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Probabilistic constellation shaping (PCS) offers a significant performance improvement over uniform signaling. It was recently discovered that long blocks are not required to achieve maximum shaping gain when transmitting over the nonlinear…

Signal Processing · Electrical Eng. & Systems 2020-12-15 Tobias Fehenberger , Helmut Griesser , Jörg-Peter Elbers

Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input…

Information Theory · Computer Science 2016-07-29 Tobias Fehenberger , Alex Alvarado , Georg Böcherer , Norbert Hanik

We propose a probabilistic shaping approach for region-of-interest signaling, where a low-rate signal controls the desired probabilistic ranges of a high-rate data stream using a flexible distribution controller. In addition, we introduce…

Signal Processing · Electrical Eng. & Systems 2022-09-05 Duc-Phuc Nguyen , Yoshifumi Shiraki , Jun Muramatsu , Takehiro Moriya

In this letter, we propose a symbol-wise puncturing scheme to support hybrid automatic repeat request (HARQ) integrated probabilistic amplitude shaping (PAS). To prevent the probability distribution distortion caused by the traditional…

Information Theory · Computer Science 2022-07-26 Li Shen , Yongpeng Wu , Derrick Wing Kwan Ng , Wenjun Zhang , Xiang-Gen Xia

The Pinching-Antenna SyStem (PASS) is a revolutionary flexible antenna technology designed to enhance wireless communication by establishing strong line-of-sight (LoS) links, reducing free-space path loss and enabling antenna array…

Information Theory · Computer Science 2025-06-13 Zhaolin Wang , Chongjun Ouyang , Xidong Mu , Yuanwei Liu , Zhiguo Ding

A new approach for combining non-binary low-density 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…

Information Theory · Computer Science 2018-09-12 Fabian Steiner , Georg Böcherer , Gianluigi Liva

On the one hand, sign-bit shaping is a popular shaping scheme where the conditional probability of the sign bit is made non-equiprobable. On the other hand, probabilistic amplitude shaping (PAS) is a popular coding scheme, to combine…

Information Theory · Computer Science 2023-03-01 Vincent Corlay , Hamidou Dembele

Probabilistic shaping (PS) has been widely studied and applied to optical fiber communications. The encoder of PS expends the number of bit slots and controls the probability distribution of channel input symbols. Not only studies focused…

Information Theory · Computer Science 2024-01-25 Tsuyoshi Yoshida , Koji Igarashi , Magnus Karlsson , Erik Agrell

Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly…

Information Theory · Computer Science 2022-06-08 Marco Secondini , Stella Civelli , Enrico Forestieri , Lareb Zar Khan

Product distribution matching (PDM) is proposed to generate target distributions over large alphabets by combining the output of several parallel distribution matchers (DMs) with smaller output alphabets. The parallel architecture of PDM…

Information Theory · Computer Science 2017-02-27 Georg Böcherer , Patrick Schulte , Fabian Steiner

Probabilistic constellation shaping has been used in long-haul optically amplified coherent systems for its capability to approach the Shannon limit and realize fine rate granularity. The availability of high-bandwidth optical-electronic…

Signal Processing · Electrical Eng. & Systems 2023-03-31 Md Sabbir-Bin Hossain , Georg Bocherer , Talha Rahman , Tom Wettlin , Nebojsa Stojanovic , Stefano Calabro , Stephan Pachnicke

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for…

Information Theory · Computer Science 2017-08-21 Fabian Steiner , Gianluigi Liva , Georg Böcherer

Signal clipping is a classic technique for reducing peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It has been widely applied in consumer electronic devices owing to its low complexity and…

Signal Processing · Electrical Eng. & Systems 2024-02-20 Yuyang Du , Liang Hao , Yiming Lei , Qun Yang , Shiqi Xu

The interplay of shaped signaling and fiber nonlinearities is reviewed in the asymptotic and finite-length regime. We present explanations and discuss implications of an optimum shaping length of just a few hundred symbols.

Signal Processing · Electrical Eng. & Systems 2020-06-23 Tobias Fehenberger

We present an autoregressive end-to-end learning approach for probabilistic shaping on nonlinear fiber channels. Our proposed scheme learns the joint symbol distribution and provides a 0.3-bits/2D achievable information rate gain over an…

Machine Learning · Computer Science 2025-07-23 Mohammad Taha Askari , Lutz Lampe , Amirhossein Ghazisaeidi

Probabilistic constellation shaping (PCS) has been widely applied to amplified coherent optical transmissions owing to its shaping gain over the uniform signaling and fine-grained rate adaptation to the underlying fiber channel condition.…

Signal Processing · Electrical Eng. & Systems 2021-09-08 Di Che , Junho Cho , Xi Chen

Performance trade-offs between linear shaping and nonlinear tolerance of the recently introduced 4D orthant-symmetric 128-ary modulation format are investigated. Numerical simulations show 9.3% reach increase with respect to the 7b4D-2A8PSK…

Information Theory · Computer Science 2020-10-20 Bin Chen , Chigo Okonkwo , Alex Alvarado

Probability Shaping (PS) is a method to improve a Modulation and Coding Scheme (MCS) in order to increase reliability of data transmission. It is already implemented in some modern radio broadcasting and optic systems, but not yet in…

Information Theory · Computer Science 2023-07-06 Evgeny Bobrov , Adyan Dordzhiev

Utilizing the multi-dimensional (MD) space for constellation shaping has been proven to be an effective approach for achieving shaping gains. Despite there exists a variety of MD modulation formats tailored for specific optical transmission…

Signal Processing · Electrical Eng. & Systems 2025-06-23 Bin Chen , Zhiwei Liang , Yi Lei , JingXin Deng , Shen Li , Gabriele Liga

Optical orthogonal frequency-division multiplexing (OFDM) and probabilistic constellation shaping (PCS) have emerged as powerful techniques to enhance the performance of optical wireless communications (OWC) systems. While PCS improves…

Systems and Control · Electrical Eng. & Systems 2025-07-11 Thanh V. Pham , Susumu Ishihara