Constellation shaping

Lore & Background

In digital signal modulation, information bits modulate a carrier wave to a set of allowed phase, frequency, and amplitude states called a constellation. Typically, all states appear with equal probability because bits are equally likely to be 0 or 1. However, optimal transmission through most practical channels, such as the AWGN channel, requires non-equal probability of transmission symbols. Constellation shaping addresses this by sending some signal combinations more often and others less frequently.

Probabilistic constellation shaping directly modifies the probability mass function by applying a distribution matcher between user data and the mapper to constellation symbols. This technique gained interest in September 2016 when Nokia Bell Labs demonstrated working 1 Tbit/s data transmission channels between German cities, followed by Alcatel-Lucent and Bell Labs claiming 65 Tbit/s transmission over 6,600 km single mode fiber in laboratory trials in October 2016. The industry's first commercial field trial was completed in 2018 by China Telecom and Huawei Technologies.

Geometric constellation shaping modifies the distribution of transmission power by optimizing the constellation states themselves. In an AWGN channel, this typically means gathering more constellation points around small amplitudes and fewer at high amplitudes. Other channels may require clipping high-amplitude points due to amplifier efficiency issues, as seen in satellite links where APSK is preferred over QAM. Geometric shaping requires no distribution matcher, simplifying digital signal processing, but does not typically allow Gray code labeling, leading to performance degradation. Probabilistic shaping is thus slightly more effective than geometric shaping.

Reader's Guide

Constellation shaping represents a significant advancement in digital signal modulation by directly addressing the inefficiency of uniform symbol distributions in practical channels. Its two main approaches—probabilistic and geometric—offer different trade-offs. Probabilistic shaping, which uses a distribution matcher, has demonstrated high-speed optical transmission records, including a 1 Tbit/s field demonstration between German cities and a 65 Tbit/s laboratory trial over 6,600 km of single mode fiber. The first commercial field trial in 2018 by China Telecom and Huawei Technologies indicates its practical viability. Geometric shaping, while simpler to implement because it avoids the distribution matcher, suffers from the inability to use Gray code labeling, which reduces its effectiveness. The technique's core insight—that transmitting low-energy symbols more frequently can approach a Gaussian power distribution in AWGN channels—enables either improved signal quality or reduced transmission energy for the same quality. This makes constellation shaping a key method for enhancing energy efficiency in modern communication systems, particularly in optical fiber links where high data rates and long distances demand optimal use of transmitted power.

Did You Know?

• Constellation shaping improves upon APSK and conventional QAM by modifying the uniform distribution of data symbols to match the channel.
• In an AWGN channel, constellation shaping transmits low-energy signals more frequently than high-energy signals to approach a Gaussian power distribution.
• Probabilistic constellation shaping uses a distribution matcher between user data and the mapper to modify the probability mass function.
• Geometric constellation shaping gathers more constellation points around small amplitudes and fewer at high amplitudes in an AWGN channel.