Generalization Bounds and Algorithms for Learning to Communicate Over Additive Noise Channels

An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem of choosing a codebook and possibly also a generalized mini...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 68; no. 3; pp. 1886 - 1921
Main Author: Weinberger, Nir
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additive noise channels
Algorithms
alternating optimization algorithm
Coders
Codes
Communications systems
Convergence
Covariance matrix
Decoders
Decoding
Entropy
entropy estimation
Error probability
Errors
expurgation
generalization bounds
Gibbs algorithm
hinge loss
Loss measurement
Machine learning
minimal distance decoding
mismatch decoding
Noise
Optimization
statistical learning
stochastic gradient descent
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem of choosing a codebook and possibly also a generalized minimal distance decoder (which is parameterized by a covariance matrix) is addressed. High probability generalization bounds for the error probability loss function, as well as for a hinge-type surrogate loss function are provided. A stochastic-gradient based alternating-minimization algorithm for the latter loss function is proposed. In addition, a Gibbs-based algorithm that gradually expurgates an initial codebook from codewords in order to obtain a smaller codebook with improved error probability is proposed, and bounds on its average empirical error and generalization error, as well as a high probability generalization bound, are stated. Various experiments demonstrate the performance of the proposed algorithms. For coded systems, the problem of maximizing the mutual information between the input and the output with respect to the input distribution is addressed, and uniform convergence bounds for two different classes of input distributions are obtained.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3129080