimensions. Rather than relying on hand-crafted source-modeling, our method utilizes a powerful conditional deep generative model to learn the distributed encoder and decoder. We evaluate our method on realistic high-dimensional datasets and show substantial improvements in distributed compression performance.
We respond to [1] which claimed that Modulo-SK scheme outperforms Deepcode [2]. We demonstrate that this statement is not true: the two schemes are designed and evaluated for entirely different settings. DeepCode is designed and evaluated for the AWG
N channel with (potentially delayed) uncoded output feedback. Modulo-SK is evaluated on the AWGN channel with coded feedback and unit delay. [1] also claimed an implementation of Schalkwijk and Kailath (SK) [3] which was numerically stable for any number of information bits and iterations. However, we observe that while their implementation does marginally improve over ours, it also suffers from a fundamental issue with precision. Finally, we show that Deepcode dominates the optimized performance of SK, over a natural choice of parameterizations when the feedback is noisy.
Designing codes that combat the noise in a communication medium has remained a significant area of research in information theory as well as wireless communications. Asymptotically optimal channel codes have been developed by mathematicians for commu
nicating under canonical models after over 60 years of research. On the other hand, in many non-canonical channel settings, optimal codes do not exist and the codes designed for canonical models are adapted via heuristics to these channels and are thus not guaranteed to be optimal. In this work, we make significant progress on this problem by designing a fully end-to-end jointly trained neural encoder and decoder, namely, Turbo Autoencoder (TurboAE), with the following contributions: ($a$) under moderate block lengths, TurboAE approaches state-of-the-art performance under canonical channels; ($b$) moreover, TurboAE outperforms the state-of-the-art codes under non-canonical settings in terms of reliability. TurboAE shows that the development of channel coding design can be automated via deep learning, with near-optimal performance.
Present-day communication systems routinely use codes that approach the channel capacity when coupled with a computationally efficient decoder. However, the decoder is typically designed for the Gaussian noise channel and is known to be sub-optimal f
or non-Gaussian noise distribution. Deep learning methods offer a new approach for designing decoders that can be trained and tailored for arbitrary channel statistics. We focus on Turbo codes and propose DeepTurbo, a novel deep learning based architecture for Turbo decoding. The standard Turbo decoder (Turbo) iteratively applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm with an interleaver in the middle. A neural architecture for Turbo decoding termed (NeuralBCJR), was proposed recently. There, the key idea is to create a module that imitates the BCJR algorithm using supervised learning, and to use the interleaver architecture along with this module, which is then fine-tuned using end-to-end training. However, knowledge of the BCJR algorithm is required to design such an architecture, which also constrains the resulting learned decoder. Here we remedy this requirement and propose a fully end-to-end trained neural decoder - Deep Turbo Decoder (DeepTurbo). With novel learnable decoder structure and training methodology, DeepTurbo reveals superior performance under both AWGN and non-AWGN settings as compared to the other two decoders - Turbo and NeuralBCJR. Furthermore, among all the three, DeepTurbo exhibits the lowest error floor.
Standard decoding approaches rely on model-based channel estimation methods to compensate for varying channel effects, which degrade in performance whenever there is a model mismatch. Recently proposed Deep learning based neural decoders address this
problem by leveraging a model-free approach via gradient-based training. However, they require large amounts of data to retrain to achieve the desired adaptivity, which becomes intractable in practical systems. In this paper, we propose a new decoder: Model Independent Neural Decoder (MIND), which builds on the top of neural decoders and equips them with a fast adaptation capability to varying channels. This feature is achieved via the methodology of Model-Agnostic Meta-Learning (MAML). Here the decoder: (a) learns a good parameter initialization in the meta-training stage where the model is exposed to a set of archetypal channels and (b) updates the parameter with respect to the observed channel in the meta-testing phase using minimal adaptation data and pilot bits. Building on top of existing state-of-the-art neural Convolutional and Turbo decoders, MIND outperforms the static benchmarks by a large margin and shows minimal performance gap when compared to the neural (Convolutional or Turbo) decoders designed for that particular channel. In addition, MIND also shows strong learning capability for channels not exposed during the meta training phase.
Designing channel codes under low-latency constraints is one of the most demanding requirements in 5G standards. However, a sharp characterization of the performance of traditional codes is available only in the large block-length limit. Guided by su
ch asymptotic analysis, code designs require large block lengths as well as latency to achieve the desired error rate. Tail-biting convolutional codes and other recent state-of-the-art short block codes, while promising reduced latency, are neither robust to channel-mismatch nor adaptive to varying channel conditions. When the codes designed for one channel (e.g.,~Additive White Gaussian Noise (AWGN) channel) are used for another (e.g.,~non-AWGN channels), heuristics are necessary to achieve non-trivial performance. In this paper, we first propose an end-to-end learned neural code, obtained by jointly designing a Recurrent Neural Network (RNN) based encoder and decoder. This code outperforms canonical convolutional code under block settings. We then leverage this experience to propose a new class of codes under low-latency constraints, which we call Low-latency Efficient Adaptive Robust Neural (LEARN) codes. These codes outperform state-of-the-art low-latency codes and exhibit robustness and adaptivity properties. LEARN codes show the potential to design new versatile and universal codes for future communications via tools of modern deep learning coupled with communication engineering insights.
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 centur
y. 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 parameterized 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.
