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Register a new userLEARN Codes: Inventing Low-latency Codes via Recurrent Neural Networks
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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 such 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.
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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 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 computationaly 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 real symbols (bypassing modulation) and yet possess an efficient, high performance decoder. The key technical innovation that renders this possible is design of a novel family of neural architectures inspired by the computation tree of the {bf K}ronecker {bf O}peration (KO) central to Reed-Muller and Polar codes. These architectures pave way for the discovery of a much richer class of hitherto unexplored nonlinear algebraic structures. The code is available at href{https://github.com/deepcomm/KOcodes}{https://github.com/deepcomm/KOcodes}
In this paper, we model Density Evolution (DE) using Recurrent Neural Networks (RNNs) with the aim of designing capacity-approaching Irregular Low-Density Parity-Check (LDPC) codes for binary erasure channels. In particular, we present a method for determining the coefficients of the degree distributions, characterizing the structure of an LDPC code. We refer to our RNN architecture as Neural Density Evolution (NDE) and determine the weights of the RNN that correspond to optimal designs by minimizing a loss function that enforces the properties of asymptotically optimal design, as well as the desired structural characteristics of the code. This renders the LDPC design process highly configurable, as constraints can be added to meet applications requirements by means of modifying the loss function. In order to train the RNN, we generate data corresponding to the expected channel noise. We analyze the complexity and optimality of NDE theoretically, and compare it with traditional design methods that employ differential evolution. Simulations illustrate that NDE improves upon differential evolution both in terms of asymptotic performance and complexity. Although we focus on asymptotic settings, we evaluate designs found by NDE for finite codeword lengths and observe that performance remains satisfactory across a variety of channels.
Recurrent Neural Networks (RNNs) are among the most popular models in sequential data analysis. Yet, in the foundational PAC learning language, what concept class can it learn? Moreover, how can the same recurrent unit simultaneously learn functions from different input tokens to different output tokens, without affecting each other? Existing generalization bounds for RNN scale exponentially with the input length, significantly limiting their practical implications. In this paper, we show using the vanilla stochastic gradient descent (SGD), RNN can actually learn some notable concept class efficiently, meaning that both time and sample complexity scale polynomially in the input length (or almost polynomially, depending on the concept). This concept class at least includes functions where each output token is generated from inputs of earlier tokens using a smooth two-layer neural network.
Recurrent Neural Networks (RNNs) are used in state-of-the-art models in domains such as speech recognition, machine translation, and language modelling. Sparsity is a technique to reduce compute and memory requirements of deep learning models. Sparse RNNs are easier to deploy on devices and high-end server processors. Even though sparse operations need less compute and memory relative to their dense counterparts, the speed-up observed by using sparse operations is less than expected on different hardware platforms. In order to address this issue, we investigate two different approaches to induce block sparsity in RNNs: pruning blocks of weights in a layer and using group lasso regularization to create blocks of weights with zeros. Using these techniques, we demonstrate that we can create block-sparse RNNs with sparsity ranging from 80% to 90% with small loss in accuracy. This allows us to reduce the model size by roughly 10x. Additionally, we can prune a larger dense network to recover this loss in accuracy while maintaining high block sparsity and reducing the overall parameter count. Our technique works with a variety of block sizes up to 32x32. Block-sparse RNNs eliminate overheads related to data storage and irregular memory accesses while increasing hardware efficiency compared to unstructured sparsity.
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity and poor performance at the low signal-to-noise ratio (SNR) region. In this letter, we adopt the penalty dual decomposition (PDD) framework and propose a PDD algorithm to address the fundamental polytope based maximum likelihood (ML) decoding problem. Furthermore, we propose to integrate machine learning techniques into the most time-consuming part of the PDD decoding algorithm, i.e., check polytope projection (CPP). Inspired by the fact that a multi-layer perception (MLP) can theoretically approximate any nonlinear mapping function, we present a specially designed neural CPP (NCPP) algorithm to decrease the decoding latency. Simulation results demonstrate the effectiveness of the proposed algorithms.
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