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convolutional code


LEARN Codes: Inventing Low-latency Codes via Recurrent Neural Networks

arXiv.org Artificial Intelligence

Designing channel codes under low latency constraints is one of the most demanding requirements in 5G standards. However, sharp characterizations of the performances of traditional codes are only available in the large block-length limit. Code designs are guided by those asymptotic analyses and require large block lengths and long latency to achieve the desired error rate. Furthermore, 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 any nontrivial performance -thereby severely lacking in robustness as well as adaptivity. Obtained by jointly designing Recurrent Neural Network (RNN) based encoder and decoder, we propose an end-to-end learned neural code which outperforms canonical convolutional code under block settings. With this gained experience of designing a novel neural block code, we propose a new class of codes under low latency constraint - Low-latency Efficient Adaptive Robust Neural (LEARN) codes, which outperforms the state-of-the-art low latency codes as well as exhibits robustness and adaptivity properties. LEARN codes show the potential of designing new versatile and universal codes for future communications via tools of modern deep learning coupled with communication engineering insights.


Communication Algorithms via Deep Learning

arXiv.org Machine Learning

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 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.


The Viterbi Algorithm Demystified - USC Viterbi School of Engineering

#artificialintelligence

Fifty years ago, I published a paper, "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm," on the important class of convolutional codes, which is particularly effective in preventing errors in digital communication over wireless and other transmission media. The algorithm, which became labeled with my name, was a crucial step in establishing the merits as well as evaluating the performance of these codes. The paper was read and understood by only a few specialists. In the next few years, clarity was provided by two papers, the first by a colleague, G.D. Forney Jr., who introduced the trellis model, and the second by myself based on a state diagram, or Markov model. A.A. Markov was a Russian mathematician who proposed and analyzed a statistical concept regarding the relationship between terms of a sequence or, more generally, of successive events; specifically, that each term (or string of terms) or event is statistically dependent only on the previous one.


A Trellis-Structured Neural Network

Neural Information Processing Systems

We have presented a locally interconnected network which minimizes a function that is analogous to the log likelihood function near the global minimum. The results of simulations demonstrate that the network can successfully decode input sequences containing no noise at least as well as the globally connected Hopfield-Tank [6] decomposition network.Simulations also strongly support the conjecture that in the noiseless case, the network can be guaranteed to converge to the global minimum. In addition, for low error rates, the network can also decode noisy received sequences. We have been able to apply the Cohen-Grossberg proof of the stability of "oncenter off-surround"networks to show that each stage will maximize the desired local "likelihood" for noisy received sequences. We have also shown that, in the large gain limit, the network as a whole is stable and that the equilibrium points correspond to the MLSE decoder output.


A Trellis-Structured Neural Network

Neural Information Processing Systems

We have presented a locally interconnected network which minimizes a function that is analogous to the log likelihood function near the global minimum. The results of simulations demonstrate that the network can successfully decode input sequences containing no noise at least as well as the globally connected Hopfield-Tank [6] decomposition network. Simulations also strongly support the conjecture that in the noiseless case, the network can be guaranteed to converge to the global minimum. In addition, for low error rates, the network can also decode noisy received sequences. We have been able to apply the Cohen-Grossberg proof of the stability of "oncenter off-surround" networks to show that each stage will maximize the desired local "likelihood" for noisy received sequences. We have also shown that, in the large gain limit, the network as a whole is stable and that the equilibrium points correspond to the MLSE decoder output. Simulations have verified this proof of stability even for relatively small gains. Unfortunately, a proof of strict Lyapunov stability is very difficult, and may not be possible, because of the cooperative connections in the network. This network demonstrates that it is possible to perform interesting functions even if only localized connections are allowed, although there may be some loss of performance.


A Trellis-Structured Neural Network

Neural Information Processing Systems

We have presented a locally interconnected network which minimizes a function that is analogous to the log likelihood function near the global minimum. The results of simulations demonstrate that the network can successfully decode input sequences containing no noise at least as well as the globally connected Hopfield-Tank [6] decomposition network. Simulations also strongly support the conjecture that in the noiseless case, the network can be guaranteed to converge to the global minimum. In addition, for low error rates, the network can also decode noisy received sequences. We have been able to apply the Cohen-Grossberg proof of the stability of "oncenter off-surround" networks to show that each stage will maximize the desired local "likelihood" for noisy received sequences. We have also shown that, in the large gain limit, the network as a whole is stable and that the equilibrium points correspond to the MLSE decoder output. Simulations have verified this proof of stability even for relatively small gains. Unfortunately, a proof of strict Lyapunov stability is very difficult, and may not be possible, because of the cooperative connections in the network. This network demonstrates that it is possible to perform interesting functions even if only localized connections are allowed, although there may be some loss of performance.