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arxiv: 1907.08468 · v1 · pith:BDAZRVEHnew · submitted 2019-07-19 · 💻 cs.IT · math.IT

Shaped On-Off Keying Using Polar Codes

Thomas Wiegart , Fabian Steiner , Patrick Schulte , Peihong Yuan This is my paper

Pith reviewed 2026-05-24 18:55 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords polar codesprobabilistic shapingon-off keyingdistribution matchingforward error correctionnon-symmetric channelspower-efficient signaling
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The pith

Polar codes jointly perform distribution matching and error correction for on-off keying to achieve asymptotically optimal signaling.

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

The paper establishes that a single polar code can handle both probabilistic shaping and forward error correction for on-off keying modulation. Traditional methods that separate the distribution matcher from the encoder only achieve a time-sharing performance that falls short of the channel's capacity-achieving distribution. By integrating the two tasks, the scheme reaches the theoretical limit for power efficiency on this non-symmetric channel. This matters because on-off keying is simple to implement yet benefits greatly from proper input distribution at low rates. Simulations with long blocks confirm a clear performance advantage over uniform transmission.

Core claim

The proposed scheme uses a polar code for joint distribution matching and forward error correction which enables asymptotically optimal signaling. Numerical simulations show a gain of 1.8 dB compared to uniform transmission at a spectral efficiency of 0.25 bits/channel use for a blocklength of 65,536 bits.

What carries the argument

The Honda-Yamamoto polar code construction adapted for joint shaping and coding on the non-symmetric OOK channel.

If this is right

  • The scheme achieves asymptotically optimal signaling rather than time-sharing performance.
  • It delivers a 1.8 dB gain at 0.25 bits per channel use with block length 65536.
  • Concatenated matcher-encoder approaches are shown to be suboptimal for non-symmetric channels like OOK.

Where Pith is reading between the lines

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

  • This method may simplify transmitter design by eliminating the need for a separate distribution matcher.
  • Similar joint constructions could improve shaping for other asymmetric channels or modulations.
  • Performance at shorter block lengths remains an open question for practical deployment.

Load-bearing premise

The Honda-Yamamoto 2013 polar shaping construction can be directly repurposed for the non-symmetric OOK channel without additional rate loss or convergence issues at finite block length.

What would settle it

If the mutual information achieved by the shaped scheme does not approach the capacity of the OOK channel under the optimal input distribution as block length grows, the asymptotic optimality claim would be falsified.

Figures

Figures reproduced from arXiv: 1907.08468 by Fabian Steiner, Patrick Schulte, Peihong Yuan, Thomas Wiegart.

Figure 1
Figure 1. Figure 1: Achievable rates for OOK with uniform and optimized i [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graphical representation of the polarization of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Rate loss comparisons for different DM architecture [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of shaped and uniform polar and LDPC codes [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

The probabilistic shaping scheme from Honda and Yamamoto (2013) for polar codes is used to enable power-efficient signaling for on-off keying (OOK). As OOK has a non-symmetric optimal input distribution, shaping approaches that are based on the concatenation of a distribution matcher followed by systematic encoding do not result in optimal signaling. Instead, these approaches represent a time sharing scheme where only a fraction of the codeword symbols is shaped. The proposed scheme uses a polar code for joint distribution matching and forward error correction which enables asymptotically optimal signaling. Numerical simulations show a gain of 1.8 dB compared to uniform transmission at a spectral efficiency of 0.25 bits/channel use for a blocklength of 65,536 bits.

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

2 major / 2 minor

Summary. The paper proposes applying the Honda-Yamamoto (2013) probabilistic shaping construction for polar codes to on-off keying (OOK) modulation. It argues that standard concatenation of a distribution matcher with systematic encoding reduces to time-sharing on the non-symmetric OOK channel and therefore cannot achieve the capacity-achieving input distribution, whereas the joint polar-code construction for distribution matching and FEC yields asymptotically optimal signaling. Simulations are reported to show a 1.8 dB gain versus uniform transmission at 0.25 bits per channel use with block length 65,536.

