Fiber-Optic Communication System pt 30pt Design : al 2018 - - PowerPoint PPT Presentation

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Security Level: Confidential Spectra as Performance Metrics for Fiber-Optic Communication System pt 30pt Design : al 2018 Munich Workshop 47pt on Information Theory of Optical Fiber 28pt Mathematical and

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pt 30pt 反白 : al 47pt 黑体 28pt 反白细黑体

Spectra as Performance Metrics for Fiber-Optic Communication System Design

2018 Munich Workshop

n Information Theory of Optical Fiber

Mathematical and Algorithmic Sciences Lab Paris Research Center Georg Böcherer December 6, 2018

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Motivation

 Recent efforts in community to provide information-theoretic tools

for design of fiber-optic communication systems.

 Nice summary in

L. Schmalen “Performance Metrics for Communication Systems with

Forward Error Correction,” ECOC 2018.

 Discuss current state and possible extensions.

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Outline

 Thresholds as performance metrics  Limitations of BER threshold  BER spectrum  Uncertainty spectrum  Conclusions Page 3

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Design by Thresholds

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Interfaces between components are defined by

thresholds

Bit error rate (BER)
Mutual information
Generalized mutual information
GMI, NGMI, ABC, AIR, RBMD,…….
Components are designed to respect thresholds

Award-winning paper:

A. Alvarado et al “Replacing the Soft-

Decision FEC Limit Paradigm in the Design of Optical Communication Systems,” JLT, Vol 34, No 2, 2016.

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Design by Thresholds

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 Crucial Assumption: ‘Infinite’ Interleavers.  Translates into latency in practical transceivers.

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What if there is no ∞-interleaver?

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Example: DVB-S2

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Simulation Results

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BER thresholds provide only limited insights for design

𝑢 = 12 BCH outer code achieves

FER = 3 × 10−6 at 0.96 dB.

With ∞-interleaver, 𝑢 = 1 BCH outer code

would achieve FER= 4 × 10−9 at 0.96 dB.

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Design by BER Spectrum

 Quantify inner code performance by BER Spectrum, i.e., the statistics of

the fraction of erroneous bits per frame.

 Use BER spectrum for design:

 For given 𝑢, design inner code with constraint Pr #errors > t < target FER.  For given inner code, choose 𝑢 so that Pr #errors > t <target FER.

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Soft-Decision FEC: Uncertainty*

*Based on Gallager’s error exponent, details on uncertainty in [1] G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems,” J. Lightw. Technol., 2019.

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Setup

Page 10  FEC Overhead: OHFEC = 1 −

𝑙 𝑜𝑛

For a given channel, what FEC-OH is achievable?

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Achievable FEC Overhead

 We don’t know the exact channel, but we have a measurement

𝑦𝑜, 𝑧𝑜 (e.g., of a QAM signal)

 How large FEC Overhead 1 −

𝑙 𝑛𝑜 is required to recover 𝑦𝑜 from 𝑧𝑜

by FEC decoding?

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Achievable FEC Overhead

 Uncertainty  Theorem Page 12

Fraction of FEC codes that cannot decode 𝑦𝑜 from 𝑧𝑜 Decoding metric, e.g., 𝑄

𝑌|𝑍 𝑜 (𝑦𝑜|𝑧𝑜)

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Interpretation

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FEC Overhead FEC Rate Uncertainty

For FEC overhead larger than uncertainty, exponent is negative.
Backing-off in FEC rate leads to exponential decay of probability to

pick a bad code.

Uncertainty identifies the phase transition to the possible.

Works for any measurement 𝑦𝑜, 𝑧𝑜 without any further assumptions.

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From Measurement Property to Channel Property

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𝑜 → ∞,

ergodicity 𝑜 ≈FEC block length, many pairs 𝑦𝑜, 𝑧𝑜 Channel property: Achievable FEC overhead

𝑉𝑟 𝑛

Channel property: Uncertainty spectrum

Put forward in:

Essiambre et al “Capacity Limits of Optical

Fiber Networks”, JLT 2010.

Alvarado et al “Achievable Information

Rates for Fiber-Optics: Applications and Computations,” JLT 2018.

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Example

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QPSK Measurement with 𝑜 =10 million bits at 1 dB SNR.
FEC block length 𝑜FEC =10 000.

Threshold  Use all 10 million samples to estimate uncertainty 𝑉𝑟 = 0.4373 bits  FEC overhead 0.4373 bits is achievable, asymptotically in the blocklength.  blocklength is finite, we have to back-

ff, how much?

Spectrum  Split measurement in

𝑜 𝑜FEC = 1000 chunks.

 Calculate 1000 uncertainties.  Plot the spectrum  Back-off to FEC overhead 0.47 bits.  Corresponds to 0.42 dB back-off in SNR.

𝑉 = 0.4373

Note: finite-length informationi theory accounts for variance, e.g., Polyankiy et al “Channel coding rate in the finite blocklength regime,” ITT 2010.

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Conclusions

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Observations

Spectra account for finite-length effects.
Spectra account for correlations created by components.

 Alternative to threshold and ∞-interleaver. Possible Directions

New criteria for design of concatenated components?
To design components with desired spectra, can we borrow

from rate-distortion theory or information-theoretic security?

Shorter interleaver, better systems?

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FEC Code Ensemble

 FEC Code

𝐷 = 𝐷𝑜 1 , 𝐷𝑜 2 , … , 𝐷𝑜 2𝑙 with symbols 𝐷𝑗(𝑥) in the channel alphabet (e.g., 16-QAM.)

 Encoder: map 𝑙 bits 𝑥 to code word 𝑦𝑜(𝑥).  Decoder:  Error probability:*

*=fraction of FEC codes that cannot decode 𝑦𝑜 from 𝑧𝑜.

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Decoding metric