### Abstract

The symbol error rate of an arbitrary multidimensional constellation in the absence of coding impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of the signal-to-noise ratio, when the minimum distance detector is used. This representation is also shown to apply to cases when the impairing noise is compound Gaussian. Using this general result, it is proved that the symbol error rate is completely monotone if the rank of its constellation matrix is either one or two. Further, a necessary and sufficient condition for the complete monotonicity of the symbol error rate of a constellation of any dimension is also obtained. Applications to stochastic ordering of wireless system performance are also discussed.

Original language | English (US) |
---|---|

Article number | 6423920 |

Pages (from-to) | 3922-3931 |

Number of pages | 10 |

Journal | IEEE Transactions on Information Theory |

Volume | 59 |

Issue number | 6 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### Keywords

- Canonical representation
- completely monotone
- convex
- stochastic ordering
- symbol error rate (SER)

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*59*(6), 3922-3931. [6423920]. https://doi.org/10.1109/TIT.2013.2243801

**A representation for the symbol error rate using completely monotone functions.** / Rajan, Adithya; Tepedelenlioglu, Cihan.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 59, no. 6, 6423920, pp. 3922-3931. https://doi.org/10.1109/TIT.2013.2243801

}

TY - JOUR

T1 - A representation for the symbol error rate using completely monotone functions

AU - Rajan, Adithya

AU - Tepedelenlioglu, Cihan

PY - 2013

Y1 - 2013

N2 - The symbol error rate of an arbitrary multidimensional constellation in the absence of coding impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of the signal-to-noise ratio, when the minimum distance detector is used. This representation is also shown to apply to cases when the impairing noise is compound Gaussian. Using this general result, it is proved that the symbol error rate is completely monotone if the rank of its constellation matrix is either one or two. Further, a necessary and sufficient condition for the complete monotonicity of the symbol error rate of a constellation of any dimension is also obtained. Applications to stochastic ordering of wireless system performance are also discussed.

AB - The symbol error rate of an arbitrary multidimensional constellation in the absence of coding impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of the signal-to-noise ratio, when the minimum distance detector is used. This representation is also shown to apply to cases when the impairing noise is compound Gaussian. Using this general result, it is proved that the symbol error rate is completely monotone if the rank of its constellation matrix is either one or two. Further, a necessary and sufficient condition for the complete monotonicity of the symbol error rate of a constellation of any dimension is also obtained. Applications to stochastic ordering of wireless system performance are also discussed.

KW - Canonical representation

KW - completely monotone

KW - convex

KW - stochastic ordering

KW - symbol error rate (SER)

UR - http://www.scopus.com/inward/record.url?scp=84877885568&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877885568&partnerID=8YFLogxK

U2 - 10.1109/TIT.2013.2243801

DO - 10.1109/TIT.2013.2243801

M3 - Article

AN - SCOPUS:84877885568

VL - 59

SP - 3922

EP - 3931

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 6

M1 - 6423920

ER -