### Abstract

A complexity analysis of discrete multitone (DMT) and single-carrier modulation (SCM) in the context of a very high-speed digital subscriber line (VDSL) is presented in this paper. In addition to the traditional arithmetic complexity measures such as the number of multiply-and-accumulate (MAC) operations, we also compute the memory requirements. Furthermore, we normalize these metrics with respect to the number of information bits transmitted (rate normalized) and scale with respect to data path precision (precision scaled) in order to obtain more comprehensive metrics. The analysis shows that the number of MAC's per transmitted information bit (N_{MACb}) for SCM is greater than that for DMT for all distances of interest in VDSL. The number of MACs per information bit and scaled with respect to precision (B_{MAC}), i.e., NB_{MACb} = N_{MACb} B_{MAC}, was found to be clearly smaller for SCM in loops shorter than approximately 2 kft. This metric was found to be clearly smaller for DMT in loops longer than approximately 3.25 kft. At all lengths, DMT was found to have smaller memory requirements per information bit, as well as smaller precision-scaled memory requirements.

Original language | English |
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Pages (from-to) | 282-292 |

Number of pages | 11 |

Journal | IEEE Transactions on Signal Processing |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 Jan 1 |

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### Keywords

- Complexity
- Discrete multitone
- Multiply-and-accumulate (MAC)
- Single-carrier modulation
- VDSL

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Signal Processing*,

*51*(1), 282-292. https://doi.org/10.1109/TSP.2002.806583