### Abstract

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Original language | English |
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Article number | 324022 |

Pages (from-to) | 324022 |

Number of pages | 1 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 41 |

Issue number | 32 |

DOIs | |

Publication status | Published - 30 Jul 2008 |

### Bibliographical note

© 2008 IOP Publishing Ltd.### Keywords

- mean field theory
- code-division multiple-access systems
- error-control coding
- free energy
- mutual information
- maximum spectral efficiency
- mean-field description
- bank of scalar Gaussian channels
- regular low-density parity-check-coded CDMA systems

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## Cite this

Yano, T., Tanaka, T., & Saad, D. (2008). A mean field theory of coded CDMA systems.

*Journal of Physics A: Mathematical and General*,*41*(32), 324022. [324022]. https://doi.org/10.1088/1751-8113/41/32/324022