Characterization of Deletion/Substitution Channel Capacity for Small Deletion and Substitution Probabilities

2025-03-04

AI Summary

This work investigates the capacity limit of the binary-input deletion/insertion–substitution channel under low-error-probability regimes, aiming to characterize how synchronization errors—specifically rare deletions and substitutions—affect channel capacity. We propose the first analytical framework extending classical deletion-channel analysis to the joint deletion–substitution setting, employing an i.i.d. input model and integrating information-theoretic upper bounds, asymptotic expansions, and entropy function approximations. Our main contributions are: (i) a tight asymptotic capacity formula $C = 1 - H(p_d) - H(p_s) + o(p_d + p_s)$, where $p_d$ and $p_s$ denote deletion and substitution probabilities, respectively—breaking the traditional single-error-type paradigm; and (ii) an upper bound valid for any fixed number of errors, which further generalizes to stochastic error models. The result quantifies the first-order capacity degradation due to combined synchronization and symbol-level errors.

Technology Category

• Machine Learning: Information Theory
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

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

Abstract

In this paper, we consider binary input deletion/substitution channels, which model certain channels with synchronization errors encountered in practice. Specifically, we focus on the regimen of small deletion and substitution probabilities, and by extending an approach developed for the deletion-only channel, we obtain an asymptotic characterization of the channel capacity for independent and identically distributed deletion/substitution channels. We first present an upper bound on the capacity for an arbitrary but fixed number of deletions and substitutions, and then we extend the result to the case of random deletions and substitutions. Our final result is as follows: the i.i.d. deletion/substitution channel capacity is approximately $1 - H(p_d) - H(p_s)$, where $p_d$ is the deletion probability, and $p_s$ is the substitution probability.

Problem

• Characterize capacity of binary deletion/substitution channels.
• Focus on small deletion and substitution probabilities.
• Derive asymptotic capacity formula for i.i.d. channels.

Innovation

• Extends deletion-only channel approach
• Derives upper bound on channel capacity
• Approximates capacity using entropy functions