Probabilistically shaped multi-level pulse modulation with gray code mapping
A method of generating a probabilistically shaped (PS), multi-level modulation signals includes encoding information bits into coded bits to which probability values are assigned according to a probability mass function, and mapping, based on a Gray coding scheme, the coded bits into symbols to which the probability values are assigned. The probability mass function is implemented by determining probabilities of the coded bits so that the probabilities of the coded bits in ascending or descending order have a Gaussian distribution, and performing a probability distribution pre-adjustment by redistributing probabilities of the coded bits corresponding to symbols probabilities of which are outside Gaussian distribution so that the symbols mapped based on the Gray coding scheme have the Gaussian distribution.
1. A method of generating a probabilistically shaped (PS), multi-level modulation signals, comprising:
encoding information bits into coded bits to which probability values are assigned according to a probability mass function; and
mapping, based on a Gray coding scheme, the coded bits into symbols,
wherein the probability mass function is implemented by:
determining probabilities of the coded bits so that the probabilities of the coded bits ascending or descending order have a Gaussian distribution; and
performing a probability distribution pre-adjustment by redistributing probabilities of the coded bits corresponding to symbols probabilities of which are outside Gaussian distribution so that the symbols mapped based on the Gray coding scheme have the Gaussian distribution,
wherein the performing the probability distribution pre-adjustment includes obtaining at least once the probability distribution of the symbols after mapping the coded bits to the symbols.
2. The method of claim 1 , wherein the performing the probability distribution pre-adjustment includes finding probabilities of information bits corresponding to symbols outside Gaussian distribution.
3. The method of claim 2 , wherein the performing the probability distribution pre-adjustment includes adjusting probabilities of coded bits corresponding to symbols outside Gaussian distribution.
4. The method of claim 1 , wherein the determining probabilities of the coded bits includes determining probability distribution of the symbols mapped based on a binary coding scheme.
5. The method of claim 1 , further comprising performing a forward error correction before mapping the coded bits into the symbols.
6. A signal transmitter apparatus, comprising:
an encoder including a probabilistic constellation shaping encoder that encodes information bits into coded bits to which probability values are assigned according to a probability mass function; and
a symbol mapper that maps, based on a Gray coding, the coded bits into symbols to which the probability values are assigned,
wherein a probability distribution after encoding the information bits into the coded bits does not have a Gaussian distribution feature, and has a Gaussian distribution feature the symbol mapping of the coded bit is performed based on a Gary coding scheme,
wherein the probability mass function is performed by:
determining probabilities of the coded bits so that the probabilities of the coded bits in ascending or descending order have a Gaussian distribution; and
performing a probability distribution pre-adjustment by redistributing probabilities of the coded bits corresponding to symbols probabilities of which are outside Gaussian distribution so that the symbols mapped based on the Gray coding have the Gaussian distribution,
wherein the performing the probability distribution pre-adjustment includes obtaining at least once the probability distribution of the symbols after mapping the coded bits to the symbols.
7. The apparatus of claim 6 , wherein the performing the probability distribution pre-adjustment includes finding probabilities of information bits corresponding to symbols outside Gaussian distribution.
8. The apparatus of claim 7 , wherein the performing the probability distribution pre-adjustment includes adjusting probabilities of coded bits corresponding to symbols outside Gaussian distribution.
9. The apparatus of claim 6 , wherein the determining probabilities of the coded bits includes determining probability distribution of the symbols mapped based on a binary coding scheme.
10. The apparatus of claim 6 , further comprising a forward error correction encoder that performs a forward error correction before mapping the coded bits into the symbols.
11. An optical transmitter apparatus, comprising:
a light source that generates a light wave as an optical carrier wave;
an encoder that encodes information bits to be transferred in a form of an optical multi-level quadrature amplitude modulation (QAM) signal using a probabilistic shaping scheme; and
a symbol mapper that assigns the coded information bits to symbols,
wherein the encoder includes a probabilistic constellation shaping encoder that encodes information bits into coded bits to which probability values are assigned according to a probability mass function, and the symbol mapper maps, based on a Gray coding, the coded information bits into the symbols to which the probability values are assigned,
wherein a probability distribution after encoding the information bits into the coded information bits does not have a Gaussian distribution feature if the symbol mapping of the coded bit is performed based on a binary coding scheme, and has a Gaussian distribution feature if the symbol mapping of the coded bit is performed based on a Gary coding scheme.
12. The apparatus of claim 11 , wherein the probability mass function is performed by:
determining probabilities of the coded bits so that the probabilities of the coded bits in ascending or descending order have a Gaussian distribution; and
performing a probability distribution pre-adjustment by redistributing probabilities of the coded bits corresponding to symbols probabilities of which are outside Gaussian distribution so that the symbols mapped based on the Gray coding have the Gaussian distribution.
13. The apparatus of claim 12 , wherein the performing the probability distribution pre-adjustment includes obtaining at least once the probability distribution of the symbols after mapping the coded bits to the symbols.
14. The apparatus of claim 13 , wherein the performing the probability distribution pre-adjustment includes finding probabilities of information bits corresponding to symbols outside Gaussian distribution.
15. The apparatus of claim 14 , wherein the performing the probability distribution pre-adjustment includes adjusting probabilities of coded bits corresponding to symbols outside Gaussian distribution.
16. The apparatus of claim 12 , wherein the determining probabilities of the coded bits includes determining probability distribution of the symbols mapped based on a binary coding scheme.