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

TL;DR

This paper develops theoretical bounds and algorithms for learning communication encoders and decoders over additive noise channels with unknown noise distributions, demonstrating improved error performance through novel algorithms and analysis.

Contribution

It introduces new generalization bounds and algorithms for learning communication systems over nonparametric noise channels, including both uncoded and coded scenarios.

Findings

High probability bounds for error and surrogate loss functions.

A stochastic-gradient based alternating-minimization algorithm.

A Gibbs-based codebook expurgation algorithm with error bounds.

Abstract

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.