VLSF Decoding with Reliability Guarantees over Correlated Noncoherent Fading Channels

TL;DR

This paper develops reliable decoding methods for variable-length codes over correlated fading channels, deriving bounds on information density to analyze decoding performance and stopping times.

Contribution

It introduces finite-blocklength bounds on information density for correlated channels, enabling reliable VLSF decoding analysis with explicit relaxation gap characterization.

Findings

Finite-blocklength bounds enable reliable decoding analysis.

Correlation impacts stopping-time distribution and decoding performance.

Numerical results for Gauss-Markov channels illustrate the theoretical findings.

Abstract

This paper studies reliability-guaranteed decoding for variable-length stop-feedback (VLSF) codes over correlated noncoherent fading channels. The decoding rule is based on the evolution of the information density associated with a given channel input-output realization. Due to channel memory, exact evaluation of this information density is intractable. To enable constructive decoding, computable finite-blocklength lower and upper bounds on the information density that hold uniformly over time along each input-output sequence are derived. The lower bound enables a stopping-time analysis for VLSF decoding and has an operational meaning, while the upper bound provides a reference for the relaxation gap, which is explicitly characterized. As a concrete application, the Gauss-Markov fading channel with Gaussian signaling is considered to numerically investigate the stopping-time distribution and the impact of fading correlation on decoding performance.