Binary PSK (BPSK) code[1] 

Description

Also called a binary antipodal modulation, phase-reversal keying (PRK), or antipodal signaling. Encodes one bit of information into a constellation of antipodal points \(\pm\alpha\) for complex \(\alpha\). These points are typically associated with two phases of an electromagnetic signal.

Rate

Achieve capacity of AGWN in the low signal-to-noise regime [2] (see also [1]). BPSK concatenated with quantum-classical polar codes achieves the Holevo capacity for the pure-loss channel [3].

Realizations

Telephone-line modems throughout 1950s and 1960s: Bell 103 and 202, as well as international standards V.21 [4] and V.23 [5].

Parents

  • Phase-shift keying (PSK) code — BPSK is also known as 2-PSK.
  • Binary antipodal code — A single-bit binary code yields a spherical \((n,2,4)\) spherical code under the antipodal mapping, which is equivalent to the BPSK code for dimension \(n=2\).

Cousins

  • Pulse-amplitude modulation (PAM) code — BPSK for real \(\alpha\) is the simplest non-trivial PAM encoding.
  • Linear binary code — Concatenating binary linear codes with BPSK yields a standard way of digitizing the analog AGWN channel [6; Ch. 29].
  • Two-component cat code — BPSK (two-component cat) codes are used to transmit classical (quantum) information using (superpositions of) antipodal coherent states over classical (quantum) channels.
  • Polar c-q code — BPSK concatenated with quantum-classical polar codes achieves the Holevo capacity for the pure-loss channel [3].
  • Binary antipodal code — A binary antipodal code can be thought of as a concatenation of a binary outer code with a BPSK inner code.
  • Binary balanced spherical code — A binary balanced spherical code can be thought of as a concatenation of a constant-weight binary outer code with a shifted and scaled BPSK-like inner code.
  • BPSK c-q code — BPSK (BPSK c-q) codes are used to transmit classical information using antipodal coherent states over classical (quantum) channels.
  • Hadamard BPSK c-q code — The Hadamard BPSK c-q code can be thought of as a concatenation of the Hadamard binary linear code with BPSK for the purposes of transmission of classical information over quantum channels.

References

[1]
C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal 27, 623 (1948) DOI
[2]
Y. Wu and S. Verdu, “The impact of constellation cardinality on Gaussian channel capacity”, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2010) DOI
[3]
S. Guha and M. M. Wilde, “Polar coding to achieve the Holevo capacity of a pure-loss optical channel”, 2012 IEEE International Symposium on Information Theory Proceedings (2012) arXiv:1202.0533 DOI
[4]
International Telecommunication Union-T, Recommendation V.21: 300 bits per second duplex modem standardized for use in the general switched telephone network, 1984
[5]
International Telecommunication Union-T, Recommendation V.23: 600/1200-baud modem standardized for use in the general switched telephone network, 1988
[6]
A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI
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Zoo Code ID: bpsk

Cite as:
“Binary PSK (BPSK) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bpsk
BibTeX:
@incollection{eczoo_bpsk, title={Binary PSK (BPSK) code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/bpsk} }
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“Binary PSK (BPSK) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/bpsk

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/spherical/modulation/bpsk.yml.