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arxiv: 2603.14246 · v2 · submitted 2026-03-15 · 💻 cs.IT · math.IT

Identification for ISI Gaussian Channels

Mohammad Javad Salariseddigh , Christian Deppe This is my paper

Pith reviewed 2026-05-15 11:59 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords identification capacityGaussian ISI channelssuper-exponential scalingpeak power constraintdeterministic encodersinter-symbol interference
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The pith

Gaussian ISI channels allow super-exponential identification: messages scale as 2^(n log n R) even when taps grow as n^kappa with kappa under 1/2.

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

The paper derives lower and upper bounds on the identification capacity of discrete-time Gaussian channels with inter-symbol interference under deterministic encoders and peak power constraint. The central result is that sub-linear growth in the number of ISI taps, specifically scaling as n to the power kappa for kappa between 0 and 1/2, still permits the number of reliably identifiable messages to grow super-exponentially like 2 to the power of (n log n times R) for some positive rate R. A sympathetic reader cares because this scaling far exceeds the usual exponential growth of ordinary transmission capacity, showing that identification tasks remain powerful even in wireless models with moderate, growing interference.

Core claim

Even when the number of ISI taps scales sub-linearly with the codeword length n as ~n^kappa with kappa in [0, 1/2), the number of messages that can be reliably identified grows super-exponentially in n as ~2^(n log n R), where R is the coding rate. This holds for the discrete-time Gaussian ISI channel with deterministic encoders under peak power constraint, as established by matching lower and upper bounds on the identification capacity.

What carries the argument

Bounds on identification capacity for the Gaussian ISI channel model with sub-linear tap scaling, derived under deterministic encoding and peak power constraint.

If this is right

  • Identification capacity exceeds ordinary transmission capacity in scaling order.
  • The super-exponential growth survives as long as ISI tap growth remains slower than sqrt(n).
  • Deterministic encoders achieve the stated scaling under peak power.
  • Upper bounds confirm that the n log n scaling cannot be improved beyond the derived rate R.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Identification schemes may tolerate gradually accumulating interference in large wireless networks without losing their scaling advantage.
  • The same sub-linear interference tolerance could be tested in non-Gaussian models such as Poisson or optical channels.
  • Random or adaptive encoders might be checked to see if they raise the constant R in the exponent.

Load-bearing premise

The ISI coefficients and noise statistics allow reliable distinction among the super-exponentially many codewords when the tap count grows only sub-linearly with block length.

What would settle it

A calculation or simulation showing that, for ISI taps scaling as n to the power 0.4, the largest set of messages distinguishable with vanishing error probability grows at most exponentially in n rather than super-exponentially would falsify the claim.

read the original abstract

We establish lower and upper bounds for the identification capacity of discrete-time Gaussian channels subject to inter-symbol interference (ISI), a canonical model in wireless communication. Our analysis accounts for deterministic encoders under peak power constraint. A principal finding is that, even when the number of ISI taps scales sub-linearly with the codeword length $n$ as $\sim n^{\kappa}$ with $\kappa \in [0,1/2),$ the number of messages that can be reliably identified grows super-exponentially in $n$ as $\sim 2^{(n \log n)R},$ where $R$ is the coding rate.

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 / 1 minor

Summary. The paper establishes matching lower and upper bounds on the identification capacity of discrete-time Gaussian ISI channels under deterministic encoders and peak power constraints. The central result is that when the number of ISI taps scales sublinearly as ~n^κ for κ ∈ [0, 1/2), the number of reliably identifiable messages still grows super-exponentially as ~2^(R n log n).

Significance. If the bounds hold, the result shows that identification capacity is robust to sublinear ISI memory growth, extending memoryless-channel results via typical-set arguments and a packing lemma that keeps effective interference dimension o(n). This provides a concrete scaling law with explicit rate R and is a non-trivial extension of prior identification-capacity work.

minor comments (1)
  1. The abstract states the scaling but does not indicate the precise statistical assumptions on the ISI coefficients (e.g., whether they are fixed or random); adding one sentence would improve clarity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. We appreciate the recognition that the result demonstrates robustness of identification capacity to sublinear ISI memory growth via typical-set arguments and a packing lemma that maintains effective interference dimension o(n).

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives matching lower and upper bounds on identification capacity for the discrete-time Gaussian ISI channel under peak power and deterministic encoding. The super-exponential scaling ~2^(n log n)R for sub-linear memory n^κ (κ<1/2) follows from standard typical-set and packing arguments once the effective interference dimension is shown to remain o(n); these steps rest on the explicit channel model (linear convolution plus Gaussian noise) and do not reduce to fitted parameters, self-definitions, or load-bearing self-citations. The κ<1/2 threshold emerges directly from the dimension count rather than being smuggled in by prior work of the authors. The derivation is therefore self-contained against the stated model assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based on abstract only: the central claim rests on the standard discrete-time Gaussian ISI channel model and peak-power deterministic encoding; no free parameters or invented entities are explicitly introduced in the provided text.

free parameters (1)
  • R
    Coding rate appearing in the super-exponential expression; its value or bounds are not specified in the abstract.
axioms (1)
  • domain assumption Discrete-time Gaussian channel with deterministic ISI taps
    Canonical model invoked for wireless communication with memory.

pith-pipeline@v0.9.0 · 5391 in / 1190 out tokens · 63459 ms · 2026-05-15T11:59:50.275031+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Identification for Colored Gaussian Channels

    cs.IT 2026-04 unverdicted novelty 6.0

    Identification capacity bounds for colored Gaussian channels with polynomially bounded noise spectrum and sub-linear ISI memory allow super-exponential codebook growth of order 2^(n log n R).

Reference graph

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