Significance. If the 2013 construction can be applied to the non-symmetric OOK channel with no additional rate loss, the work would supply a concrete, polar-code-based method for achieving the optimal Bern(p) input distribution (p < 0.5) jointly with error correction, which is relevant for power-limited optical and wireless links that employ OOK.

major comments (2)
  1. [Abstract / Introduction] The central optimality claim rests on the direct repurposing of the Honda-Yamamoto 2013 polar-shaping construction for the asymmetric OOK channel. The manuscript provides no explicit derivation or verification that the polarization indices selected for the non-symmetric transition probabilities still allow the effective rate to approach I(X;Y) without a vanishing but non-zero gap at finite block length; this adaptation is load-bearing for the asymptotic-optimality statement.
  2. [Numerical results] The reported 1.8 dB gain at spectral efficiency 0.25 bits/channel use (n = 65,536) is presented without error-bar information, Monte-Carlo trial count, or an explicit statement of the OOK channel model (e.g., exact transition probabilities or noise variance). These omissions make it impossible to judge whether the observed gain is statistically distinguishable from the time-sharing baseline that the paper criticizes.
minor comments (2)
  1. [Introduction] Notation for the target input distribution Bern(p) and the resulting mutual information I(X;Y) should be introduced with an equation reference in the introduction so that the optimality claim can be stated quantitatively.
  2. [Numerical results] The block-length value 65,536 should be written consistently (either as 2^16 or 65536) and the corresponding code-rate and shaping-rate parameters should be tabulated for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the major comments point by point below and will incorporate the suggested clarifications in the revised version.

read point-by-point responses

  1. Referee: [Abstract / Introduction] The central optimality claim rests on the direct repurposing of the Honda-Yamamoto 2013 polar-shaping construction for the asymmetric OOK channel. The manuscript provides no explicit derivation or verification that the polarization indices selected for the non-symmetric transition probabilities still allow the effective rate to approach I(X;Y) without a vanishing but non-zero gap at finite block length; this adaptation is load-bearing for the asymptotic-optimality statement.

    Authors: The Honda-Yamamoto construction is formulated for general binary-input discrete memoryless channels. Since the OOK channel is a binary-input DMC, the polarization results apply directly, and the index selection based on the polarized mutual informations ensures the achievable rate approaches the mutual information I(X;Y) asymptotically. We will add a short paragraph in the introduction or preliminaries section to explicitly state this generality and reference the relevant theorems from the 2013 paper to address the concern about the adaptation. revision: yes

  2. Referee: [Numerical results] The reported 1.8 dB gain at spectral efficiency 0.25 bits/channel use (n = 65,536) is presented without error-bar information, Monte-Carlo trial count, or an explicit statement of the OOK channel model (e.g., exact transition probabilities or noise variance). These omissions make it impossible to judge whether the observed gain is statistically distinguishable from the time-sharing baseline that the paper criticizes.

    Authors: We acknowledge that the simulation details were insufficiently specified. The revised manuscript will include the precise OOK channel parameters used (transition probabilities or equivalent noise model), the number of Monte Carlo trials performed, and error bars on the BER or gain figures. This will enable verification that the gain is statistically significant compared to the time-sharing approach. revision: yes

Circularity Check

0 steps flagged

No significant circularity; asymptotic optimality grounded in external Honda-Yamamoto 2013 result

full rationale

The paper's central claim of asymptotically optimal signaling for non-symmetric OOK rests on direct application of the Honda-Yamamoto 2013 polar shaping construction for joint distribution matching and FEC. This is an external citation with no author overlap to the present work. The reported 1.8 dB gain is obtained from finite-blocklength simulations at n=65536 rather than any fitted parameter or self-referential quantity. No equations reduce a prediction to its own inputs by construction, and the derivation chain does not invoke self-citation load-bearing or ansatz smuggling. The result is therefore self-contained against external benchmarks, warranting only a minor score for reliance on prior literature.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the correctness of the 2013 Honda-Yamamoto polar shaping construction (treated as an external axiom) and on the assumption that the OOK channel is memoryless with a known non-symmetric capacity-achieving distribution. No new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Honda-Yamamoto 2013 polar-code shaping construction achieves the target input distribution for any binary channel when the block length tends to infinity.
    Invoked to claim asymptotic optimality for the OOK case.

pith-pipeline@v0.9.0 · 5649 in / 1336 out tokens · 15945 ms · 2026-05-24T18:55:59.019568+00:00 · methodology

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Reference graph

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