Constellation shaping is an energy efficiency enhancement method for

digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital i ...

signal

modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...

that improves upon

amplitude and phase-shift keying Amplitude and phase-shift keying (APSK) is a digital modulation scheme that conveys data by modulating both the amplitude and the phase of a carrier wave. In other words, it combines both amplitude-shift keying (ASK) and phase-shift keying (PSK) ...

(APSK) and conventional

quadrature amplitude modulation Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signal ...

(QAM) by modifying the uniform distribution of the data symbols to match the channel. In a channel corrupted by an additive white

Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

noise (AWGN), this implies transmitting low-energy signals more frequently than high-energy signals with the target to approach a Gaussian distribution of the transmission power. In

signal

, information bits modulate the carrier

electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

signal to a set of desired phase, frequency and amplitude states. This set of allowed states is called a ''constellation''. Typically, the probability of an information bit to be a 0 is the same as that of a 1, leading to all states from the constellation to appear with an equal probability. However, optimal transmission through most practical channels, like the AWGN, require a non-equal probability of the transmission symbols. A ''shaped constellation'' transmission sends some signal combinations more often and others less frequently to optimize the signal quality at the destination, or to maintain the same quality using less transmission energy.

Probabilistic constellation shaping

Probabilistic constellation shaping attempts to directly modify the

Probability mass function In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete density function. The probability mass ...

by applying a distribution matcher between the user data and the mapper to constellation symbols. A practical transmitter and receiver architecture which achieves that was proposed in. This technique gathered more interest in September 2016 when

Nokia Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

demonstrated working 1

Tbit/s In telecommunications, data-transfer rate is the average number of bits (bitrate), characters or symbols (baudrate), or data blocks per unit time passing through a communication link in a data-transmission system. Common data rate units are multi ...

data transmission channels between German cities. In October 2016, Alcatel-Lucent and Bell Labs claimed to have achieved 65 Tbit/s transmission over a 6,600 km (4,100 mile) single mode fiber in laboratory trials. The industry's first commercial field trial was completed in 2018 by China Telecom and Huawei Technologies.

Geometric constellation shaping

Geometric constellation shaping attempts to modify the distribution of transmission power by optimizing the constellation states themselves. In an AWGN channel, this typically implies gathering more constellation points around the area where the amplitude is small, and fewer points in the areas of high amplitude. Other types of channels require that high-amplitude points are clipped altogether, due to e.g. problems with amplifier efficiency. A notable examples are satellite links, where an APSK constellation is preferred to QAM. The benefits of geometric constellation shaping is that no distribution matcher is required, which simplifies the digital signal processing at the transmitter and receiver. However, geometric constellation shaping does not typically allow

Gray code The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representati ...

labeling of the constellation points, leading to a performance degradation. Probabilistic shaping is thus slightly more effective than geometric shaping.

References

External links

* * * * {{Cite journal, arxiv=1209.5221 , title=Design of APSK Constellations for Coherent Optical Channels with Nonlinear Phase Noise , journal=IEEE Transactions on Communications , volume=61 , issue=8 , pages=3362–3373 , date=2012-09-24 , last1=Häger , first1=Christian , author2=Alexandre Graell i Amat , last3=Alvarado , first3=Alex , last4=Agrell , first4=Erik , doi=10.1109/TCOMM.2013.061913.120713 , bibcode=2012arXiv1209.5221H , s2cid=14595512
Simulation of optical coherent transmission using probabilistic shaping

Explanation of how Probabilistic Constellation Shaping works
Quantized radio modulation modes