## 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) |
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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 |

## Keywords

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

## ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering