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Register a new userNeural Mutual Information Estimation for Channel Coding: State-of-the-Art Estimators, Analysis, and Performance Comparison
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Added by
Rick Fritschek
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Deep learning based physical layer design, i.e., using dense neural networks as encoders and decoders, has received considerable interest recently. However, while such an approach is naturally training data-driven, actions of the wireless channel are mimicked using standard channel models, which only partially reflect the physical ground truth. Very recently, neural network based mutual information (MI) estimators have been proposed that directly extract channel actions from the input-output measurements and feed these outputs into the channel encoder. This is a promising direction as such a new design paradigm is fully adaptive and training data-based. This paper implements further recent improvements of such MI estimators, analyzes theoretically their suitability for the channel coding problem, and compares their performance. To this end, a new MI estimator using a emph{``reverse Jensen} approach is proposed.
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In this paper, we investigate the impacts of transmitter and receiver windows on orthogonal time-frequency space (OTFS) modulation and propose a window design to improve the OTFS channel estimation performance. Assuming ideal pulse shaping filters at the transceiver, we first identify the role of window in effective channel and the reduced channel sparsity with conventional rectangular window. Then, we characterize the impacts of windowing on the effective channel estimation performance for OTFS modulation. Based on the revealed insights, we propose to apply a Dolph-Chebyshev (DC) window at either the transmitter or the receiver to effectively enhance the sparsity of the effective channel. As such, the channel spread due to the fractional Doppler is significantly reduced, which leads to a lower error floor in channel estimation compared with that of the rectangular window. Simulation results verify the accuracy of the obtained analytical results and confirm the superiority of the proposed window designs in improving the channel estimation performance over the conventional rectangular or Sine windows.
Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes provide accurate approximations to the mutual information but this approach is restricted to continuous variables because the calculation of Fisher information requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations of the mutual information based on Kullback--Leibler divergence and R{e}nyi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding. While our asymptotic formulas all work for discrete variables, one of them has consistent performance and high accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating the mutual information between the stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.
Estimators for mutual information are typically biased. However, in the case of the Kozachenko-Leonenko estimator for metric spaces, a type of nearest neighbour estimator, it is possible to calculate the bias explicitly.
The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric MSE convergence rate. However, most of the previously proposed estimators have the high computational complexity of at least $O(N^2)$. We propose a unified method for empirical non-parametric estimation of general MI function between random vectors in $mathbb{R}^d$ based on $N$ i.i.d. samples. The reduced complexity MI estimator, called the ensemble dependency graph estimator (EDGE), combines randomized locality sensitive hashing (LSH), dependency graphs, and ensemble bias-reduction methods. We prove that EDGE achieves optimal computational complexity $O(N)$, and can achieve the optimal parametric MSE rate of $O(1/N)$ if the density is $d$ times differentiable. To the best of our knowledge EDGE is the first non-parametric MI estimator that can achieve parametric MSE rates with linear time complexity. We illustrate the utility of EDGE for the analysis of the information plane (IP) in deep learning. Using EDGE we shed light on a controversy on whether or not the compression property of information bottleneck (IB) in fact holds for ReLu and other rectification functions in deep neural networks (DNN).
We point out a limitation of the mutual information neural estimation (MINE) where the network fails to learn at the initial training phase, leading to slow convergence in the number of training iterations. To solve this problem, we propose a faster method called the mutual information neural entropic estimation (MI-NEE). Our solution first generalizes MINE to estimate the entropy using a custom reference distribution. The entropy estimate can then be used to estimate the mutual information. We argue that the seemingly redundant intermediate step of entropy estimation allows one to improve the convergence by an appropriate reference distribution. In particular, we show that MI-NEE reduces to MINE in the special case when the reference distribution is the product of marginal distributions, but faster convergence is possible by choosing the uniform distribution as the reference distribution instead. Compared to the product of marginals, the uniform distribution introduces more samples in low-density regions and fewer samples in high-density regions, which appear to lead to an overall larger gradient for faster convergence.
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