Probabilistic shaping and non-binary codes

Boutros, Joseph J.; Jardel, Fanny; Méasson, Cyril

doi:10.1109/isit.2017.8006941

Cited by 15 publications

(28 citation statements)

References 29 publications

(33 reference statements)

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“…Second, the use of PAS enables the achievement of large shaping gains and attaining a remarkable degree of flexibility with respect to transmission rates. This large flexibility comes at no visible performance loss with respect to SMD applied to NB-LDPC codes [7], [8]. Our findings are validated by Monte Carlo density evolution (DE) [10, Ch.…”

Section: Introductionsupporting

confidence: 56%

Bit-Metric Decoding of Non-Binary LDPC Codes With Probabilistic Amplitude Shaping

2018

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A new approach for combining non-binary lowdensity parity-check (NB-LDPC) codes with higher-order modulation and probabilistic amplitude shaping (PAS) is presented. Instead of symbol-metric decoding (SMD), a bit-metric decoder (BMD) is used so that matching the field order of the nonbinary code to the constellation size is not needed, which increases the flexibility of the coding scheme. Information rates, density evolution thresholds and finite-length simulations show that the flexibility comes at no loss of performance if PAS is used.

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Section: Introductionsupporting

confidence: 56%

Bit-Metric Decoding of Non-Binary LDPC Codes With Probabilistic Amplitude Shaping

2018

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“…If PAS (with, e.g., standard LDPC, Turbo, or polar codes) tends to map uniformly-distributed parity bits into the signs of PAM points, then parity bits do not perturb amplitude shaping. The generalization of this property to alternative (non-binary) information representations is enabled by specific QAM format, among others q × q-CQAM as in [32] when the underlying alphabet is assumed to be a finite 1 The proof [19], [32] over Fq involves the q roots of the unity as a generalization of the sign symmetry over F 2 . This generalization motivates the construction of CQAM over Fq with the use of circular symmetry [32].…”

Section: Shaping and Optical Communicationsmentioning

confidence: 99%

“…where B represents the fundamental region. In [32], the main goal is to explore the use of q-ary codes by generalizing PAS and the binary sign flipping technique to the q-ary case. In this paper, the goal is slightly different.…”

Section: Shaping and Optical Communicationsmentioning

confidence: 99%

“…For evolved architectures or advanced fiber channel models, they may be chosen to maximize the CM capacity. Recall that the latter case is considered in [32] and experimented with in [42]; it is indicated as the 'true' CQAM reference in Fig. 2 where several CQAM-like examples are depicted.…”

Section: A Geometric Shaping Via Circular Qam Formatsmentioning

confidence: 99%

“…In the last years, practice-oriented works related to optical transmissions have successfully implemented different shaping methods, from many-to-one and geometrically-shaped formats to non-uniform signaling. The latter, more often called probabilistic shaping in the optical community [28]- [32], has perhaps received most attention. Various transmission demonstrations and record experiments using shaped modulation formats have indeed been reported as, e.g., in [33]- [40], [42].…”

Section: Introduction a Historical Notesmentioning

confidence: 99%

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Exploring and Experimenting With Shaping Designs for Next-Generation Optical Communications

Jardel

Eriksson

Méasson

et al. 2018

J. Lightwave Technol.

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A class of circular 64-QAM that combines 'geometric' and 'probabilistic' shaping aspects is presented. It is compared to square 64-QAM in back-to-back, single-channel, and WDM transmission experiments. First, for the linear AWGN channel model, it permits to operate close to the Shannon limits for a wide range of signal-to-noise ratios. Second, WDM simulations over several hundreds of kilometers show that the obtained signal-to-noise ratios are equivalent to -or slightly exceed -those of probabilistic shaped 64-QAM. Third, for real-life validation purpose, an experimental comparison with unshaped 64-QAM is performed where 28% distance gains are recorded when using 19 channels at 54.2 GBd. This again is in line -or slightly exceeds -the gains generally obtained with probabilistic shaping. Depending upon implementation requirements (core forward-error correcting scheme for example), the investigated modulation schemes may be key alternatives for next-generation optical systems.

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A Time Sharing Hybrid Probabilistic Shaping Scheme for Nonbinary LDPC Codes

Kang

2020

IEEE Access

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A time sharing (TS) hybrid probabilistic shaping (HPS) scheme for nonbinary (NB) LDPC codes is proposed. For the conventional probabilistic shaping (CPS) scheme, the demodulator uses bit-metric decoding (BMD) for binary LDPC codes and NB LDPC codes. However, the demodulator for NB LDPC codes adopts symbol-metric decoding (SMD) on the AWGN channel to avoid the loss of symbol-to-bit mapping and obtain better performance than binary LDPC codes. In order to take advantage of SMD demodulation for NB LDPC codes, the NB-LDPC information symbols use constant composition distribution matcher (CCDM) to generate quadrature amplitude modulation (QAM) symbols with unequal probability distribution, while the NB-LDPC parity symbols are utilized to yield QAM symbols with approximately uniform distribution. The SMD demodulation of the proposed NB-LDPC-coded TS HPS scheme has lower demodulation complexity than the NB-LDPC-coded CPS scheme. The information-theoretical analysis of the CPS system and the TS HPS system turns out that the proposed NB-LDPC-coded TS HPS scheme is superior to the NB-LDPC-coded CPS scheme for 8QAM and 32QAM format. Simulation results verify the theoretical average mutual information (AMI) analysis and show that the proposed NB-LDPC-coded TS HPS scheme has up-to-0.24 dB and 1.10 dB performance gain compared with the NB-LDPC-coded CPS scheme for 8QAM and 32QAM format, respectively. Compared with the binary LDPC-coded regular Nyquist scheme for 8QAM and 32QAM format, the proposed NB-LDPC-coded TS HPS scheme has up-to-1.31 dB and 2.04 dB performance gain, respectively. Meanwhile, the LDPC code rate of the proposed TS HPS scheme is more flexible than the CPS scheme. Therefore, the proposed NB-LDPC-coded TS HPS scheme is more reliable, efficient, and flexible for 8QAM and 32QAM, and thus suitable for the sixth generation (6G) communication system.INDEX TERMS Time sharing hybrid probabilistic shaping (HPS), bit-metric decoding (BMD), symbol-metric decoding (SMD), nonbinary (NB) LDPC, average mutual information (AMI). I. INTRODUCTION

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Probabilistic shaping and non-binary codes

Cited by 15 publications

References 29 publications

Bit-Metric Decoding of Non-Binary LDPC Codes With Probabilistic Amplitude Shaping

Bit-Metric Decoding of Non-Binary LDPC Codes With Probabilistic Amplitude Shaping

Exploring and Experimenting With Shaping Designs for Next-Generation Optical Communications

A Time Sharing Hybrid Probabilistic Shaping Scheme for Nonbinary LDPC Codes

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