Channel Coding for Gaussian Channels with Multifaceted Power Constraints

2025-11-18

AI Summary

This paper investigates the fundamental limits of coding performance over Gaussian channels subject to multi-faceted power constraints. Addressing the fragmentation of conventional power models—such as peak, average, and variance constraints—it introduces a unified “multi-faceted power constraint” framework, wherein expectations of arbitrary continuous functions of the normalized average power are constrained. Leveraging compactness of probability measure spaces, Bauer’s maximum principle, extremal analysis under the Prokhorov metric, normal approximation, and limit theorems for stochastic processes, the authors derive, for the first time under mild growth and continuity assumptions, exact first- and second-order asymptotic expansions for the minimum average error probability. The results subsume and generalize classical power-constrained settings, while significantly advancing the understanding of channel capacity and finite-blocklength performance under nonstandard, functionally defined power constraints.

Technology Category

• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Motivated by refined asymptotic results based on the normal approximation, we study how higher-order coding performance depends on the mean power $Gamma$ as well as on finer statistics of the input power. We introduce a multifaceted power model in which the expectation of an arbitrary number of arbitrary functions of the normalized average power is constrained. The framework generalizes existing models, recovering the standard maximal and expected power constraints and the recent mean and variance constraint as special cases. Under certain growth and continuity assumptions on the functions, our main theorem gives an exact characterization of the minimum average error probability for Gaussian channels as a function of the first- and second-order coding rates. The converse proof reduces the code design problem to minimization over a compact (under the Prokhorov metric) set of probability distributions, characterizes the extreme points of this set and invokes the Bauer's maximization principle.

Problem

• Characterizing coding performance under multifaceted power constraints
• Generalizing power constraint models for Gaussian channels
• Deriving minimum error probability with first/second-order rates

Innovation

• Multifaceted power model constraining arbitrary functions
• Exact error probability characterization via first-second order rates
• Converse proof using compact distribution set minimization