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arxiv: 2604.16062 · v1 · submitted 2026-04-17 · 💻 cs.IT · math.IT

VLSF Decoding with Reliability Guarantees over Correlated Noncoherent Fading Channels

Guodong Sun , Samir M. Perlaza , Philippe Mary , Jean-Marie Gorce This is my paper

Pith reviewed 2026-05-10 07:44 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords VLSF decodinginformation density boundscorrelated noncoherent fadingstopping time analysisfinite blocklengthreliability guaranteesGauss-Markov fadingGaussian signaling
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The pith

Computable bounds on the information density allow VLSF decoding with reliability guarantees over correlated noncoherent fading channels.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that exact computation of the information density is intractable for channels with memory, so it derives finite-blocklength lower and upper bounds that hold uniformly over time for each input-output sequence. These bounds are computable and the lower one has an operational meaning for deciding when to stop in variable-length stop-feedback decoding. This provides concrete reliability guarantees for the decoder. The upper bound quantifies the relaxation introduced by using the bounds instead of the exact value. Numerical results for the Gauss-Markov model illustrate how fading correlation influences the stopping times and overall performance.

Core claim

The paper derives computable finite-blocklength lower and upper bounds on the information density associated with a given channel input-output realization that hold uniformly over time along each sequence. 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.

What carries the argument

The central object is the pair of computable lower and upper bounds on the information density that are uniform over time for each input-output sequence and substitute for the intractable exact value.

Load-bearing premise

The derived bounds are sufficiently tight and computable to provide practical reliability guarantees without excessive relaxation gap.

What would settle it

A numerical study where the gap between the bound-based stopping time and the exact information density produces error rates or delays that exceed the target reliability specifications.

Figures

Figures reproduced from arXiv: 2604.16062 by Guodong Sun, Jean-Marie Gorce, Philippe Mary, Samir M. Perlaza.

Figure 1
Figure 1. Figure 1: Top: four realizations of the information density lower bound [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper derives computable finite-blocklength lower and upper bounds on the information density process for correlated noncoherent fading channels. These bounds hold uniformly over all times t along any input-output sequence. The lower bound enables a stopping-time analysis for variable-length stop-feedback (VLSF) decoding with controlled error probability and carries an operational meaning, while the upper bound explicitly characterizes the relaxation gap. The construction is demonstrated on the Gauss-Markov fading channel with Gaussian inputs, including numerical investigation of stopping-time distributions and the impact of fading correlation.

Significance. If the uniform bounds hold and are sufficiently tight and computable, the work supplies a constructive method for achieving reliability guarantees in VLSF decoding over channels with memory where exact information density evaluation is intractable. The explicit operational interpretation of the lower bound, the quantified gap via the upper bound, and the numerical validation on a standard model constitute clear strengths. This advances finite-blocklength analysis for noncoherent settings with practical decoding rules.

minor comments (2)
  1. Abstract: the claim that the bounds are 'computable' would benefit from a brief indication of the computational approach or complexity to allow readers to assess practicality immediately.
  2. The numerical section would be strengthened by including a direct comparison of the derived bounds against the exact information density (where feasible for small blocklengths) to quantify the relaxation gap empirically.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were provided in the report, so we have no points to address point-by-point. We will incorporate any minor suggestions during revision.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from channel model

full rationale

The paper derives computable finite-blocklength lower and upper bounds on the information density process directly from the statistical properties of the correlated noncoherent fading channel (with Gaussian inputs in the Gauss-Markov case). These bounds are shown to hold uniformly over time t for any input-output sequence via explicit mathematical analysis, which then directly supports the stopping-time rule for VLSF decoding and the explicit characterization of the relaxation gap. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation; the operational meaning follows from the channel model without circular reduction to the target result.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on abstract; no explicit free parameters, axioms, or invented entities stated. Relies on standard information-theoretic concepts like information density.

pith-pipeline@v0.9.0 · 5445 in / 956 out tokens · 36696 ms · 2026-05-10T07:44:17.026363+00:00 · methodology

discussion (0)

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Reference graph

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