### Abstract

In the bit-interleaved coded modulation with iterative decoding, it is desired that any two Hamming neighbors, i.e., signal constellation points whose binary labels are at unit Hamming distance, be separated by a large Euclidean distance. This paper determines the mappings for the 32-ary four-dimensional generalized cross constellation (32-4D-GCC) so that the minimum squared Euclidean distance d2min between Hamming neighbors is maximized. Among such mappings, those with minimum multiplicity N(d2min) are selected. To reduce the large search space, a set of ¿mapping templates,¿ each producing a collection of mappings with the same set partitions of binary labels, is introduced. Via enumeration of mapping templates, it is shown that the optimum d2min=16 and the optimum N(d2min)=16. Among thousands optimum mappings found by computer search, two of the best performance are presented.

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

Article number | 6895385 |

Pages (from-to) | 64-73 |

Number of pages | 10 |

Journal | China Communications |

Volume | 11 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2014 |

### Fingerprint

### Keywords

- AWGN
- BICM-ID
- hamming cube
- mapping template
- signal mapping

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Networks and Communications

### Cite this

*China Communications*,

*11*(7), 64-73. [6895385]. https://doi.org/10.1109/CC.2014.6895385

**Mapping design of a four-dimensional 32-ary signal constellation over an AWGN channel.** / Zhang, Jianyong; Djordjevic, Ivan B.

Research output: Contribution to journal › Article

*China Communications*, vol. 11, no. 7, 6895385, pp. 64-73. https://doi.org/10.1109/CC.2014.6895385

}

TY - JOUR

T1 - Mapping design of a four-dimensional 32-ary signal constellation over an AWGN channel

AU - Zhang, Jianyong

AU - Djordjevic, Ivan B

PY - 2014/7/1

Y1 - 2014/7/1

N2 - In the bit-interleaved coded modulation with iterative decoding, it is desired that any two Hamming neighbors, i.e., signal constellation points whose binary labels are at unit Hamming distance, be separated by a large Euclidean distance. This paper determines the mappings for the 32-ary four-dimensional generalized cross constellation (32-4D-GCC) so that the minimum squared Euclidean distance d2min between Hamming neighbors is maximized. Among such mappings, those with minimum multiplicity N(d2min) are selected. To reduce the large search space, a set of ¿mapping templates,¿ each producing a collection of mappings with the same set partitions of binary labels, is introduced. Via enumeration of mapping templates, it is shown that the optimum d2min=16 and the optimum N(d2min)=16. Among thousands optimum mappings found by computer search, two of the best performance are presented.

AB - In the bit-interleaved coded modulation with iterative decoding, it is desired that any two Hamming neighbors, i.e., signal constellation points whose binary labels are at unit Hamming distance, be separated by a large Euclidean distance. This paper determines the mappings for the 32-ary four-dimensional generalized cross constellation (32-4D-GCC) so that the minimum squared Euclidean distance d2min between Hamming neighbors is maximized. Among such mappings, those with minimum multiplicity N(d2min) are selected. To reduce the large search space, a set of ¿mapping templates,¿ each producing a collection of mappings with the same set partitions of binary labels, is introduced. Via enumeration of mapping templates, it is shown that the optimum d2min=16 and the optimum N(d2min)=16. Among thousands optimum mappings found by computer search, two of the best performance are presented.

KW - AWGN

KW - BICM-ID

KW - hamming cube

KW - mapping template

KW - signal mapping

UR - http://www.scopus.com/inward/record.url?scp=84907481042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907481042&partnerID=8YFLogxK

U2 - 10.1109/CC.2014.6895385

DO - 10.1109/CC.2014.6895385

M3 - Article

VL - 11

SP - 64

EP - 73

JO - China Communications

JF - China Communications

SN - 1673-5447

IS - 7

M1 - 6895385

ER -